Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> In this work, we propose a game theoretic framework to analyze the behavior of cognitive radios for distributed adaptive channel allocation. We define two different objective functions for the spectrum sharing games, which capture the utility of selfish users and cooperative users, respectively. Based on the utility definition for cooperative users, we show that the channel allocation problem can be formulated as a potential game, and thus converges to a deterministic channel allocation Nash equilibrium point. Alternatively, a no-regret learning implementation is proposed for both scenarios and it is shown to have similar performance with the potential game when cooperation is enforced, but with a higher variability across users. The no-regret learning formulation is particularly useful to accommodate selfish users. Non-cooperative learning games have the advantage of a very low overhead for information exchange in the network. We show that cooperation based spectrum sharing etiquette improves the overall network performance at the expense of an increased overhead required for information exchange. <s> BIB001 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> We study a spectrum sharing problem in an unlicensed band where multiple systems coexist and interfere with each other. We first analyze a cooperative setting where all the systems collaborate to achieve a common goal. Under the assumptions that the systems communicate with Gaussian signals and treat interference as noise, we study the structure of the optimal power allocations. We show that any Pareto efficient vector of rates can be achieved with piece-wise constant power allocations. Moreover, if a strong interference condition among all the systems is satisfied, we show that frequency division multiplexing is optimal. We then consider a non-cooperative situation, where the systems act in a selfish and rational way, and investigate how the lack of cooperation can affect performance. Using game theory, we first analyze the possible outcomes of a one shot game, and observe that in many cases an inefficient solution results. We show that by extending the game definition to that of a repeated game, the possibility of building reputations and applying punishments allows to enlarge the set of achievable rates. We present examples that show that in many cases, the performance loss due to lack of cooperation is small. We also provide a converse theorem that proves that our results are tight and quantify the best achievable performance in a non-cooperative scenario <s> BIB002 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> We study auction mechanisms for sharing spectrum among a group of users, subject to a constraint on the interference temperature at a measurement point. The users access the channel using spread spectrum signaling and so interfere with each other. Each user receives a utility that is a function of the received signal-to-interference plus noise ratio. We propose two auction mechanisms for allocating the received power. The first is an auction in which users are charged for received SINR, which, when combined with logarithmic utilities, leads to a weighted max-min fair SINR allocation. The second is an auction in which users are charged for power, which maximizes the total utility when the bandwidth is large enough and the receivers are co-located. Both auction mechanisms are shown to be socially optimal for a limiting "large system" with co-located receivers, where bandwidth, power and the number of users are increased in fixed proportion. We also formulate an iterative and distributed bid updating algorithm, and specify conditions under which this algorithm converges globally to the Nash equilibrium of the auction. <s> BIB003 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> In order to fully utilize the scarce spectrum resources, with the development of cognitive radio technologies, dynamic spectrum allocation becomes a promising approach to increase the efficiency of spectrum usage. In this paper, we consider the spectrum allocation in wireless networks with multiple selfish legacy spectrum holders and unlicensed users as multi-stage dynamic games. A belief-assisted dynamic pricing approach is proposed to optimize overall spectrum efficiency while keeping the participating incentives of the users based on double auction rules. Moreover, considering the budget constraints of the unlicensed users, a dynamic programming approach is further developed to optimize the spectrum allocation over time. The simulation results show that our proposed scheme not only approaches optimal outcomes with low overhead compared to general continuous double auction mechanisms, but also fully exploits the time diversity of spectrum resources when budget constraints exist <s> BIB004 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> In order to fully utilize the scarce spectrum resources, with the development of cognitive radio technologies, dynamic spectrum sharing becomes a promising approach to increase the efficiency of spectrum usage. Game theoretical dynamic spectrum sharing has been extensively studied for more flexible, efficient, and fair spec- trum usage through analyzing the intelligent behaviors of network users equipped with cogni- tive radio devices. This article provides a game theoretical overview of dynamic spectrum shar- ing from several aspects: analysis of network users' behaviors, efficient dynamic distributed design, and optimality analysis. <s> BIB005 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> "Cognitive radio" is an emerging technique to improve the utilization of radio frequency spectrum in wireless networks. In this paper, we consider the problem of spectrum sharing among a primary user and multiple secondary users. We formulate this problem as an oligopoly market competition and use a Cournot game to obtain the spectrum allocation for secondary users. Nash equilibrium is considered as the solution of this game. We first present the formulation of a static Cournot game for the case when all secondary users can observe the adopted strategies and the payoff of each other. However, this assumption may not be realistic in some cognitive radio systems. Therefore, we formulate a dynamic Cournot game in which the strategy of one secondary user is selected solely based on the pricing information obtained from the primary user. The stability condition of the dynamic behavior for this spectrum sharing scheme is investigated. <s> BIB006 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> Cognitive radio has been proposed as a novel approach for improving the utilization of the precious limited radio resources by dynamically accessing the spectrum. One of the major design challenges is to coordinate and cooperate in accessing the spectrum opportunistically among multiple distributive users with only local information. In this paper, we propose a game theoretical approach with a new solution concept, the correlated equilibrium, which is better compared to the non-cooperative Nash equilibrium in terms of spectrum utilization efficiency and fairness among the distributive users. To achieve this correlated equilibrium, we construct an adaptive algorithm based on no-regret learning that guarantees convergence. From the simulation results, the optimal correlated equilibria achieve better fairness and 5% ~15% performance gain, compared to the Nash equilibria. <s> BIB007 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> We propose a real-time spectrum auction framework to distribute spectrum among a large number wireless users under interference constraints. Our approach achieves conflict-free spectrum allocations that maximize auction revenue and spectrum utilization. Our design includes a compact and yet highly expressive bidding language, various pricing models to control tradeoffs between revenue and fairness, and fast auction clearing algorithms to compute revenue-maximizing prices and allocations. Both analytical and experimental results verify the efficiency of the proposed approach. We conclude that bidding behaviors and pricing models have significant impact on auction outcomes. A spectrum auction system must consider local demand and spectrum availability in order to maximize revenue and utilization. <s> BIB008 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> We address the problem of spectrum pricing in a cognitive radio network where multiple primary service providers compete with each other to offer spectrum access opportunities to the secondary users. By using an equilibrium pricing scheme, each of the primary service providers aims to maximize its profit under quality of service (QoS) constraint for primary users. We formulate this situation as an oligopoly market consisting of a few firms and a consumer. The QoS degradation of the primary services is considered as the cost in offering spectrum access to the secondary users. For the secondary users, we adopt a utility function to obtain the demand function. With a Bertrand game model, we analyze the impacts of several system parameters such as spectrum substitutability and channel quality on the Nash equilibrium (i.e., equilibrium pricing adopted by the primary services). We present distributed algorithms to obtain the solution for this dynamic game. The stability of the proposed dynamic game algorithms in terms of convergence to the Nash equilibrium is studied. However, the Nash equilibrium is not efficient in the sense that the total profit of the primary service providers is not maximized. An optimal solution to gain the highest total profit can be obtained. A collusion can be established among the primary services so that they gain higher profit than that for the Nash equilibrium. However, since one or more of the primary service providers may deviate from the optimal solution, a punishment mechanism may be applied to the deviating primary service provider. A repeated game among primary service providers is formulated to show that the collusion can be maintained if all of the primary service providers are aware of this punishment mechanism, and therefore, properly weight their profits to be obtained in the future. <s> BIB009 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> In order to fully utilize scarce spectrum resources, dynamic spectrum allocation becomes a promising approach to increase the spectrum efficiency for wireless networks. However, the collusion among selfish network users may seriously deteriorate the efficiency of dynamic spectrum sharing. The network users' behaviors and dynamics need to be taken into consideration for efficient and robust spectrum allocation. In this paper, we model the spectrum allocation in wireless networks with multiple selfish legacy spectrum holders and unlicensed users as multi-stage dynamic games. In order to combat user collusion, we propose a pricing-based collusion-resistant dynamic spectrum allocation approach to optimize overall spectrum efficiency, while not only keeping the participating incentives of the selfish users but also combating possible user collusion. The simulation results show that the proposed scheme achieves high efficiency of spectrum usage even with the presence of severe user collusion. <s> BIB010 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> Dynamic spectrum access has become a promising approach to improve spectrum efficiency by adaptively coordinating different users' access according to spectrum dynamics. However, users who are competing with each other for spectrum may have no incentive to cooperate, and they may even exchange false private information about their channel conditions in order to get more access to the spectrum. In this paper, we propose a repeated spectrum sharing game with cheat-proof strategies. By using the punishment-based repeated game, users get the incentive to share the spectrum in a cooperative way; and through mechanism-design-based and statistics-based approaches, user honesty is further enforced. Specific cooperation rules have been proposed based on the maximum total throughput and proportional fairness criteria. Simulation results show that the proposed scheme can greatly improve the spectrum efficiency by alleviating mutual interference. <s> BIB011 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> Dynamic spectrum access (DSA), enabled by cognitive radio technologies, has become a promising approach to improve efficiency in spectrum utilization, and the spectrum auction is one important DSA approach, in which secondary users lease some unused bands from primary users. However, spectrum auctions are different from existing auctions studied by economists, because spectrum resources are interference-limited rather than quantity-limited, and it is possible to award one band to multiple secondary users with negligible mutual interference. To accommodate this special feature in wireless communications, in this paper, we present a novel multi-winner spectrum auction game not existing in auction literature. As secondary users may be selfish in nature and tend to be dishonest in pursuit of higher profits, we develop effective mechanisms to suppress their dishonest/collusive behaviors when secondary users distort their valuations about spectrum resources and interference relationships. Moreover, in order to make the proposed game scalable when the size of problem grows, the semi-definite programming (SDP) relaxation is applied to reduce the complexity significantly. Finally, simulation results are presented to evaluate the proposed auction mechanisms, and demonstrate the complexity reduction as well. <s> BIB012 </s> Advances in cognitive radio networks: A survey <s> H. Spectrum Sharing Game <s> We design truthful double spectrum auctions where multiple parties can trade spectrum based on their individual needs. Open, market-based spectrum trading motivates existing spectrum owners (as sellers) to lease their selected idle spectrum to new spectrum users, and provides new users (as buyers) the spectrum they desperately need. The most significant challenge is how to make the auction economic-robust (truthful in particular) while enabling spectrum reuse to improve spectrum utilization. Unfortunately, existing designs either do not consider spectrum reuse or become untruthful when applied to double spectrum auctions. We address this challenge by proposing TRUST, a general framework for truthful double spectrum auctions. TRUST takes as input any reusability-driven spectrum allocation algorithm, and applies a novel winner determination and pricing mechanism to achieve truthfulness and other economic properties while significantly improving spectrum utilization. To our best knowledge, TRUST is the first solution for truthful double spectrum auctions that enable spectrum reuse. Our results show that economic factors introduce a tradeoff between spectrum efficiency and economic robustness. TRUST makes an important contribution on enabling spectrum reuse to minimize such tradeoff. <s> BIB013
Game theory is a well-developed mathematical tool that studies the intelligent behaviors of rational decision makers in strategic interactions, such as cooperation and competition. In dynamic spectrum sharing, secondary users compete for the limited spectrum resources. If they do not belong to the same network entity, secondary users only aim at maximizing their own benefit from utilizing the spectrum resources. Therefore, their strategies in dynamic spectrum sharing can be well analyzed via game theoretical approaches BIB005 . A game theoretic modeling is presented in BIB001 that analyzes the behavior of cognitive users in distributed adaptive channel allocation. Both cooperative and non-cooperative scenarios are considered, and a no-regret learning approach is proposed. In BIB002 , a repeated game approach for spectrum allocations is proposed, in which the spectrum sharing strategy could be enforced using the Nash Equilibrium of dynamic games. Mechanism design is proposed in BIB011 ,  to suppress the cheating behavior of secondary users in open spectrum sharing by introducing a transfer function to user's utility. Spectrum pricing problem with analysis of the market equilibrium is studied in BIB006 and BIB009 . Correlated equilibrium concept is used in BIB007 that can achieve better spectrum sharing performance than noncooperative Nash equilibrium in terms of spectrum utilization efficiency and fairness. A game-theoretic overview for dynamic spectrum sharing is provided in BIB005 . Auction mechanisms for spectrum sharing have also been proposed in BIB003 , where the utility of each user is defined as a function of the received signal-to-noise-and-interference ratio (SINR). Considering the potential price of anarchy due to the non-cooperative nature of selfish users, the spectrum manager charges each user a unit price for their received SINR or power, so that the auction mechanism achieves the maximum social utility as well as maximal individual utility. A real-time spectrum auction framework is proposed in BIB008 to assign spectrum packages to proper wireless users under interference constraints. In BIB004 and BIB010 , a belief-assisted double auction mechanism is proposed to achieve efficient dynamic spectrum allocation, with collusion-resistant strategies that combat possible user collusive behavior using optimal reserve prices. A scalable multi-winner spectrum auction scheme is proposed in BIB012 that awards one spectrum band to multiple secondary users with negligible mutual interference. Effective mechanisms to suppress dishonest/collusive behaviors are also considered, in case secondary users distort their valuations about spectrum resources and interference relationships. Other truthful and efficient spectrum auction mechanisms have been studied in  and BIB013 .