a class of algorithms originated for minimizing or maximizing a function , while satisfying some constraints . in the history of optimization , the function and the constraints linear and the problem was known as linear programming ( lp ) .one of the early published algorithms for solving the linear programming was given by dantzig , popularly known as simplex method . as the number of dimensions and constraints increased , solving the lp using simplex method became hard .the inability of simplex method was that it could not solve lp in polynomial time .khachiyan proposed ellipsoid algorithm as an alternative to simplex method and proved that it could reach the solution iteratively in polynomial time .the practical infeasible condition of ellipsoid algorithm led to the evolution of several interior or barrier point methods .one of the well known interior point methods is karmarkar s method proposed by narendra karmarkar .binary classification is one of the active research areas in machine learning .there are several ways to train a binary classifier .the class labels of a data set can be stored and retrieved during classification using the approach of nearest neighbor .a hyperplane is learnt for classification by training a neural network , which may not always be optimal .vapnik and others formulated the problem of classification as optimization .this method is known as support vector machines ( svms ) .sequential minimal optimization ( smo ) is a technique which solves the optimization problem in svms .decision trees , bagging , and boosting techniques are also used in binary classification .nearest neighbor method does not involve any modeling to reduce the storage of the training data set . on the other hand , neural network and svm model the data with an objective function to estimate a hyperplane , which is used in classification . in neural network approach ,the objective function is a least squares , which is quadratic in nature and is minimized for the given data set .the hyperplane obtained from a neural network may or may not be optimal , since it depends on the number of layers and weights used to train the network .svm uses quadratic programming formulation with linear constraints for minimizing the objective function .several variants of even though the objective function used in neural network or svm is a quadratic programming problem , the constraints are linear .  if there is a way to model linear constraints as quadratic constraints , then the objective function becomes quadratically constrained quadratic programming ( qcqp ) . in this paper , binary classificationis posed as a qcqp problem and a novel solution is proposed using particle swarm optimization ( pso ) .one of the advantages of this approach is that it solves the qcqp problem without the need for gradient estimation .the paper is organized as follows : qcqp and pso are described in the background section and the solution for quadratically constrained quadratic programming using particle swarms is described in sec .the proposed method is compared with khachiyan s and karmarkar s algorithms for linear programming and with neural networks and svm for quadratic programming in sec . 4 on experiments and results .section 5 concludes the paper with suggestions for future work .the formulation of qcqp and pso are described in the subsections below .a general quadratically constrained quadratic programming problem is expressed as follows : where .if are positive semi - definite , then the problem becomes convex qcqp .particle swarm optimization was proposed for optimizing in the weights space of a neural network .pso has been applied to numerous applications for optimizing non - linear functions .pso evolved by simulating bird flocking and fish schooling .the advantages of pso are that it is simple in conception and easy to implement .particles are deployed in search space and each particle is evaluated against an optimization function .the best particle is chosen as a directing agent for the rest .the velocity of each particle is controlled by both the particle s personal best and the global best . during the movement of the particles ,a few of them may reach the global best .the movement of particles is adapted from the genetic algorithms or evolutionary programming .let * x * = be the particles deployed in the search space of the optimization function , where is the number of particles and * v * = are the velocities of the respective particles . for all the particles .a simple pso update is as follows ,  * velocity update equation + where is the weight for the previous velocity ; , are constants and , are random values varied in each iteration . is the personal best value for particle and is the global best value among all the particles . is the updated velocity of the particle in the iteration and is the velocity value in the iteration . is the position of the particle after the iteration . * for position update, the updated velocity is added to the existing position of the particle .the position update equation is + interest lies in determining the shortest path between the two non - intersecting ellipsoids .the shortest path between the two ellipsoids in can be formulated as a convex qcqp problem .arriving at the two end points of the shortest path , one on each ellipsoid , can be posed as minimization of in a quadratic form and formulated as follows . where and , are non - intersecting regions in , . and are the matrices depicting the ellipsoids used in the optimization .  in casethe euclidean distance metric is used for minimization of the path length , then is the identity matrix .the modified equation is ,   suppose one end point in the shortest path is known and fixed as .then , eq ( 5 ) can be reformulated as ,   figure [ theoryexample ] shows the ellipsoid with the covariance matrix with points ( inside ) , ( on the boundary ) and ( outside ) .the boundary point is nearest to the point outside the ellipsoid .we need to determine the unknown by the minimization of .the novelty of this paper is the application of particle swarms for solving the qcqp problem .particle swarms are deployed within the ellipsoid to determine .the function is evaluated for each particle in the search space .the particle with the minimum is considered as the closest to the point .only one particle of the swarm is shown in figure [ theoryexample ] for ease of representation .   inside anda point on its boundary nearest to the point outside it ( boundary point on the other ellipsoid ) .the dotted lines connecting the point to the points and are shown .the desired direction of movement from is also shown by an arrow , which is required to reach point .,width=453 ]  pso is a stochastic evolutionary algorithm , which takes several generations to reach the optimal value and its performance depends on the initialization .the velocity update equation of the pso algorithm is modified by including the function .the addition of evaluation function restricts the particle from moving away from the actual course towards the global best position .this addition provides an advantage in computation .however , it also constrains the particle to move in a particular direction . to counter this effect, we add a craziness term in the velocity update equation .the modified velocity update equation is :    where and are constants , and is a random value that is varied during each iteration . the value of is chosen such that the term does not take the particle outside the ellipsoid . is a random point on the surface of a sphere of dimension with randomly varying radius . forms the craziness term .  the velocity vector of particle should be directed towards the minimization of .the function needs to be evaluated .we use instead of using as the objective function .the value of is unknown and needs to be arrived at by minimizing the function .the value of the function for the particle at the iteration is evaluated as   let the present position of the particle be split into the previous position and the velocity vector of the particle .  here , is fixed and the particle position in the objective function is dependent on the velocity vector .so , one possible option for minimizing the function is by changing the direction of the velocity vector of the particle as follows :    thus , the function is minimized if the direction of the velocity vector is as given by eq ( 10 ) .the velocity vector update equation ( 2 ) does not have any term relating to minimization , but the modified eq ( 7 ) includes the direction for minimization .it improves the convergence rate and thus reduces the computation time .the arrow ( for representation purpose ) shown in figure [ theoryexample ] is in the direction of minimizing the function given by eq ( 6 ) .  on the assumption that one end point is known in the shortest path ,particle swarms are placed in the search space of the other region and the other end point of the shortest path is determined . in order to evaluate the objective function in eq ( 5 ) , we need to determine one end point from region and the other from region .two sets of particle swarms , one for each region , are placed within the search spaces of the respective regions .the objective function is evaluated based on the particles present in both the regions . in every iteration ,the best position of a particle in one region is used as the known end point in the shortest path in the velocity update equation of the particles of the other region .the objective function reaches its optimal value after several generations .  in the process of optimization, some particles may often go out of the search space . to limit the particles within the search space , we inspect after every tentative position update as to whether the particle is lying within the search space by carrying out a check on the qcqp constraints .if the intended new position of a particle is going to violate the constraint , then its position is not updated . in other words , the particles likely to go out of the search space are redeployed back to their previous positions .the proposed solution may be used in control system problems such as optimization of sensor networks or collaborative data mining , which are based on multiple agents or gradient projection .general consensus problem may be solved using the proposed method , where multiple agents need to reach a common goal .consensus or distributed optimization is discussed in as ` consensus and sharing ' using alternating direction method of multipliers ( admom ) .admom uses one agent for each constraint .such solvers are used for solving svm in distributed format .table [ patab1 ] presents a pseudo code for the algorithm .the parameters ,,, , and are set to fixed values and the randomly varying parameters ,, , and are updated in each iteration . the position , velocity , personal best , and global best of each particle are stored .the maximum number of iterations for the algorithm is specified as in the experiments and the size of swarm used in the algorithm is ` 10 ' . the proposed algorithm is implemented in matlab ..proposed algorithm for qcqp using pso [ cols= " < " , ]   the performance of our method is close to that of the variants of svm and is superior to that of the neural network .we notice that in iris and wine datasets , the cross - validation error obtained by our technique is better than those achieved by svm with linear and rbf kernels and also the neural network . in pima and thyroid datasets ,the cross - validation error is high , due to the high degree of correlation .we have developed a classification method and optimization algorithm for solving qcqp problems .the novelty in this method is the application of particle swarms , an evolutionary technique , for optimization .the results indicate that our approach is a possible method in solving general qcqp problems without gradient estimation .we have shown the results of our algorithm under quadratic constraints by evaluating different optimization functions .the issue with pso based methods is their computational complexity and the need for parameter tuning .the number of function evaluations linearly increases with the number of particles employed and the number of iterations carried out .  in future , we intend to learn multiple hyperplanes by placing multiple kernels in each class and evaluating the performance against multiple - kernel learning algorithms .the hyperplanes estimated for different kernels may reduce the cross - validation error for the pima and thyroid datasets .boyd , s. , parikh , n. , chu , e. , peleato , b. , eckstein , j. : distributed optimization and statistical learning via the alternating direction method of multipliers .foundations and trends in machine learning , volume 3 , issue 1 , p.1 - 122 ( 2010 )     derrac , j. , garca , s. , herrera , f. : fuzzy nearest neighbor algorithms : taxonomy , experimental analysis and prospects .information sciences , volume 260 , p.98 - 119 ( 2014 ) doi : http://dx.doi.org/10.1016/j.ins.2013.10.038   fernndez , a. , lpez , v. , galar , m. , jesus , m.j . ,herrera , f. : analysing the classification of imbalanced data - sets with multiple classes : binarization techniques and ad - hoc approaches .knowledge - based systems , p.97 - 110 ( 2013 )   galar , m. , fernndez , a. , barrenechea , e. , herrera , f. : eusboost : enhancing ensembles for highly imbalanced data - sets by evolutionary undersampling .pattern recognition ( 2013 ) doi : http://dx.doi.org/10.1016/j.patcog.2013.05.006   gonzalez - abril , l. , nuez , h. , angulo , c. , velasco , f. : gsvm : an svm for handling imbalanced accuracy between classes in bi - classification problems . applied soft computing , volume 17 , p.23 - 31 ( 2014 ) doi : http://dx.doi.org/10.1016/j.asoc.2013.12.013       lpez , v. , fernndez , a. , garca , s. , palade , v. , herrera , f. : an insight into classification with imbalanced data : empirical results and current trends on using data intrinsic characteristics , information sciences ( 2013 ) doi : http://dx.doi.org/10.1016/j.ins.2013.07.007  matei , i. , baras , j.s . : a performance comparison between two consensus - based distributed optimization algorithms .3rd ifac workshop on distributed estimation and control in networked systems , p.168 - 173 , santa barbara , ca , usa ( 2012 )    platt , j. : fast training of support vector machines using sequential minimal optimization . in b. schoelkopf andc. burges and a. smola , editors , advances in kernel methods - support vector learning ( 1998 )  spadoni , m. , stefanini , l. : a differential evolution algorithm to deal with box , linear and quadratic - convex constraints for boundary optimization journal of global optimization 52(1 ) , p.171 - 192 ( 2012 )   zanella , f. , varagnolo , d. , cenedese , a. , pillonetto , g. , schenato , l. : multidimensional newton - raphson consensus for distributed convex optimization .the 2012 american control conference ( acc ) , p.1079 - 1084 , montreal , qc ( 2012 )

Abstract: particle swarm optimization is used in several combinatorial optimization problems . in this work , particle swarms are used to solve quadratic programming problems with quadratic constraints . the approach of particle swarms is an example for interior point methods in optimization as an iterative technique . this approach is novel and deals with classification problems without the use of a traditional classifier . our method determines the optimal hyperplane or classification boundary for a data set . in a binary classification problem , we constrain each class as a cluster , which is enclosed by an ellipsoid . the estimation of the optimal hyperplane between the two clusters is posed as a quadratically constrained quadratic problem . the optimization problem is solved in distributed format using modified particle swarms . our method has the advantage of using the direction towards optimal solution rather than searching the entire feasible region . our results on the iris , pima , wine , and thyroid datasets show that the proposed method works better than a neural network and the performance is close to that of svm .   * keywords * quadratic programming ; particle swarms ; hyperplane ; quadratic constraints ; binary classification .


a first generation quantum computer will be expensive and high - maintenance , and therefore will be implemented in a cloud " style like today s supercomputers . in such a cloud quantum computing ,the most important problem is to guarantee the client s privacy .blind quantum computation  is a new secure quantum computing protocol which can protect the security of client s privacy in such a cloud quantum computing .protocols of blind quantum computation enable a client ( alice ) , who does not have enough quantum technologies at her disposal , to delegate her quantum computation to a server ( bob ) , who has a full - fledged quantum computer , in such a way that alice s input , output , and program are hidden to bob  .an unconditionally secure protocol of blind quantum computation with almost classical alice was first proposed by broadbent , fitzsimons , and kashefi ( bfk )  .their protocol uses measurement - based quantum computation ( mbqc ) on the cluster state ( graph state ) by raussendorf and briegel  . a proof - of - principle experiment of the bfk protocolhas also been achieved recently with a quantum optical system  .the bfk protocol has been generalized to other blind quantum computing protocols which use mbqc on the affleck - kennedy - lieb - tasaki ( aklt ) state  , continuous - variable mbqc  , topological mbqc  , and the ancilla - driven model  .  in these bfk - based protocols ,alice has to possess a device which emits randomly - rotated single - particle states , such as single - photon states .if alice s device is not perfect , and sometimes wrongly emits more than two photons , extra photons can be exploited by malicious bob to learn alice s information , by using , for example , the photon number splitting attack  .therefore , it is necessary for alice to precisely control the number of emitted photons , which is not easy with today s technology .  in ref . , a complementary protocol of the bfk - type protocol , so called measuring - alice ( ma ) protocol , was proposed by morimae and fujii . in this protocol, alice has only to perform measurements in stead of state preparations .these measurements are not necessary to be single - photon measurements : they can be polarization measurements with a threshold detector .since a polarization measurement with a threshold detector is much easier than a creation of a single - photon state , ma protocol eases alice s burden .furthermore , as is shown in ref . , this protocol offers the device - independent security for alice , which means that alice does not need to trust her device : even if alice s device does not work correctly , bob can not learn alice s information .finally , it was shown  that the security of ma protocol is based on the no - signaling principle , which is more fundamental than quantum physics  .because of the no - signaling principle , the proof of the security of ma protocol becomes very simple .if bob can not learn anything about alice s computation whatever he does , we say that the protocol offers blindness "  .( here , we ignore unavoidable leakage of trivial information , such as the upper bound of the computational size , or whether alice s output is classical or quantum , etc . . ) in fact , all bfk - type blind protocols and ma protocol satisfy the blindness .the verifiability " is another important concept in could quantum computing .the verifiability means that alice can check whether bob is following the correct protocol .if malicious bob deviates from the correct protocol , the verifiability enables alice to detect it with high probability , and therefore the probability for alice of accepting a wrong result can be exponentially small .fitzsimons and kashefi ( fk ) recently introduced a modified version of the bfk protocol which satisfies the verifiability  .the verifiability of ma protocol was shown in ref . .  however , all previous results ( except for ref . ) consider only stand - alone security .the stand - alone security means that the protocol is secure during a single execution of it in an isolated environment .the stand - alone security is often proven by showing that the mutual information between honest party and malicious party is exponentially small .the stand - alone security establishes the security of a protocol as a primitive , and often gives important insights for deep understanding of protocols .therefore , it is a first goal to show the stand - alone security of a cryptographic protocol .however , the stand - alone security is not sufficient if we consider a protocol in a broader and hence more realistic scenario .for example , the ( stand - alone ) unconditional security of the quantum key distribution protocol ( qkd )  has been proven by many researchers by showing that the accessible information is exponentially small . here , the accessible information is the mutual information between the distributed key and the outcome of an optimal measurement on the adversary s system .however , it was pointed out in ref .  that even if the accessible information is small , the key might not be enough secure if it is used in another protocol , such as the one - time pad encryption , due to the locking  , which is a purely non - classical property .if we want to guarantee the security of a protocol in such a broader context , we have to show the composable security  .the composable security means the security of a primitive protocol in a general environment .for example , a protocol is secure even if it is used many times as subroutines of a larger protocol .the composable security of qkd was shown in ref .the composable security of the key recycling in authentication was studied in ref . .the composable security of the bfk - type protocols were studied in ref .they showed the composable blindness of the bfk protocol and the composable blind - verifiability of the fk protocol by using the constructive cryptography  .although the composable security of ma protocol was also studied in ref . , it is not sufficient , since they showed only the composable blindness : the composable device - independent blindness , which is a new feature of ma protocol , was not shown .furthermore , the composable blind - verifiability of ma protocol was neither considered .  in this paper, we study the composable security of ma protocol . for that purpose, we utilize the framework of the constructive cryptography  .we will introduce two types of ma protocols , one is without verification and the other is with verification , and will show the composable security of them .hence , the device - independent blindness and the verifiability of ma protocol are shown to be composable .we will see that our proofs of the composable security are much simpler than those of bfk type protocols due to the simplicity of the stand - alone security of ma protocol based on the no - signaling principle .this paper is organized as follows .we will first review some necessary backgrounds , including the no - signaling principle ( sec .[ sec : ns ] ) , mbqc ( sec .[ sec : mbqc ] ) , ma protocol ( sec .[ sec : ma ] ) , and the constructive cryptography and the composable security ( sec . [ sec : comp ] ) .we will then show our results in sec .[ sec : result1 ] and sec .[ sec : result2 ] . the discussion is given in sec .[ sec : discussion ] .no - signaling principle is one of the most fundamental principles in physics , and quantum theory also respects it .formally , it is explained as follows .let us assume that alice and bob share a physical system , which might be classical , quantum , or even super - quantum ( fig .[ ns ] ) . for example, alice and bob share the bell pair , , alice chooses her measurement parameter ( such as the measurement angles of a spin ) , and performs measurement .she obtains the result .bob also chooses his measurement parameter , and performs measurement .he obtains the result . the no - signaling principle ( from alice to bob )is defined by for all , , , and , where is the conditional probability distribution of given .equation ( [ no - signaling ] ) means that the change of alice s measurement parameter does not affect the probability distribution of bob s measurement result . in other words ,the shared system can not transmit any message from alice to bob .interestingly , the no - signaling principle is more fundamental than quantum theory in the sense that there is a theory which is more non - local than quantum theory , but respects the no - signaling principle  .in this section , we will review the basics of measurement - based quantum computing ( mbqc )  .readers who are familiar with it can skip this section .mbqc is a new model of quantum computation whose computational power is equivalent to the traditional circuit model . in mbqc , we first prepare a highly - entangled qubit ( or more generally , qudit ) state , which we call the resource state .we next perform measurement of each qubit .the measurement angle of a qubit depends on the results of the previous measurements .if the resource state is a universal resource state , we can simulate any quantum circuit with the adaptive local measurements .a canonical example of universal resource states is the cluster state  : where , qubits are allocated on sites of the two - dimensional square lattice , is the controlled- gate between qubit and qubit , and is a pair of nearest - neighbour sites . here, is the identity operator acting on qubit , and is the pauli operator acting on qubit .  let us see fig .[ figmbqc ] .we first prepare the cluster state ( fig . [ figmbqc ] ( a ) ) .we then perform local adaptive measurements ( figs .[ figmbqc ] ( b ) and ( c ) ) . by changing measurement angles, we can generate any state on the last layer of the cluster state ( fig .[ figmbqc ] ( d ) ) , where is any -qubit unitary operator .( actually , what we create on the last layer is where are random binaries .we call the byproduct , and we say that we can implement up to a byproduct . since are determined by measurement results , we can correct byproduct . )in this section , we will review ma protocol  . let and be the input and the program ( unitary operation ) of alice s computation , respectively . in other words, alice wants to implement on , and obtain .if alice s input is classical , i.e. , she knows the classical description of the input quantum state , or her input is a classical data , she does not need to start with : she can start with the standard state , such as , which is prepared by bob , and the preparation of the initial state can be included in .bellow , we will introduce two ma protocols .we will first explain a simpler one : a protocol without the verification .we will next explain a protocol with verification .these two protocols satisfy the device - independent blindness .note that the device - independent verifiability is not guaranteed in the second protocol , because , as we will see later , the device - independent verifiability is impossible : a malicious device can always cheat alice by pretending that all tests are passed .let us consider mbqc between two parties , alice and bob ( fig .[ ma1 ] ) : bob first prepares a resource state , such as the cluster state , in his laboratory ( fig .[ ma1 ] ( a ) ) .he next sends each particle to alice one by one , and alice measures each particle in a certain angle which is determined by her program ( fig .[ ma1 ] ( b ) ) .the program is kept secret to bob .if bob behaves honestly , i.e. , generates the correct resource state and sends each particle correctly , the last layer of his resource state becomes ( up to byproducts ) ( fig .[ ma1 ] ( c ) ) .if bob sends it to alice , alice can obtain the correct quantum outcome ( or if she needs the classical outcome , she can obtain the correct result by measuring it ) .  since there is no message transmission from alice to bob , the no - signaling principle guarantees that bob can not learn anything about alice s input , measurement angles ( i.e. , program ) , and outputs , whatever he does on his system  .( as we said , we ignore trivial leakage of alice s information . in this case, bob can know the upper bound of the size of alice s mbqc , since he creates the resource state . )this protocol also satisfies the device - independent blindness , which means that whatever alice s device does , bob can not learn alice s secret .this is again shown by using the no - signaling principle : due to the no - signaling principle , alice can not send any message to bob whatever she does .therefore , even if her measuring device does not work correctly , bob can not gain any information about alice s secret  .  .if he is malicious , he might create completely different state .( b ) he sends each particle to alice one by one .alice measures each particle according to her program .( c ) the last layer of bob s resource state is ( up to byproduct ) if he is honest ., scaledwidth=40.0% ]   the above protocol does not satisfy the verifiability . in other words , if bob behaves maliciously , alice accepts a wrong result although bob can not learn alice s secret . in order to achieve the verifiability ,we modify the above protocol in the following manner .let us define the -qubit state latexmath:[\ ] ] where , , and are certain states , and and are certain cptp maps . if we consider as the simulator for , this shows eq .( [ comp1 ] ) .t. sueki , t. koshiba , and t. morimae , ancilla - driven universal blind quantum computation .a * 87 * , 060301(r ) ( 2013 ) .v. dunjko , j. f. fitzsimons , c. portmann , and r. renner , composable security of delegated quantum computation .arxiv:1301.3662             c. h. bennett and g. brassard , quantum cryptography : public key distribution and coin tossing . in proceedings of ieee international conference on computers , systems , and signal processing , bangalore , india ( ieee , new york , 1984 ) , pp .175 - 179 .we assume that there is no unwanted leakage of information from alice s laboratory to bob .for example , alice s laboratory is not bugged by bob .this is a standard assumption in many cryptographic protocols , such as the quantum key distribution ( qkd ) .without such a natural assumption , all cryptographic protocols are trivially broken .m. ben - or and d. mayers , quantum universal composability , november 2002 .presentation at quantum information and cryptography " workshop .m. ben - or and d. mayers , general security definition and composability for quantum and classical protocols , arxiv:0409062

Abstract: blind quantum computing [ a. broadbent , j. fitzsimons , and e. kashefi , proceedings of the 50th annual ieee symposium on foundations of computer science 517 ( 2009 ) ] is a secure cloud quantum computing protocol which enables a client ( who does not have enough quantum technology at her disposal ) to delegate her quantum computation to a server ( who has a universal quantum computer ) without leaking any relevant information to the server . in [ t. morimae and k. fujii , phys . rev . a * 87 * , 050301(r ) ( 2013 ) ] , a new blind quantum computing protocol , so called the measuring - alice protocol , was proposed . this protocol offers several advantages over previous protocols , such as the device - independent security , less demanding requirements for the client , and a simpler and stronger security based on the no - signaling principle . in this paper , we show composable security of the measuring - alice protocol by using the formalism of the constructive cryptography [ u. maurer , proceedings of theory of security and applications , tosca 2011 , pages 33 - 56 . springer ( 2011 ) ] . the above advantages of measuring - alice protocol enable more intuitive and transparent proofs for the composable security .


game theory has been used extensively as a quantitative framework for studying communication networks and distributed control systems among its other applications in engineering and economics .game theoretic models provide not only a basis for analysis but also for design of network protocols and decentralized control schemes  . despite widespread use of ( noncooperative ) game theory in engineering, there is surprisingly little work on _ how to design games _ such that their outcome satisfies certain global objectives .  while there is a general agreement on the usefulness of game theory , the issues of * price of anarchy * or _ efficiency loss _ associated with noncooperative games even under the existence of pricing mechanisms , have been the subject of many investigations  .consequently , different pricing schemes have been proposed in the literature aiming to improve nash equilibrium ( ne ) efficiency with respect to a chosen criterion in specific settings  .the research community has revisited the issue of game design again very recently  .these studies are limited either to special problem formulations or adopt specific efficiency criteria such as the `` system problem '' of . a related early line of work focuses specifically on three agent ( player ) dynamic noncooperative games with multi - levels of hierarchy  , where it has been shown that the leader has an optimal incentive policy which is linear in the partial dynamic measurement and induces the desired behavior on the two followers . in addition, a separate but substantial literature exists under the umbrella of implementation theory , especially in the field of economics , which focuses on finding fundamental bounds for games where the outcome satisfies some given criteria  .these works , however , are often not algorithmic and do not have an engineering perspective .the * main contribution * of this paper is a treatment of game design from an optimization and control theoretic perspective .a fairly general class of games are considered , which have been applied to a number of settings including network congestion control , wireless uplink power control , and optical power control  .this paper -to the best of our knowledge- constitutes one of the few efforts aiming to investigate the general problem of game design in a constructive manner _ from an optimization and control theoretic perspective _  while it is straightforward to optimize ne according to some criterion under full information , the problem is much more complicated under information and communication constraints .the game or system designer ( figure [ fig : nedesign1 ] ) usually does not have full information about the system parameters such as user preferences or utility functions . under this kind of information constraints , the designer either deploys additional dynamic feedback mechanisms or requires side information from the system depending on the specific design objectives .an example for the former case is a dynamic pricing scheme operating as an `` outer feedback loop '' .if the objective is to achieve a social optimum ( e.g. maximization of sum of user utilities ) or satisfying some quality of service ( qos ) conditions , then the designer often needs limited but accurate ( honest ) information from users or the system .it is important to note that if the users have the capability of manipulating such side information , then the design problem can be more involved or even ill - defined . for example , the goal of reaching a social optimum without knowing true user utilities but having only access to manipulated data may not be a realistic or even feasible one  .although mechanisms such as vcg have been proposed to circumvent these issues , the resulting schemes are often limited and demanding in terms of communication requirements  . as a starting point ,the treatment in this paper is restricted to a class of games where * players do not manipulate the game * by deceiving the system designer .such players are sometimes called `` _ _ price - taking _ _ '' as opposed to manipulative or `` price - anticipating '' .thus , the utility functions are assumed here to accurately reflect player preferences .as an * additional contribution * , this paper analyzes dynamic systems arising from game formulations and the general case of non - separable player utilities . in such cases of coupled utility functions ,the utility of each player is affected by decisions of other players .the control theoretic approach adopted here based on game dynamics provides a more realistic model for a number of applications compared to a static optimization one .stability properties of game and pricing dynamics are investigated under the assumption of time - scale separation and in two separate time - scales using lyapunov theory and singular perturbation approach .the sufficient conditions derived , which ensure system stability , are illustrated with examples .the rest of the paper is organized as follows .the next section introduces the underlying game model and problem formulation . section [ sec : static ] studies static design of games . in section [ sec : dynamic ] , a dynamic control of games is discussed .section [ sec : incomplete ] discusses game design under incomplete information followed by a numerical simulation in section [ sec : simulation ] .the paper concludes with remarks of section [ sec : conclusion ] .consider a generic class of player static noncooperative games , denoted by , on the action ( strategy ) space .the actions of players , who are autonomous decision makers , are denoted by the vector , with being the player s action .furthermore , the player is associated with a smooth ( continuously differentiable ) cost function , , , parametrized by a scalar `` pricing '' or game parameter . in some formulations, there may be ( coupled ) restrictions on the domain of these parameters such that .assuming a set of sufficient conditions for the existence of at least one nash equilibrium ( ne ) are satisfied , define a game mapping , ( an inverse game mapping ) that maps game parameters to ne points ( ne points to parameters ) : such that for any ne point and corresponding parameter vector .notice that the mappings and are highly nonlinear , often not explicitly expressible , and may not be one - to - one or invertible except for special cases , i.e. games with special properties .we now define * a class of games * , , by assuming a cost structure of the form where , the continuously differentiable functions and are convex and strictly concave with respect to for any given , respectively .let in addition the strategy space to be convex , compact , and nonempty .thus , a game belongs to class , if the following assumptions are satisfied :  [ assm1 ] the strategy space is convex , compact , and has a nonempty interior , .[ assm2 ] the cost function of the player in ( [ e : cost1 ] ) is twice continuously differentiable in all its arguments and strictly convex in , i.e. , .  then , under the assumptions [ assm1 ] and [ assm2 ] the game admits a nash equilibrium from theorem 4.4 in  .next , we consider * a specific class of games * , , as a special case of with additional conditions on the cost structure , such that they admit a unique ne solution for each given . toward this end , define the pseudo - gradient operator ^t  : = q(x).\ ] ] subsequently , let the matrix be the jacobian of with respect to : where and are defined as and , respectively .the following assumptions have to be satisfied in addition to assumptions [ assm1 ] and [ assm2 ] , in order for a game to be in class :  [ assm3 ] the symmetric matrix , where is defined in ( [ e : g1 ] ) , is positive definite , i.e. for all .[ assm4 ] the strategy space of the class of games can be described as where , is convex in its arguments for all , and the set is bounded and has a nonempty interior .in addition , the derivative of at least one of the constraints with respect to , , is nonzero for , .if assumptions [ assm1]-[assm4 ] are satisfied , then the class of games admits a unique nash equilibrium .furthermore , this unique ne can be an inner or a boundary solution .we refer to appendix as well as for the details and an extensive analysis .notice that a large set of network games belong to this class with notable examples of network congestion games  , power control games in wireless networks  and optical networks  .assume that the utility function accurately reflects the preferences of users or players , who are _ autonomous ( independent ) decision makers_. then , the pricing function and parameters are in this setting the _ only _ tools for the system designer to influence ( optimize or control ) the game outcome in order to achieve a desired objective .this task described in problem [ problem1 ] is similar -in spirit- to the goal of implementation theory or mechanism design in the economics literature  with the important difference of not allowing users to knowingly manipulate the system , i.e. assuming price - taking users only .this game design problem is illustrated in figure [ fig : ne1 ] .is moved to a feasible desired region or a specific optimal point .[ fig : ne1 ] ]  [ problem1 ] how to choose the pricing function and parameters such that the ne of games of class satisfies some desirable properties ?two specific but common examples of such properties are  1 .the ne coincides with the solution of a global optimization problem , e.g. welfare maximization : 2 .the ne satisfies some system or user - dependent constraints such as capacity constraints , non - negativity , or performance bounds .for example , the favorable set can be defined as where is a capacity constraint , is a quality of service ( qos ) measure such as signal - to - interference ratio ( sir ) , and denotes the minimum acceptable qos level .an important aspect of problem [ problem1 ] is the amount of knowledge available to the system designer in optimization of ne .if there is complete knowledge of player preferences and global system objective , then the approach to be adopted can be quite different from the one when the designer has very limited information . in cases when the game dynamics are very fast , it is appropriate to focus on static optimization of the ne point. then , the actions of the system designer are assumed to be on a slower time - scale than the actual game dynamics between the players resulting in a hierarchical structure .this scenario is discussed in the next section .when the game designer has a way of estimating game parameters , the game design can be posed as a static optimization problem , especially when the game dynamics are very fast and the actions of the system designer are on a slower time - scale than the actual game dynamics between the players .in contrast , section [ sec : dynamic ] presents a dynamic control approach appropriate when the game dynamics are slow or there are external disturbances .then , the game is treated as a control system that needs to be stabilized around a desired point .when is it feasible to design a game such that the ne point can be located by the system designer to a point or region with desirable properties ? in the point case , let target point be .then , the problem is to find an such that , for any desirable feasible .the following surprisingly simple result addresses this problem for a fairly general class of games .[ thm : pricing ] for games of class with the cost structure given in ( [ e : cost1 ] ) and under complete information assumption , affine pricing of the form , , is sufficient to locate the unique ne point of the game to any desirable feasible point , , as long as   the proof immediately follows from the first order necessary optimality conditions of player cost optimization problems due to the convexity of the cost structure and uniqueness of ne .^{-1 }  \dfrac{\partial u_i({\hat{x}})}{\partial x_i}\;\ ; \forall i \ ] ] for any feasible .theorem [ thm : pricing ] can easily be extended to the case where users actions are on a multi - dimensional subspace if the users utility function is separable .notice that even a simple linear pricing function satisfies the conditions of the theorem and is sufficient for ne optimization . in this caseany is feasible .however , a symmetric pricing scheme , where , is not sufficient in general .as other examples , for any is feasible , while for any is feasible .if a game admits multiple ne , e.g. games of class , then reaching a single desirable point does not make much sense .furthermore , the problem of locating all ne points to a desirable region can be rather complex .such cases can be handled either by exploiting any special structure of the game due to its specific problem domain or using numerical methods .it is interesting to note that due to the form of the player cost structure in ( [ e : cost1 ] ) , i.e. additive linear pricing , the optimization problem of individual players in the game can be interpreted as a variant of _ legendre transform _  .in other words , given the other players actions , the utility function best response of a player is transformed to a best response function which takes the pricing parameter as argument .although tragedy of commons or price of anarchy are unavoidable in `` pure '' games without any external factors , they can be circumvented when additional mechanisms such as `` pricing '' are included in the game formulation . in parallel to some earlier results  , theorem [ thm : pricing ] clearly establishes that _ `` loss of efficiency '' or `` price of anarchy '' _ are not an inherent feature of a fairly general class of games with built - in pricing systems .if there is sufficient information , then any game of class can be designed through simple ( e.g. linear ) pricing mechanisms in such a way that any desirable criteria such as welfare maximization or qos requirements are met at the unique ne solution .   in order to illustrate the underlying issues in game design problems with accurate but limited information , consider a noncooperative game formulation of the single - cell spread - spectrum uplink power control problem in wireless networks  .specifically , the game is played in a single cell with mobiles competing for quality of service in terms of signal - to - interference ratio ( sir ) and the base station acts as the game designer .this can be formulated as a class game with the following general cost structure where the objective is to locate the ne to a region that satisfies some feasibility and qos constraints .further assume that the utility function of user in this game is here , represents the sir with denoting channel gain parameters and a noise term .then , each user decides on its own power level and is associated with the cost function in ( [ e : expgameform1 ] ) .the desired region for the ne of this game could be shaped by feasibility constraints such as positivity of user actions ( here uplink transmission power levels ) and an upper - bound on the sum of them , and/or some chosen minimum sir levels ( assuming these are chosen such that the region is not empty ) .a concrete example region can be defined as where are user - specific minimum sir levels .a detailed analysis of an example case is provided next . for a separate but similar example of this formulationwe refer to .  as a special case, the pricing function is chosen next to be linear in such that where is defined in ( [ e : exsir ] ) . under appropriate assumptions ,the game is one of class and admits a unique inner ne solution , .  for notational convenience ,we define the matrix then , the ne is the solution of where .\ ] ]  the desired qos region in ( [ e : qosregion1 ] ) can be alternatively described in terms of received power levels at the base stations and in matrix form  : where the matrix is defined as and ^t .\ ] ]  if the designer , here the base station , has full information , then given a feasible target sir level it is possible to solve for a pricing vector such that the ne is on the boundary of , i.e. .this is due to both matrices and being nonsingular as .hence , the appropriate pricing vector can be immediately obtained from the boundary solution and the definition of .many games are solved in a distributed manner .hence , the convergence of the system trajectory to the equilibrium point may not be very fast and the time - scale separation between system designers actions and actual game dynamics may fail . then , the game design can be modeled as a * feedback control system * which utilizes pricing as the control input and the desired target as the reference ( see figure [ fig : control1 ] ) .this formulation also brings a certain robustness with respect to initial conditions or game ( system ) parameters .the latter case is especially relevant for systems that are non - stationary over longer time periods and can also be formulated as a tracking problem .specific examples are congestion and power control game formulations ,  .  ) using pricing as the control parameter and as the desired reference signal .[ fig : control1 ] ]  the counterpart of the feasibility question in the case of static game optimization relates in the dynamic control setting to the * controllability * of the system shown in figure [ fig : control1 ] , or reachability of a state . in order to provide a concrete example to the problem of controllability ,consider a game of class where the players adopt a gradient algorithm to optimize their own cost .then , the game dynamics are : where acts as the feedback control on the outcome of the game . here, the objective is to investigate the conditions under which the game system is controllable .we write ( [ e : system1 ] ) in vector form as where ^t ] is the lie bracket of and , and denote higher order lie brackets defined recursively by (x) ] , . in this case on all pricing parameters , , and is not diagonal . however , we can still explicitly find , and it can be shown that , under non - singularity conditions on , is non - singular .an example of dynamic game control is obtained by extending example 1 to the limited information case where the designer does not have access to user preferences .then , a dynamic a pricing mechanism can be deployed . toward this end , define a set of penalty functions to bring the system within the desired region where the scalar function is smooth and nondecreasing in its argument , and for example , could be a quadratic function .a possible pricing function is then it is assumed here that the designer ( base station ) has access to system parameters , and .the other terms can be estimated through iterative observations  .finally , this pricing mechanism ensures that the ne point of the underlying game , , enters the desired qos region . to show this ,define the lyapunov function on the compact game domain .taking the derivative of with respect to time along the pricing dynamics ( [ e : pricing0 ] ) yields with outside the set and if and only if .hence , the system converges to the desired region under the pricing mechanism .the previous analysis has focused on pricing dynamics under the time - scale separation , where game dynamics are assumed to be sufficiently fast . removing this assumption for a complete treatment , two loops ( on two time - scales )will be considered : one outer loop for pricing ( ) and an inner loop for actions ( ) .the next result presents the full analysis taking both user and pricing dynamics into account and is based on a * singular perturbation * or boundary layer approach ,  . towards this end , theorem [ thm : sepconv ]is extended to analyze both pricing ( slow ) dynamics and user ( fast ) dynamics by using a combined lyapunov function .[ thm : sepconv_twoscales ] define an objective function which admits a unique inner global maximum under suitable assumptions for user utilities in a class game .then , under the pricing mechanism ( [ e : pricing2 ] ) the user dynamics ( [ e : system1 ] ) globally asymptotically converges to the maximum of the social welfare function , , if the two systems are on separate time - scales , the jacobian matrix of the mapping with respect to pricing vector , , \;\ ; i , j=1,\dots , n,\ ] ] is non - singular and the jacobian matrix of , ( [ e : system1 ] ) , with respect to  , \;\ ;i , j=1,\dots , n,\ ] ] is positive definite .consider the pricing dynamics ( [ e : pricing2 ] ) or ( [ e : pricing1v ] ) on the slow time - scale , and the user dynamics ( [ e : system1 ] ) or ( [ e : system2 ] ) on the fast time - scale , . here , with a small scaling parameter .the equilibrium of the full system ( [ e : system1 ] ) , ( [ e : pricing1v ] ) is described by and . in * singular perturbation * formthe full system is written in the shifted coordinates as ^t  \right|_{x={\tilde{x}}+{\hat{x } } } \nonumber \\ \epsilon \dot{{\tilde{x } } } & = &  f({\tilde{x}}+ { \hat{x } } ) + g({\tilde{x}}+ { \hat{x } } ) \ , ( { \tilde{\alpha}}+ { \hat{\alpha}})\end{aligned}\ ] ] where , , and the origin is its equilibrium .  in the shiftedcoordinates the * slow manifold * is defined as by taking and solving on the right - hand side of ( [ e : sp1 ] ) , i.e., since for , the foregoing yields , so that for defined by  .once the slow manifold is determined , a solution that starts in the manifold is known to stay inside for all times . in order to analyze the behavior in the neighborhood of this manifold ,an additional change of variables is used on the * fast dynamics * with respect to the slow manifold . using this change of variables the full system ( [ e : sp1 ] )is written in the coordinates as ^t\right|_{x = y+{\mathcal{t}}({\tilde{\alpha}}+{\hat{\alpha } } ) }  \\\epsilon \dot{y } & = &  f(y+{\mathcal{t}}({\tilde{\alpha}}+{\hat{\alpha } } ) ) + g(y+{\mathcal{t}}({\tilde{\alpha}}+{\hat{\alpha } } ) ) \ , ( { \tilde{\alpha}}+ { \hat{\alpha } } ) \nonumber\\ & & - \epsilon \frac{\partial h({\tilde{\alpha } } ) } { \partial { \tilde{\alpha } } } h^t({\tilde{\alpha}}+{\hat{\alpha } } ) \left [ \left .\frac{\partial { \mathcal{u}}(x)}{\partial x } \right]^t \right|_{x = y+{\mathcal{t}}({\tilde{\alpha}}+{\hat{\alpha } } ) } \nonumber\end{aligned}\]]where and ( [ e : h_def ] ) have been used to obtain .  on the slow manifold ( for ) , the dynamics of in ( [ e : sp2 ] ) define the reduced system , i.e. , ^t \right|_{x={\mathcal{t}}({\tilde{\alpha}}+{\hat{\alpha}})}\ ] ] on the fast time - scale , the dynamics of in ( [ e : sp2 ] ) define the boundary - layer system  and has been used on the right - hand side of ( [ e : sp2 ] ) .using ( [ e : system1 ] ) , yields component - wise from ( [ e : blsys ] )   to analyze the behavior and stability properties of the full system ( [ e : sp2 ] ) , an overall * composite lyapunov function * is defined based on lyapunov functions for the reduced ( [ e : redsys ] ) and boundary - layer systems , ( [ e : blsys1 ] ) , respectively . for the reduced system ( [ e : redsys ] )the same lyapunov function is used , i.e. , as shown in the proof of theorem [ thm : sepconv ] , the derivative of with respect to time along the reduced system dynamics ( [ e : redsys ] ) is negative , for the boundary - layer system ( [ e : blsys1 ] ) the following candidate lyapunov function is defined where note that and , by using ( [ e : blsys1 ] ) , derivative of with respect to time along the boundary - layer system trajectory ( [ e : blsys ] ) is given as , by using ( [ e : phidot ] ) , , at . in vector formthis yields since by assumption .moreover , for any in an appropriate domain around an upper bound that depends only on can be found for ( [ e : w2dot ] ) . finally , using the lyapunov functions for the reduced ( [ e : w1 ] ) and boundary - layer systems ( [ e : w2 ] ), the following candidate lyapunov function is defined for the full singularly perturbed system ( [ e : sp2 ] ) for some . then based on ( [ e :w1dot ] , [ e : w2dot ] ) using standard arguments as in the proof of theorem 11.3 in  , it can be shown that there exists an such that for every , is a lyapunov function for the full system ( [ e : sp2 ] ) and the system is asymptotically stable around the origin .the bound and required interconnection relations follow immediately if , the stronger condition is imposed that the reduced and boundary - layer systems are exponentially stable as in theorem 11.4 in  .consider the example 2 with cost a special case of ( [ e : cost1 ] ) , for linear pricing and osnr - like utility such an utility that may arise due to specific constraints on individual channel power ensures the existence of a unique maximum for .the nash equilibrium can be obtained from .if are selected such that the following diagonal dominance condition holds then is explicitly expressed as  and is a vector with elements .hence , is clearly non - singular .the second condition in theorem [ thm : sepconv_twoscales ] is that , where is for this example : it can be immediately seen that if ( [ e : nashosnr ] ) holds , then the matrix is strictly diagonal dominant .if in addition , it can be shown that is strictly diagonal dominant , hence is positive definite .the closed loop system ( [ e : pricing2 ] ) , ( [ e : system1 ] ) is ^t\ ] ] where is defined in ( [ e : exh ] ) , and based on ( [ exiv_c ] ) , the element in , for , is given as with thus ( [ e : expricingvect ] ) , ( [ e : exuservect ] ) represent the closed - loop dynamic system .the objective function satisfies for a nonempty set of the design variables , , but the conditions are very complicated and as such the details are omitted .the following section presents an example based on realistic parameters for the two channel case .the dynamic system described by ( [ e : expricingvect ] ) and ( [ e : exuservect ] ) of example 6 in the previous section is simulated numerically in the two players case .consider an optical fiber link with ten amplifiers , each with a parabolic gain shape according to the formula db , where denotes a channel wavelength , and a span loss of 10 db .the system matrix is obtained as \nonumber\ ] ] the following parameters are used : ,  ] milliwatt ( mw ) and  ] and ^t$ ] as initial conditions and run for ( ) iterations of the pricing ( users ) algorithm , show a clear convergence to the equilibrium solution , and to the osnr values of approximately in figures [ fig : x ] and[fig : osnr ] ) .the figure [ fig : price ] depicts the evolution of channel prices , , as a function of time ., as a function of time.,title="fig : " ] +   ( ) as a function of time.,title="fig : " ] +   +the nash equilibrium design of noncooperative games is discussed from an optimization and control theoretic perspective . it is shown that for a fairly general class of noncooperative games , pricing mechanisms can be used as a design tool to optimize and control the outcome of the game such that certain predefined global objectives are satisfied .the class of games studied are applicable to a number of problems , such as network congestion control , wireless uplink power control , and optical power control .the game design problem is analyzed under full and limited information assumptions , perfect and imperfect time - scale separation between game and pricing dynamics , and both for separable and non - separable utility functions .sufficient conditions are derived , which allow the designer to place the nash equilibrium solution or to guide the system trajectory to a desired region or point .the results obtained are illustrated through a number of examples from wireless and optical networks .there are many directions for extending the results presented .one of them is further application of game design methods to specific problems such as power control in optical networks .others include secure communication and spectrum allocation in wireless networks .yet another interesting direction is the analysis of estimation error effects on mechanism stability for the limited information case .in addition , the stability of the combined pricing and game system can be analyzed under time delays , which often have a nonnegligible effect .the authors thank holger boche for helpful discussions and pointing out the legendre transform interpretation .this work is in part supported by deutsche telekom laboratories .earlier versions of this work have appeared partly in the international conference on game theory for networks ( gamenets ) , in istanbul , turkey in may 2009  and in the conference on decision and control ( cdc ) , shanghai , china , in december 2009  .    in view of assumption [ assm4 ] , the lagrangian function for player in this gameis given by where are the lagrange multipliers of player  .we now provide a proposition for games with conditions similar to the well known karush - kuhn - tucker necessary conditions ( proposition 3.3.1 , p. 310,  ) .[ kuhntucker ] let be a ne point of a game and assumptions [ assm1]-[assm4 ] hold. there exists then a unique set of lagrange multipliers , , such that where is the set of active constraints in player s minimization problem at ne point .the proof essentially follows lines similar to the ones of the proposition 3.3.1 of  , where the penalty approach is used to approximate the original constrained problem by an unconstrained problem that involves a violation of the constraints .the main difference here is the repetition of this process for each individual at the ne point .   by proposition [ kuhntucker ] andassumption [ assm4 ] , a ne point satisfies where is unique for each .assume there are two different ne points and .then , one can also write the counterpart of ( [ e : proofunique1 ] ) for . following an argument similar to the one in the proof of theorem 2 in , one can show that this leads to a contradiction .we present a brief outline of a simplified version of that proof for the sake of completeness .   define the strategy vector as a convex combination of the two equilibrium points : where .take the derivative of with respect to , where is defined in ( [ e : g1 ] ) . integrating ( [ e : gdiff ] ) over yields (x^{(1)}-x^{(0 ) } ) .\ ] ] multiplying ( [ e : gintegral ] ) from left by , the transpose of ( [ e : gintegral ] ) from right by , and adding these two terms yields (x^{(1)}-x^{(0 ) } ) .\ ] ] since is positive definite by assumption [ assm3 ] and the sum of two positive definite matrices is positive definite , the matrix is positive definite .similarly , we have where is the jacobian of and positive definite due to convexity of by definition .the third term in ( [ e : contradict ] ) , \end{array}\ ] ] is less than [ h_j(x^{(1)})-h_j(x^{(0 ) } ) ] , \ ] ] due to convexity of . since for each constraint , , , and is positive definite , where the latter two follow from karush - kuhn - tucker conditions , this term is also non - positive .the sum of the first two terms in ( [ e : contradict ] ) are the negative of ( [ e : gintegral2 ] ) , which is strictly positive for all .hence , ( [ e : contradict ] ) is strictly negative which leads to a contradiction unless .thus , there exists a unique ne point in the class of games .m. cesana , n. gatti , and i. malanchini , `` a game - theoretic approach to decentralized optimal power allocation for cellular networks , '' in _ proc . of 2nd intl workshop on game theory in communication networks _ , athens , greece , october 2008 .t. alpcan and t. baar , `` a game theoretic analysis of intrusion detection in access control systems , '' in _ proc . of the 43rd ieee conference on decision and control_ , paradise island , bahamas , december 2004 , pp . 15681573 .   y. pan and l. pavel , `` games with coupled propagated constraints in optical networks : the multi - link case , '' in _ proc . of the 46th ieee conference on decision and control _ , new orleans , usa , december 2007 , pp . 34433449 .r. t. maheswaran and t. basar , `` social welfare of selfish agents : motivating efficiency for divisible resources , '' in _43rd ieee conf . on decision and control ( cdc )_ , paradise island , bahamas , december 2004 , vol . 2 ,1550 1555 .

Abstract: this paper investigates design of noncooperative games from an optimization and control theoretic perspective . pricing mechanisms are used as a design tool to ensure that the nash equilibrium of a fairly general class of noncooperative games satisfies certain global objectives such as welfare maximization or achieving a certain level of quality - of - service ( qos ) . the class of games considered provide a theoretical basis for decentralized resource allocation and control problems including network congestion control , wireless uplink power control , and optical power control .   the game design problem is analyzed under different knowledge assumptions ( full versus limited information ) and design objectives ( qos versus utility maximization ) for separable and non - separable utility functions . the `` price of anarchy '' is shown not to be an inherent feature of full - information games that incorporate pricing mechanisms . moreover , a simple linear pricing is shown to be sufficient for design of nash equilibrium according to a chosen global objective for a fairly general class of games . stability properties of the game and pricing dynamics are studied under the assumption of time - scale separation and in two separate time - scales . thus , sufficient conditions are derived , which allow the designer to place the nash equilibrium solution or to guide the system trajectory to a desired region or point . the obtained results are illustrated with a number of examples .


according to ironport s 2008 security trend report  , as much as 90% of inbound mail is spam today .morever , spam is no longer simply an irritant but becomes increasingly dangerous .83% of spam contains a url .thus , phishing sites and trojan infections of office and home systems alike are just one click away .state - of - the - art spam filtering techniques are based on content analysis ( e.g. spamassassin  ) , host reputation ( spamcop  , spamhaus  ) or authentication services ( spf  , dkim  ) . yet , with the increased use of attachment spam , success rate of content filtering decreases while its cost increases . at the same time , despite the initial reported success of blacklists , it has been shown recently that their effectiveness is challenged by a new generation of low profile , short - lived , and highly dynamic botnets used to send spam  .  consequently , new methods are needed to keep up with the spam arms race .one promising new approach to counteract this development is to focus on network - level characteristics of spammers .first , the network footprint of spamming activity can not be adapted as easily as the content of an email .second , the rapid increase of spam traffic poses significant processing , storage , and scalability challenges for end - host systems , creating a need to at least perform some fast `` pre - filtering '' on the network level .although the email content is not available in flow data , it can be used to profile potential spammers according to activities on other protocols and services offered .the network behavior of a legitimate email server is likely to be very different from a user pc acting as a botnet drone and sending spam .  to this end, a number of efforts have turned their attention towards network - level characteristics of spammers .for example , in an interesting recent study ramachandran et al . have studied spam with respect to ip address and as space and have demonstrated that clustering techniques can be applied to detect target domain patterns that are similar to those of spammers  . link analysis in mta graphs has been applied by  to identify potentially malicious nodes .gomes et al . showed that analysis of both static and evolving graph models allows to discriminate between socially unrelated spammer - receiver connections and socially related legitimate email traffic .finally , an extensive characterization of spam traffic was given by gomes et al .the authors highlighted differences between spam and legitimate emails with respect to a variety of aspects ( not necessarily network - related ) , such as workload , temporal patterns , or sender and receiver distributions .the majority of these works base their findings on mail server logs ( e.g.  ) while a smaller minority on network flow data  .log analysis provides detailed information about the local smtp traffic _ and the local spam filtering knowledge _( i.e. which connections got accepted or rejected , along with the reasons thereupon ) that goes far beyond simple reputation mechanisms , but is missing network - wide traffic statistics .collecting server logs from many email servers can somewhat improve the situation . yet , gathering logs from a large number of administration domains is a tedious process also involving privacy issues . on the other hand ,flow data contains information for a much larger number of hosts , collected passively in the core of the network .furthermore , flow traces are not limited to smtp traffic and could allow one to correlate the behavior between different protocols or services . yet , flow traces do not contain details about the content of smtp sessions as they are restricted to packet header information .most importantly , they do not right - away reveal the `` identity '' of a given connection with respect to the endpoints intentions ( legitimate , spam , scanning , etc . ) .we find that an `` either / or '' approach fails to combine the advantages of both methods , and suggest a different direction .our proposal is to try to exploit and combine the valuable ( and _ non - overlapping _ ) knowledge of local mail servers , on a network - wide scale , _ without actually collecting or looking at the individual server logs_.  as a first step towards this goal , this paper presents two main contributions ._ first _ , we show that email server s pre - filtering decisions can be accurately inferred directly from flow traces and therefore collected at the network core as illustrated in fig .[ fig : ispview ] . in particular , the distributions of smtp flow properties , such as byte or packet count , reliably indicate which smtp sessions were closed by the server before accepting contents . based on this , mta hosts can be classified as good or bad ( sending spam ) relying solely on packet header information .our approach is validated using server logs and public black- and white - lists . in other words , _ spammer identities and the countermeasures deployed by mail servers become visible in flow traces_.  to demonstrate the utility of these preliminary results , our _ second _ contribution in this paper is to discuss a number of potential applications that could benefit from our approach , including anti - spam technique validation , global spam monitoring , server monitoring , and novel network - level spam countermeasures . in short , we believe that the rich information offered by flow traces will be crucial in the fight against current and next - generation spammers .the rest of the paper is structured as follows . in the next section ,we describe our methodology and datasets used in this study . section [ sec : results ] we present our results with respect to the flow characteristics of accepted and rejected connections on single - server , and network - wide scales .section [ sec : discussion ] describes a number of potential applications , as well as some limitations of our approach .finally , we conclude this work in section [ sec : conclusion ] .in this section , we briefly describe our methodology and the datasets used for our study .as stated earlier , our goal is to combine the local knowledge available at individual email servers , on a network - wide level . to this end , we need first a model of the network - level behavior of an email server .  consider the email reception process depicted in fig .[ fig : filteringphases ] .the first phase is the tcp three - way handshake initialized by the client . in the second phase ,the email envelope is sent , according to the smtp protocol  . at this stage, the server may apply certain pre - filtering rules to early close smtp sessions from suspected spammers and in turn save valuable network , cpu and storage resources .if the server decides to go on , the email content is then transmitted in the third and last phase .  here, we are interested in the pre - filtering phase . during this phase ,the server combines local and global knowledge to decide whether a new connection is a spam attempt .local knowledge , for example , helps to decide whether the receiver address actually belongs to the server s domain ( open relay attempt ) or targets an existing user .furthermore , greylisting could be used as a local reputation - based service .global knowledge refers to the various open and commercial services , known as `` blacklists '' , listing whether a sender has been known to send unsolicited content in the past . only if the client does not `` clear ''the pre - filtering phase the smtp session is closed by the server .  we analyzed the logs of a university email server and show the top reject reasons in table [ tab : reject ] . as much as 78.3% of the smtp sessions were rejected in the pre - filtering phase .rejects based on local information ( including many reasons subsumed in _ others _ ) make up for roughly 45% of the reject reasons ._ these results nicely illustrate the importance of local mail server knowledge for spam detection . _  .reject reasons in pre - filtering . [ cols="<,>",options="header " , ]the above classification was derived from the logs of a single server .the question arises whether the results can be extended to other servers in the network . to address this question we now look at the total smtp traffic of the 50 most active email servers of the network .  because we could not get the server logs of all the servers we classify flows according to the membership of the sender in either a black- or whitelist .we are interested whether flows originating from blacklisted hosts exhibit characteristics similar to the rejected flows of the previous section .similarly , whitelisted hosts should mainly send accepted traffic and thus exhibit according flow characteristics .exemplified for flow sizes , figure [ fig : sizeslist ] shows that , indeed , the shape of rejected and accepted flows is nicely reflected by the black-/whitelisted curves .the cdf of blacklisted traffic rises in the region of 300 bytes and achieves a ratio of 92% at 1500 bytes . in contrast , the cdf ot the whitelisted traffic stays on a low level of 10% up to 1500 bytes and starts to increase above 1500 bytes .yet , the fraction of whitelisted flows below 1500 bytes is not so small as for accepted traffic in fig .[ fig : sizeslog ] .we assume this is due to applied greylisting in servers , which leads to a number of rejected flows even for whitelisted hosts .in addition , whereas the fraction of rejected flows smaller than 1500 bytes was 99% in fig . [fig : sizeslog ] , we now have a slightly smaller ratio of about 92% for blacklisted flows .this means that the ensemble of the top 50 servers has a less aggressive pre - filtering configuration than the single email server studied before .also , if other servers use a blacklist that performs worse than spamhaus , the blacklist used by our server , this effect would be expected .that also implies that less knowledgeable servers could benefit from the knowledge of servers that are better configured , that is , servers that exhibit a sharper reject curve .again , the curve of all traffic is dominated by blacklisted flows .  summing up, these results imply that the discriminating power of the three metrics ( bytes per flow , packets per flow , and bytes per packet ) with regard to spamming activity is also valid in a network - wide setting .[ [ impact ] ] impact + + + + + +  in this paper , we established a passive measurement method for detecting the mail server s acceptance of email sending attempts .the method requires no additional communication or configuration changes on the mail server . to our best knowledge , this is the first method that scales to _ large networks _ and _ passively _ transfers knowledge about spam from the edge of the network ( servers ) to the core ( as shown in fig .[ fig : ispview ] ) .although the proposed method is quite simple and based on few basic flow characteristics , we believe it paves the way towards more sophisticated algorithms for network - level spam detection that could successfully complement existing methods .  servers at the edge of the network have local knowledge , such as the user database or the email envelope , that is not accessible at the core of the network .further on , servers correlate this knowledge with services ( dbl , spf ) to improve the accuracy of their decision . with the presented method it is possible to concentrate the local decisions of several email servers in the core of the network .this approach can be interpreted as a distributed computer cluster where the email servers perform a detection algorithm on part of the global smtp traffic and we are then collecting the results .  mail servers only see their own traffic . in the core of the networkwe have the `` bird s eye view '' over the activity of all nodes .this allows to correlate the gained information from one email server with the information of many others .further on , our approach is not restricted to smtp traffic and , therefore , one can try to find suspicious behavior in other protocols , too ( a subject of future work ) .although being only a first step , we believe the proposed method has important potential applications in production networks and also paves the way for future research in the area of network - level and network - wide characteristics of spam traffic . in the rest , we try to illustrate some of these applications .[ [ isp - use - case ] ] isp use case + + + + + + + + + + + +  _ network - wide spam monitoring : _ by looking at the flow characteristics of incoming email traffic , an isp is now able to _ estimate the total spam traffic _ collected by its network .furthermore , it is possible to focus on the statistics of a specific server and to _ detect potential performance problems_. for example , figure [ fig : overtime ] shows the three categories of flows that arrive at an email server inside the network in 15 min. intervals . on 18 .feb at 6:00 , the server rejects up to 80,000 flows .we think that this event corresponds to a spam campaign arriving at the server . during this time , the server is probably overloaded and starts rejecting connection attempts .three similar events are visible at the end of the week . these events are visible on other severs as well and are therefore of a distributed nature .we believe that an isp could monitor its network thus , and re - act in near real - time to such suspicious events .  as a second observation ,note how the diurnal pattern of rejected / failed flows has an offset of approximately 6h compared to accepted flows .since the local time zone of the server is gmt+1h , this indicates that most spam to that server is sent from time zone gmt-5h ( including eastern usa ) .  _internal server monitoring : _ in addition , the isp could _ rate servers _ by calculating the ratio of accepted vs. rejected flows for each server .this ratio could be used to to detect open relay servers or servers with a suboptimal pre - filtering process , triggered by an unusually high number of accepted flows .these misconfigured servers produce unnecessary and costly traffic .the isp can now take counteractive measures .for example , fig .[ fig : perserver ] shows the flow size curves for different mail servers in our network .some of the servers perform a very aggressive pre - filtering ( server a ) while others do not seem to care too much about it ( server c ) .  by monitoring the three categories of outgoing smtp traffic ,the isp could infer the reputation of internal sources .for example , the reputation could be calculated as the ratio of accepted versus total flows .based on this value , the isp would be able to _ detected blacklisted internal servers _ or servers abused for a spam campaign . with the same method , _ spamming botnet members _ inside the networkcould possibly be detected by the isp ._ rating external email sources : _ further the internal servers could be used as agents of a collaborative filtering system .the external mail senders could be rated based on the three categories of their incoming and outgoing smtp traffic .this system could be used to possibly even filter out spam on the edge of the network .the rating of the external email sources could be published as a service for other email servers .given that an operator is already collecting flow data , e.g. for accounting , the data required by the outlined applications is already available .there is _ no need to correlate the traffic again _ with different blacklists or other sources .the email servers have already done this work . to implement a similar service without flow data ,the isp would have to contact each mail server administrator to get access to their local server log .this process is bound to be cumbersome or even impossible due to privacy issues . with our approachonly one sensor must be maintained .[ [ limitations ] ] limitations + + + + + + + + + + +  tracing the footprints of pre - filtering methods in network traffic has the inherent limitation that it only detects patterns if pre - filtering is applied by servers in the first place .however , in production environments it is the email administrator s intention to block spam as early as possible to save network , cpu and storage resources .pre - filtering is the preferred choice to achieve this .moreover , pre - filtering allows to reduce the amount of non - delivery messages to be sent  .therefore , we believe it is reasonable to rely on the presence of pre - filtering in production networks .  in principle , spammers could adapt to our method by prolonging the envelope phase , e.g. by sending multiple rcpt or helo commands or providing very long sender email addresses .however , any deviation from normal smtp behavior could again be detected and mail servers could enforce the shortness of the envelope as there is no need to be overly long .mail server administrators are engaged in an arms race against spammers .they urgently need new approaches to fight state - of - the - art attachment spam increasingly originating from low - profile botnet spammers .  in this paper, we demonstrated that simple flow metrics , such as byte count , packet count , and bytes per packet , successfully discriminate between spam and ham flows when pre - filtering is deployed in mail servers .thus , one could infer individual mail server s decisions with respect to the legitimacy and acceptance of a given connection .this allows an operator i ) to concentrate dispersed mail server knowledge at the network core and ii ) to passively accumulate network - wide spam statistics , profile filtering performance of servers , and rate clients .thus , the advantages of flow and server log analysis finally meet at the network core .we believe this is an important step towards successfully fighting spammers at the network - level .s. frei , g. ollmann , and i. silvestri .mail ddos attacks through non delivery messages .http://www.techzoom.net / papers / mail_non_delivery_notice_attacks_2004.pd% f[http://www.techzoom.net / papers / mail_non_delivery_notice_attacks_2004.pd% f ] , 2004 .   l. h. gomes , c. cazita , j. m. almeida , v. almeida , and j. wagner meira . characterizing a spam traffic . in _imc 04 : proceedings of the 4th acm sigcomm conference on internet measurement _ , pages 356369 , new york , ny , usa , 2004 .

Abstract: despite a large amount of effort devoted in the past years trying to limit unsolicited mail , spam is still a major global concern . content - analysis techniques and blacklists , the most popular methods used to identify and block spam , are beginning to lose their edge in the battle . we argue here that one not only needs to look into the network - related characteristics of spam traffic , as has been recently suggested , but also to look deeper into the network core , in order to counter the increasing sophistication of spam - ing methods . yet , at the same time , local knowledge available at a given server can often be irreplaceable in identifying specific spammers .  to this end , in this paper we show how the local intelligence of mail servers can be gathered and correlated _ passively _ at the isp - level providing valuable network - wide information . specifically , we use first a large network flow trace from a medium size , national isp , to demonstrate that the pre - filtering decisions of individual mail servers can be tracked and combined at the flow level . then , we argue that such aggregated knowledge not only can allow isps to develop and evaluate powerful new methods for fighting spam , but also to monitor remotely what their `` own '' servers are doing .