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18
The complexity of computing a Nash equilibrium
, 2006
"... We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recently-established equivalence between polynomialtime solvability of n ..."
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Cited by 329 (23 self)
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We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recently-established equivalence between polynomialtime solvability of normal-form games and graphical games, and shows that these kinds of games can implement arbitrary members of a PPAD-complete class of Brouwer functions. 1
Making Decisions Based on the Preferences of Multiple Agents
"... People often have to reach a joint decision even though they have conflicting preferences over the alternatives. Examples range from the mundane—such as allocating chores among the members of a household—to the sublime—such as electing a government and thereby charting the course for a country. The ..."
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Cited by 28 (8 self)
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People often have to reach a joint decision even though they have conflicting preferences over the alternatives. Examples range from the mundane—such as allocating chores among the members of a household—to the sublime—such as electing a government and thereby charting the course for a country. The joint decision can be reached by an informal negotiating process or by a carefully specified protocol. Philosophers, mathematicians, political scientists, economists, and others have studied the merits of various protocols for centuries. More recently, especially over the course of the past decade or so, computer scientists have also become deeply involved in this study. The perhaps surprising arrival of computer scientists on this scene is due to a variety of reasons, including the following. 1. Computer networks provide a new platform for communicating
Discovering theorems in game theory: Two-person games with unique pure Nash equilibrium payoffs
, 2007
"... In this paper we provide a logical framework for using computers to discover theorems in two-person finite games in strategic form, and apply it to discover classes of games that have unique pure Nash equilibrium payoffs. We consider all possible classes of games that can be expressed by a conjuncti ..."
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Cited by 10 (4 self)
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In this paper we provide a logical framework for using computers to discover theorems in two-person finite games in strategic form, and apply it to discover classes of games that have unique pure Nash equilibrium payoffs. We consider all possible classes of games that can be expressed by a conjunction of two binary clauses, and our program rediscovered Kats and Thisse’s class of weakly unilaterally competitive two-person games, and came up with several other classes of games that have unique pure Nash equilibrium payoffs. It also came up with new classes of strict games that have unique pure Nash equilibria, where a game is strict if for both player different profiles have different payoffs.
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.
The Power of Integrated Abstraction for Data-Centric Human/Machine Computations
"... Humans are recognized as important data sources in data-centric applications today. This paper discusses the potential of integrated abstraction of data-centric human/machine computations, where data provided by people plays an important role. We show the potential by using a language named CyLog, o ..."
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Cited by 2 (2 self)
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Humans are recognized as important data sources in data-centric applications today. This paper discusses the potential of integrated abstraction of data-centric human/machine computations, where data provided by people plays an important role. We show the potential by using a language named CyLog, our first attempt to develop such abstractions. In CyLog, the closed world assumption is interpreted in a broader world in which people are included as rational data sources, that behave rationally in given games. We argue that such abstractions give us opportunities to appropriately deal with computations not closed in machines. 1.
Fast Equilibrium Computation for Infinitely Repeated Games
"... It is known that an equilibrium of an infinitely repeated two-player game (with limit average payoffs) can be computed in polynomial time, as follows: according to the folk theorem, we compute minimax strategies for both players to calculate the punishment values, and subsequently find a mixture ove ..."
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Cited by 2 (1 self)
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It is known that an equilibrium of an infinitely repeated two-player game (with limit average payoffs) can be computed in polynomial time, as follows: according to the folk theorem, we compute minimax strategies for both players to calculate the punishment values, and subsequently find a mixture over outcomes that exceeds these punishment values. However, for very large games, even computing minimax strategies can be prohibitive. In this paper, we propose an algorithmic framework for computing equilibria of repeated games that does not require linear programming and that does not necessarily need to inspect all payoffs of the game. This algorithm necessarily sometimes fails to compute an equilibrium, but we mathematically demonstrate that most of the time it succeeds quickly on uniformly random games, and experimentally demonstrate this for other classes of games. This also holds for games with more than two players, for which no efficient general algorithms are known.
Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data
"... We formalize and study the problem of learning the structure and parameters of graphical games from strictly behavioral data. We cast the problem as a maximum likelihood estimation (MLE) based on a generative model defined by the pure-strategy Nash equilibria (PSNE) of the game. The formulation brin ..."
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Cited by 1 (1 self)
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We formalize and study the problem of learning the structure and parameters of graphical games from strictly behavioral data. We cast the problem as a maximum likelihood estimation (MLE) based on a generative model defined by the pure-strategy Nash equilibria (PSNE) of the game. The formulation brings out the interplay between goodness-offit and model complexity: good models capture the equilibrium behavior represented in the data while controlling the true number of PSNE, including those potentially unobserved. We provide a generalization bound for MLE. We discuss several optimization algorithms including convex loss minimization (CLM), sigmoidal approximations and exhaustive search. We formally prove that games in our hypothesis space have a small true number of PSNE, with high probability; thus, CLM is sound. We illustrate our approach, show and discuss promising results on synthetic data and the U.S. congressional voting records. 1
Evolutionary solutions and internet applications for algorithmic game theory
, 2009
"... been accepted for inclusion in Computer Science Faculty Publications by an authorized administrator of Digital Commons @ Connecticut College. For more information, please contact ..."
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been accepted for inclusion in Computer Science Faculty Publications by an authorized administrator of Digital Commons @ Connecticut College. For more information, please contact
Game theory pragmatics: a challenge for AI
- Proceeding of the 22’nd AAAI Conference on Artificial Intelligence (AAAI
, 2008
"... Game theory has been playing an increasingly visible role in computer science in general and AI in particular, most no-tably in the area of multiagent systems. I briefly list the areas where most of the action has been in the past decade or so. I then suggest that going forward, the most dramatic in ..."
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Cited by 1 (0 self)
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Game theory has been playing an increasingly visible role in computer science in general and AI in particular, most no-tably in the area of multiagent systems. I briefly list the areas where most of the action has been in the past decade or so. I then suggest that going forward, the most dramatic inter-action between computer science and game theory – with a special role for AI – could be around what might be called game theory pragmatics.1 1
