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221
Double-oracle Algorithm for Computing an Exact Nash Equilibrium in Zero-sum Extensive-form Games.
- In Proc. of AAMAS,
, 2013
"... ABSTRACT We investigate an iterative algorithm for computing an exact Nash equilibrium in two-player zero-sum extensive-form games with imperfect information. The approach uses the sequence-form representation of extensive-form games and the double-oracle algorithmic framework. The main idea is to ..."
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Cited by 8 (2 self)
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ABSTRACT We investigate an iterative algorithm for computing an exact Nash equilibrium in two-player zero-sum extensive-form games with imperfect information. The approach uses the sequence-form representation of extensive-form games and the double-oracle algorithmic framework. The main idea is to restrict the game by allowing the players to play only some of the sequences of available actions, then iteratively solve this restricted game, and exploit fast best-response algorithms to add additional sequences to the restricted game for the next iteration. In this paper we (1) extend the sequence-form double-oracle method to be applicable on non-deterministic extensive-form games, (2) present more efficient methods for maintaining valid restricted game and computing bestresponse sequences, and finally we (3) provide theoretical guarantees of the convergence of the algorithm to a Nash equilibrium. We experimentally evaluate our algorithm on two types of games: a search game on a graph and simplified variants of Poker. The results show significant running-time improvements compared to the previous variant of the double-oracle algorithm, and demonstrate the ability to find an exact solution of much larger games compared to solving full linear program for the complete game.
Fully Proportional Representation as Resource Allocation: Approximability Results
- PROCEEDINGS OF THE TWENTY-THIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2013
"... We study the complexity of (approximate) winner determination under Monroe’s and Chamberlin-Courant’s multiwinner voting rules, where we focus on the total (dis)satisfaction of the voters (the utilitarian case) or the (dis)satisfaction of the worstoff voter (the egalitarian case). We show good appro ..."
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Cited by 8 (6 self)
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We study the complexity of (approximate) winner determination under Monroe’s and Chamberlin-Courant’s multiwinner voting rules, where we focus on the total (dis)satisfaction of the voters (the utilitarian case) or the (dis)satisfaction of the worstoff voter (the egalitarian case). We show good approximation algorithms for the satisfaction-based utilitarian cases, and inapproximability results for the remaining settings.
Promoting honesty in electronic marketplaces: combining trust modeling and incentive mechanism design (Ph.D
, 2009
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis work is in the area of modeling trust in m ..."
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Cited by 7 (2 self)
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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis work is in the area of modeling trust in multi-agent systems, systems of software agents designed to act on behalf of users (buyers and sellers), in ap-plications such as e-commerce. The focus is on developing an approach for buyers to model the trustworthiness of sellers in order to make effective decisions about which sellers to select for business. One challenge is the problem of unfair ratings, which arises when modeling the trust of sellers relies on ratings provided by other buyers (called advisors). Existing approaches for coping with this problem fail in scenarios where the majority of advisors are dishonest, buyers do not have much personal experience with sellers, advisors try to flood the trust modeling system with unfair ratings, and sellers vary their behavior widely. We propose a novel
On the Complexity of Iterated Weak Dominance in Constant-Sum Games
, 2009
"... In game theory, a player’s action is said to be weakly dominated if there exists another action that, with respect to what the other players do, is never worse and sometimes strictly better. We investigate the computational complexity of the process of iteratively eliminating weakly dominated action ..."
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Cited by 7 (2 self)
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In game theory, a player’s action is said to be weakly dominated if there exists another action that, with respect to what the other players do, is never worse and sometimes strictly better. We investigate the computational complexity of the process of iteratively eliminating weakly dominated actions (IWD) in two-player constant-sum games, i.e., games in which the interests of both players are diametrically opposed. It turns out that deciding whether an action is eliminable via IWD is feasible in polynomial time whereas deciding whether a given subgame is reachable via IWD is NP-complete. The latter result is quite surprising as we are not aware of other natural computational problems that are intractable in constant-sum games. Furthermore, we slightly improve a result by Conitzer and Sandholm [6] by showing that typical problems associated with IWD in win-lose games with at most one winner are NP-complete.
Local Search Techniques for Computing Equilibria in Two-Player General-Sum Strategic-Form Games (Extended Abstract)
"... The computation of a Nash equilibrium in a game isachallenging problem in artificial intelligence. This is because the computational time of the algorithms provided by the literature is, in the worst case, exponential in the size of the game. To deal with this problem, itiscommon the resort to conce ..."
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Cited by 7 (4 self)
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The computation of a Nash equilibrium in a game isachallenging problem in artificial intelligence. This is because the computational time of the algorithms provided by the literature is, in the worst case, exponential in the size of the game. To deal with this problem, itiscommon the resort to concepts of approximate equilibrium. In this paper, we follow a different route, presenting, to the best of our knowledge, the first algorithm based on the combination of support enumeration methods and local search techniques to find an exact Nash equilibrium in two-player general-sum games and, in the case no equilibrium is found within a given deadline, to provide an approximate equilibrium. We design some dimensions for our algorithm and we experimentally evaluate them with games that are unsolvable with the algorithms known in the literature within a reasonable time. Our preliminary results are promising, showing that our techniques can allow one to solve hard games in a short time.
Optimal coalition structure generation in cooperative graph games
- In Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI
, 2013
"... Abstract Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inherent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is computationally to optimize and solve such games. One prominen ..."
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Abstract Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inherent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is computationally to optimize and solve such games. One prominent such language is the simple yet expressive Weighted Graph Games (WGGs) representation (Deng and Papadimitriou 1994), which maintains knowledge about synergies between agents in the form of an edge weighted graph. We consider the problem of finding the optimal coalition structure in WGGs. The agents in such games are vertices in a graph, and the value of a coalition is the sum of the weights of the edges present between coalition members. The optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions. We show that finding the optimal coalition structure is not only hard for general graphs, but is also intractable for restricted families such as planar graphs which are amenable for many other combinatorial problems. We then provide algorithms with constant factor approximations for planar, minorfree and bounded degree graphs.
Anti-jamming games in multichannel cognitive radio networks
- IEEE Transactions on Information Forensics and Security, submitted
"... Abstract—Crucial to the successful deployment of cognitive radio networks, security issues have begun to receive research interests recently. In this paper, we focus on defending against the jamming attack, one of the major threats to cognitive radio networks. Secondary users can exploit the flexibl ..."
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Abstract—Crucial to the successful deployment of cognitive radio networks, security issues have begun to receive research interests recently. In this paper, we focus on defending against the jamming attack, one of the major threats to cognitive radio networks. Secondary users can exploit the flexible access to multiple channels as the means of anti-jamming defense. We first investigate the situation where a secondary user can access only one channel at a time and hop among different channels, and model it as an anti-jamming game. Analyzing the interaction between the secondary user and attackers, we derive a channel hopping defense strategy using the Markov decision process approach with the assumption of perfect knowledge, and then propose two learning schemes for secondary users to gain knowledge of adversaries to handle cases without perfect knowledge. In addition, we extend to the scenario where secondary users can access all available channels simultaneously, and redefine the anti-jamming game with randomized power allocation as the defense strategy. We derive the Nash equilibrium for this Colonel Blotto game which minimizes the worst-case damage. Finally, simulation results are presented to verify the performance. Index Terms—Cognitive radio, anti-jamming games, learning schemes, defense strategies. I.
An algorithmic game theory primer
, 2008
"... We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory. ..."
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Cited by 6 (0 self)
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We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory.
Essentials of game theory
, 2008
"... doi:10.1145/1378704.1378721 The most dramatic interaction between CS and GT may involve game-theory pragmatics. ..."
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Cited by 6 (1 self)
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doi:10.1145/1378704.1378721 The most dramatic interaction between CS and GT may involve game-theory pragmatics.
A truth serum for sharing rewards.
- In Proceedings of the 10th international conference on autonomous agents and multiagent systems
, 2011
"... ABSTRACT We study a problem where a group of agents has to decide how a joint reward should be shared among them. We focus on settings where the share that each agent receives depends on the subjective opinions of its peers concerning that agent's contribution to the group. To this end, we int ..."
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ABSTRACT We study a problem where a group of agents has to decide how a joint reward should be shared among them. We focus on settings where the share that each agent receives depends on the subjective opinions of its peers concerning that agent's contribution to the group. To this end, we introduce a mechanism to elicit and aggregate subjective opinions as well as for determining agents' shares. The intuition behind the proposed mechanism is that each agent who believes that the others are telling the truth has its expected share maximized to the extent that it is well-evaluated by its peers and that it is truthfully reporting its opinions. Under the assumptions that agents are Bayesian decision-makers and that the underlying population is sufficiently large, we show that our mechanism is incentive-compatible, budgetbalanced, and tractable. We also present strategies to make this mechanism individually rational and fair.
