Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with what we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required.
There are other pseudo-telepathy games that are related to the magic square game. Ad 'an Cabello's game @cite_31 @cite_26 does not resembles the magic square game on first approach. However, closer analysis reveals that the two games are totally equivalent!
@cite_31 @cite_26
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In this paper, we examine the use of Monte Carlo tree search (MCTS) for a variant of one of the most popular and profitable games in the world: the card game Magic: The Gathering (M:TG). The game tree for M:TG has a range of distinctive features, which we discuss here; it has incomplete information through the opponent's hidden cards and randomness through card drawing from a shuffled deck. We investigate a wide range of approaches that use determinization, where all hidden and random information is assumed known to all players, alongside MCTS. We consider a number of variations to the rollout strategy using a range of levels of sophistication and expert knowledge, and decaying reward to encourage play urgency. We examine the effect of utilizing various pruning strategies in order to increase the information gained from each determinization, alongside methods that increase the relevance of random choices. Additionally, we deconstruct the move generation procedure into a binary yes no decision tree and apply MCTS to this finer grained decision process. We compare our modifications to a basic MCTS approach for M:TG using fixed decks, and show that significant improvements in playing strength can be obtained. Part I of this paper has described a new theory for the analysis of games with incomplete information. It has been shown that, if the various players' subjective probability distributions satisfy a certain mutual-consistency requirement, then any given game with incomplete information will be equivalent to a certain game with complete information, called the “Bayes-equivalent” of the original game, or briefly a “Bayesian game.” Part II of the paper will now show that any Nash equilibrium point of this Bayesian game yields a “Bayesian equilibrium point” for the original game and conversely. This result will then be illustrated by numerical examples, representing two-person zero-sum games with incomplete information. We shall also show how our theory enables us to analyze the problem of exploiting the opponent's erroneous beliefs. However, apart from its indubitable usefulness in locating Bayesian equilibrium points, we shall show it on a numerical example the Bayes-equivalent of a two-person cooperative game that the normal form of a Bayesian game is in many cases a highly unsatisfactory representation of the game situation and has to be replaced by other representations e.g., by the semi-normal form. We shall argue that this rather unexpected result is due to the fact that Bayesian games must be interpreted as games with “delayed commitment” whereas the normal-form representation always envisages a game with “immediate commitment.” We present an empirical framework for testing game strategies in The Settlers of Catan, a complex win-lose game that lacks any analytic solution. This framework provides the means to change different components of an autonomous agent's strategy, and to test them in suitably controlled ways via performance metrics in game simulations and via comparisons of the agent's behaviours with those exhibited in a corpus of humans playing the game. We provide changes to the game strategy that not only improve the agent's strength, but corpus analysis shows that they also bring the agent closer to a model of human players. Pseudo-random number generation on the Atari 2600 was commonly accomplished using a Linear Feedback Shift Register (LFSR). One drawback was that the initial seed for the LFSR had to be hard-coded into the ROM. To overcome this constraint, programmers sampled from the LFSR once per frame, including title and end screens. Since a human player will have some random amount of delay between seeing the title screen and starting to play, the LFSR state was effectively randomized at the beginning of the game despite the hard-coded seed. Other games used the player’s actions as a source of randomness. Notable pseudo-random games include Adventure in which a bat randomly steals and hides items around the game world and River Raid which used randomness to make enemy movements less predictable. Relying on the player to provide a source of randomness is not sufficient for computer controlled agents which are capable of memorizing and repeating pre-determined sequences of actions. Ideally, the games themselves would provide stochasticity generated from an external source such as the CPU clock. In practice, this was not an option presented by the hardware. Atari games are deterministic given a fixed policy leading to a set sequence of actions. This article discusses different approaches for adding stochasticity to Atari games and examines how effective each approach is at derailing an agent known to memorize action sequences. Additionally it is the authors’ hope that this article will spark discussion in the community over the following questions: We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G=(V, E), with local rewards r: E→ℝ, and three types of vertices: black VB, white VW, and random VR forming a partition of V. It is a long-standing open question whether a polynomial time algorithm for BWR-games exists, or not. In fact, a pseudo-polynomial algorithm for these games would already imply their polynomial solvability. In this paper, we show that BWR-games with a constant number of random nodes can be solved in pseudo-polynomial time. That is, for any such game with a few random nodes |VR|=O(1), a saddle point in pure stationary strategies can be found in time polynomial in |VW|+|VB|, the maximum absolute local reward R, and the common denominator of the transition probabilities. In order to obtain the best-known guarantees, algorithms are traditionally tailored to the particular problem we want to solve. Two recent developments, the Unique Games Conjecture (UGC) and the Sum-of-Squares (SOS) method, surprisingly suggest that this tailoring is not necessary and that a single efficient algorithm could achieve best possible guarantees for a wide range of different problems. The Unique Games Conjecture (UGC) is a tantalizing conjecture in computational complexity, which, if true, will shed light on the complexity of a great many problems. In particular this conjecture predicts that a single concrete algorithm provides optimal guarantees among all efficient algorithms for a large class of computational problems. The Sum-of-Squares (SOS) method is a general approach for solving systems of polynomial constraints. This approach is studied in several scientific disciplines, including real algebraic geometry, proof complexity, control theory, and mathematical programming, and has found applications in fields as diverse as quantum information theory, formal verification, game theory and many others. We survey some connections that were recently uncovered between the Unique Games Conjecture and the Sum-of-Squares method. In particular, we discuss new tools to rigorously bound the running time of the SOS method for obtaining approximate solutions to hard optimization problems, and how these tools give the potential for the sum-of-squares method to provide new guarantees for many problems of interest, and possibly to even refute the UGC. We examine the impact of independent agents failures on the solutions of cooperative games, focusing on totally balanced games and the more specific subclass of convex games. We follow the reliability extension model, recently proposed in [1] and show that a (approximately) totally balanced (or convex) game remains (approximately) totally balanced (or convex) when independent agent failures are introduced or when the failure probabilities increase. One implication of these results is that any reliability extension of a totally balanced game has a non-empty core. We propose an algorithm to compute such a core imputation with high probability. We conclude by outlining the effect of failures on non-emptiness of the core in cooperative games, especially in totally balanced games and simple games, thereby extending observations in [1]. Simple coalitional games are a fundamental class of cooperative games and voting games which are used to model coalition formation, resource allocation and decision making in computer science, artificial intelligence and multiagent systems. Although simple coalitional games are well studied in the domain of game theory and social choice, their algorithmic and computational complexity aspects have received less attention till recently. The computational aspects of simple coalitional games are of increased importance as these games are used by computer scientists to model distributed settings. This thesis fits in the wider setting of the interplay between economics and computer science which has led to the development of algorithmic game theory and computational social choice. A unified view of the computational aspects of simple coalitional games is presented here for the first time. Certain complexity results also apply to other coalitional games such as skill games and matching games. The following issues are given special consideration: influence of players, limit and complexity of manipulations in the coalitional games and complexity of resource allocation on networks. The complexity of comparison of influence between players in simple games is characterized. The simple games considered are represented by winning coalitions, minimal winning coalitions, weighted voting games or multiple weighted voting games. A comprehensive classification of weighted voting games which can be solved in polynomial time is presented. An efficient algorithm which uses generating functions and interpolation to compute an integer weight vector for target power indices is proposed. Voting theory, especially the Penrose Square Root Law, is used to investigate the fairness of a real life voting model. Computational complexity of manipulation in social choice protocols can determine whether manipulation is computationally feasible or not. The computational complexity and bounds of manipulation are considered from various angles including control, false-name manipulation and bribery. Moreover, the computational complexity of computing various cooperative game solutions of simple games in dierent representations is studied. Certain structural results regarding least core payos extend to the general monotone cooperative game. The thesis also studies a coalitional game called the spanning connectivity game. It is proved that whereas computing the Banzhaf values and Shapley-Shubik indices of such games is #P-complete, there is a polynomial time combinatorial algorithm to compute the nucleolus. The results have interesting significance for optimal strategies for the wiretapping game which is a noncooperative game defined on a network. Game balancing is the fine-tuning phase in which a functioning game is adjusted to be deep, fair, and interesting. Balancing is difficult and time-consuming, as designers must repeatedly tweak parameters and run lengthy playtests to evaluate the effects of these changes. Only recently has computer science played a role in balancing, through quantitative balance analysis. Such methods take two forms: analytics for repositories of real gameplay, and the study of simulated players. In this work I rectify a deficiency of prior work: largely ignoring the players themselves. I argue that variety among players is the main source of depth in many games, and that analysis should be contextualized by the behavioral properties of players. Concretely, I present a formalization of diverse forms of game balance. This formulation, called 'restricted play', reveals the connection between balancing concerns, by effectively reducing them to the fairness of games with restricted players. Using restricted play as a foundation, I contribute four novel methods of quantitative balance analysis. I first show how game balance be estimated without players, using simulated agents under algorithmic restrictions. I then present a set of guidelines for using domain-specific models to guide data exploration, with a case study of my design work on a major competitive video game. I extend my work on this game with novel data visualization techniques, which overcome limitations of existing work by decomposing data in terms of player skill. I finally present an advanced formulation of fairness in games—the first to take into account a game's metagame, or player community. These contributions are supported by a detailed exploration of common understandings of game balance, a survey of prior work in quantitative balance analysis, a discussion of the social benefit of this work, and a vision of future games that quantitative balance analysis might one day make possible. This work deals with four classical prediction settings, namely full information, bandit, label efficient and bandit label efficient as well as four different notions of regret: pseudo-regret, expected regret, high probability regret and tracking the best expert regret. We introduce a new forecaster, INF (Implicitly Normalized Forecaster) based on an arbitrary function ψ for which we propose a unified analysis of its pseudo-regret in the four games we consider. In particular, for ψ(x)=exp(η x) + γ K, INF reduces to the classical exponentially weighted average forecaster and our analysis of the pseudo-regret recovers known results while for the expected regret we slightly tighten the bounds. On the other hand with ψ(x)=(η -x)q + γ K, which defines a new forecaster, we are able to remove the extraneous logarithmic factor in the pseudo-regret bounds for bandits games, and thus fill in a long open gap in the characterization of the minimax rate for the pseudo-regret in the bandit game. We also provide high probability bounds depending on the cumulative reward of the optimal action. Finally, we consider the stochastic bandit game, and prove that an appropriate modification of the upper confidence bound policy UCB1 (, 2002a) achieves the distribution-free optimal rate while still having a distribution-dependent rate logarithmic in the number of plays. We consider the problem of distributed convergence to efficient outcomes in coordination games through dynamics based on aspiration learning. Our first contribution is the characterization of the asymptotic behavior of the induced Markov chain of the iterated process in terms of an equivalent finite-state Markov chain. We then characterize explicitly the behavior of the proposed aspiration learning in a generalized version of coordination games, examples of which include network formation and common-pool games. In particular, we show that in generic coordination games the frequency at which an efficient action profile is played can be made arbitrarily large. Although convergence to efficient outcomes is desirable, in several coordination games, such as common-pool games, attainability of fair outcomes, i.e., sequences of plays at which players experience highly rewarding returns with the same frequency, might also be of special interest. To this end, we demonstrate through analysis and simulations that aspiration learning also establishes fair outcomes in all symmetric coordination games, including common-pool games. @PARASPLIT Read More: http: epubs.siam.org doi abs 10.1137 110852462 (This article originally appeared in Management Science, November 1967, Volume 14, Number 3, pp. 159-182, published by The Institute of Management Sciences.) The paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation, such as the payoff functions, the strategies available to various players, the information other players have about the game, etc. However, each player has a subjective probability distribution over the alternative possibilities. In most of the paper it is assumed that these probability distributions entertained by the different players are mutually "consistent," in the sense that they can be regarded as conditional probability distributions derived from a certain "basic probability distribution" over the parameters unknown to the various players. But later the theory is extended also to cases where the different players' subjective probability distributions fail to satisfy this consistency assumption. In cases where the consistency assumption holds, the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution, and the outcome of this lottery will decide which particular subgame will be played, i.e., what the actual values of the relevant parameters will be in the game. Yet, each player will receive only partial information about the outcome of the lottery, and about the values of these parameters. However, every player will know the "basic probability distribution" governing the lottery. Thus, technically, the resulting game will be a game with complete information. It is called the Bayes-equivalent of the original game. Part I of the paper describes the basic model and discusses various intuitive interpretations for the latter. Part II shows that the Nash equilibrium points of the Bayes-equivalent game yield "Bayesian equilibrium points" for the original game. Finally, Part III considers the main properties of the "basic probability distribution." A class of characteristic function games arising from maximum flow problems is introduced and is shown to coincide with the class of totally balanced games. The proof relies on the max flow-min cut theorem of Ford and Fulkerson and on the observation that the class of totally balanced games is the span of the additive games with the minimum operation. In this paper, the cross-layer design problem of joint multiuser detection and power control is studied, using a game-theoretic approach that focuses on energy efficiency. The uplink of a direct-sequence code-division multiple-access data network is considered, and a noncooperative game is proposed in which users in the network are allowed to choose their uplink receivers as well as their transmit powers to maximize their own utilities. The utility function measures the number of reliable bits transmitted by the user per joule of energy consumed. Focusing on linear receivers, the Nash equilibrium for the proposed game is derived. It is shown that the equilibrium is one where the powers are signal-to-interference-plus-noise ratio-balanced with the minimum mean-square error (MMSE) detector as the receiver. In addition, this framework is used to study power-control games for the matched filter, the decorrelator, and the MMSE detector; and the receivers' performance is compared in terms of the utilities achieved at equilibrium (in bits joule). The optimal cooperative solution is also discussed and compared with the noncooperative approach. Extensions of the results to the case of multiple receive antennas are also presented. In addition, an admission-control scheme based on maximizing the total utility in the network is proposed. This study examines the usability challenges faced by new players of massively multiplayer online role-playing games (MMORPGs), one of the fastest-growing segments of the video game industry. Played in completely online worlds, these games allow players to communicate with one another, form groups and communities, and compete in a variety of fantasy environments.Nineteen subjects participated in an exploratory usability study of four games, three MMORPGs and a similar single-player game used for comparison. Results reveal that many people not usually considered as potential players of these games may be interested in them, but a wide variety of usability issues present serious problems for players inexperienced with the genre. Based on an analysis of the usability data and player feedback, specific recommendations are made to improve the experience of these games for new players. These results further demonstrate the applicability and importance of usability testing to video games. We investigate a new class of congestion games, called Totally Unimodular Congestion Games, in which the strategies of each player are expressed as binary vectors lying in a polyhedron defined using a totally unimodular constraint matrix and an integer right-hand side. We study both the symmetric and the asymmetric variants of the game. In the symmetric variant, all players have the same strategy set, i.e. the same constraint matrix and right-hand side. Network congestion games are an example of this class. proved that a pure Nash equilibrium of symmetric network congestion games can be found in strongly polynomial time, while the asymmetric network congestion games are PLS-complete. We give a strongly polynomial-time algorithm to find a pure Nash equilibrium of any symmetric totally unimodular congestion game. We also identify four totally unimodular congestion games, where the players' strategy sets are matchings, vertex covers, edge covers and stable sets of a given bipartite graph. For these games we derive specialized combinatorial algorithms to find a pure Nash equilibrium in the symmetric variant, and show the asymmetric variant is PLS-complete. We study topology control problems in ad hoc networks where network nodes get to choose their power levels in order to ensure desired connectivity properties. Unlike most other work on this topic, we assume that the network nodes are owned by different entities, whose only goal is to maximize their own utility that they get out of the network without considering the overall performance of the network. Game theory is the appropriate tool to study such selfish nodes: we define several topology control games in which the nodes need to choose power levels in order to connect to other nodes in the network to reach their communication partners while at the same time minimizing their costs. We study Nash equilibria and show that-among the games we define-these can only be guaranteed to exist if each network node is required to be connected to all other nodes (we call this the STRONG CONNECTIVITY GAME). For a variation called CONNECTIVITY GAME, where each node is only required to be connected (possibly via intermediate nodes) to a given set of nodes, we show that Nash equilibria do not necessarily exist. We further study how to find Nash equilibria with incentive-compatible algorithms and compare the cost of Nash equilibria to the cost of a social optimum, which is a radius assignment that minimizes the total cost in a network where nodes cooperate. We also study variations of the games; one where nodes not only have to be connected, but k-connected, and one that we call the REACHABILITY GAME, where nodes have to reach as many other nodes as possible, while keeping costs low. We extend our study of the STRONG CONNECTIVITY GAME and the CONNECTIVITY GAME to wireless networks with directional antennas and wireline networks, where nodes need to choose neighbors to which they will pay a link. Our work is a first step towards game-theoretic analyses of topology control in wireless and wireline networks. In this paper, we introduce a simple coalition formation game in the environment of bidding, which is a special case of the weighted majority game (WMG), and is named the weighted simple-majority game (WSMG). In WSMG, payoff is allocated to the winners proportional to the players’ powers, which can be measured in various ways. We define a new kind of stability: the counteraction-stability (C-stability), where any potential deviating players will confront counteractions of the other players. We show that C-stable coalition structures in WSMG always contains a minimal winning coalition of minimum total power. For the variant where powers are measured directly by their weights, we show that it is NP-hard to find a C-stable coalition structure and design a pseudo-polynomial time algorithm. Sensitivity analysis for this variant, which shows many interesting properties, is also done. We also prove that it is NP-hard to compute the Holler-Packel indices in WSMGs, and hence in WMGs as well. Background: The application of digital games for training medical professionals is on the rise. So-called ‘serious’ games form training tools that provide a challenging simulated environment, ideal for future surgical training. Ultimately, serious games are directed at reducing medical error and subsequent healthcare costs. The aim was to review current serious games for training medical professionals and to evaluate the validity testing of such games. Methods: PubMed, Embase, the Cochrane Database of Systematic Reviews, PsychInfo and CINAHL were searched using predefined inclusion criteria for available studies up to April 2012. The primary endpoint was validation according to current criteria. Results: A total of 25 articles were identified, describing a total of 30 serious games. The games were divided into two categories: those developed for specific educational purposes (17) and commercial games also useful for developing skills relevant to medical personnel (13). Pooling of data was not performed owing to the heterogeneity of study designs and serious games. Six serious games were identified that had a process of validation. Of these six, three games were developed for team training in critical care and triage, and three were commercially available games applied to train laparoscopic psychomotor skills. None of the serious games had completed a full validation process for the purpose of use. Conclusion: Blended and interactive learning by means of serious games may be applied to train both technical and non-technical skills relevant to the surgical field. Games developed or used for this purpose need validation before integration into surgical teaching curricula. We present a study focused on constructing models of players for the major commercial title Tomb Raider: Underworld (TRU). Emergent self-organizing maps are trained on high-level playing behavior data obtained from 1365 players that completed the TRU game. The unsupervised learning approach utilized reveals four types of players which are analyzed within the context of the game. The proposed approach automates, in part, the traditional user and play testing procedures followed in the game industry since it can inform game developers, in detail, if the players play the game as intended by the game design. Subsequently, player models can assist the tailoring of game mechanics in real-time for the needs of the player type identified.