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32
Breeding hybrid strategies: Optimal behaviour for oligopolists
 Journal of Evolutionary Economics
, 1992
"... Abstract. Oligopolistic pricing decisions in which the choice variable is not dichotomous as in the simple prisoner's dilemma but continuous have been modeled as a generalized prisoner's dilemma (GPD) by Fader and Hauser, who sought, in the two MIT Computer Strategy Tournaments, to obtai ..."
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Cited by 35 (9 self)
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Abstract. Oligopolistic pricing decisions in which the choice variable is not dichotomous as in the simple prisoner's dilemma but continuous have been modeled as a generalized prisoner's dilemma (GPD) by Fader and Hauser, who sought, in the two MIT Computer Strategy Tournaments, to obtain an effective generalization of Rapoport's Tit for Tat for the threeperson repeated game. Holland's genetic algorithm and Axelrod's representation of contingent strategies provide a means of generating new strategies in the computer, through machine learning, without outside submissions. The paper discusses how findings from twoperson tournaments can be extended to the GPD, in particular how the author's winning strategy in the Second MIT Competitive Strategy Tournament could be bettered. The paper provides insight into how oligopolistic pricing competitors can successfully compete, and underlines the importance of "niche " strategies, successful against a particular environment of competitors. Bootstrapping, or breeding strategies against their peers, provides a means of
Lossless abstraction of imperfect information games
 Journal of the ACM
, 2007
"... Abstract. Finding an equilibrium of an extensive form game of imperfect information is a fundamental problem in computational game theory, but current techniques do not scale to large games. To address this, we introduce the ordered game isomorphism and the related ordered game isomorphic abstractio ..."
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Cited by 33 (14 self)
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Abstract. Finding an equilibrium of an extensive form game of imperfect information is a fundamental problem in computational game theory, but current techniques do not scale to large games. To address this, we introduce the ordered game isomorphism and the related ordered game isomorphic abstraction transformation. For a multiplayer sequential game of imperfect information with observable actions and an ordered signal space, we prove that any Nash equilibrium in an abstracted smaller game, obtained by one or more applications of the transformation, can be easily converted into a Nash equilibrium in the original game. We present an algorithm, GameShrink, for abstracting the game using our isomorphism exhaustively. Its complexity is Õ(n2), where n is the number of nodes in a structure we call the signal tree. It is no larger than the game tree, and on nontrivial games it is drastically smaller, so GameShrink has time and space complexity sublinear in the size of the game tree. Using GameShrink, we find an equilibrium to a poker game with 3.1 billion nodes—over four orders of magnitude more than in the largest poker game solved previously. To address even larger games, we introduce approximation methods that do not preserve equilibrium, but nevertheless yield (ex post) provably closetooptimal strategies.
Computing Normal Form Perfect Equilibria For Extensive TwoPerson Games
 ECONOMETRICA
, 2001
"... This paper presents an algorithm for computing an equilibrium of an extensive twoperson game with perfect recall. The method is computationally e#cient by virtue of using the sequence form, whose size is proportional to the size of the game tree. The equilibrium is traced on a piecewise linear p ..."
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Cited by 14 (1 self)
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This paper presents an algorithm for computing an equilibrium of an extensive twoperson game with perfect recall. The method is computationally e#cient by virtue of using the sequence form, whose size is proportional to the size of the game tree. The equilibrium is traced on a piecewise linear path in the sequence form strategy space from an arbitrary starting vector. If the starting vector represents a pair of completely mixed strategies, then the equilibrium is normal form perfect. Computational experiments compare the sequence form and the reduced normal form, and show that only the sequence form is tractable for larger games.
The Coevolution of Morality and Legal Institutions  An indirect evolutionary approach
 In
, 2002
"... Evolutionary game theory is often used to analyze the evolution of moral preferences. A few studies also examine the coevolution of preferences and an institutional aspect of the decision environment. ..."
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Cited by 13 (2 self)
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Evolutionary game theory is often used to analyze the evolution of moral preferences. A few studies also examine the coevolution of preferences and an institutional aspect of the decision environment.
Evolutionary stability and efficiency
 Economics Letters
, 1993
"... ‘One of the advantages of moral philosophy over game theory is that moralists give sensible advice to moral agents while game theory can give stupid advice to game theorists ’ Ian Hacking. 1. ..."
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Cited by 11 (2 self)
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‘One of the advantages of moral philosophy over game theory is that moralists give sensible advice to moral agents while game theory can give stupid advice to game theorists ’ Ian Hacking. 1.
A gradientbased approach for computing Nash equilibria of large sequential games
, 2007
"... We propose a new gradient based scheme to approximate Nash equilibria of large sequential twoplayer, zerosum games. The algorithm uses modern smoothing techniques for saddlepoint problems tailored specifically for the polytopes used in the Nash equilibrium problem. ..."
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Cited by 8 (5 self)
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We propose a new gradient based scheme to approximate Nash equilibria of large sequential twoplayer, zerosum games. The algorithm uses modern smoothing techniques for saddlepoint problems tailored specifically for the polytopes used in the Nash equilibrium problem.
Algorithms for abstracting and solving imperfect information games
, 2007
"... Game theory is the mathematical study of rational behavior in strategic environments. In many settings, most notably twoperson zerosum games, game theory provides particularly strong and appealing solution concepts. Furthermore, these solutions are efficiently computable in the complexitytheory s ..."
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Cited by 6 (2 self)
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Game theory is the mathematical study of rational behavior in strategic environments. In many settings, most notably twoperson zerosum games, game theory provides particularly strong and appealing solution concepts. Furthermore, these solutions are efficiently computable in the complexitytheory sense. However, in most interesting potential applications in artificial intelligence, the solutions are difficult to compute using current techniques due primarily to the extremely large statespaces of the environments. In this thesis, we propose new algorithms for tackling these computational difficulties. In one stream of research, we introduce automated abstraction algorithms for sequential games of imperfect information. These algorithms take as input a description of a game and produce a description of a strategically similar, but smaller, game as output. We present algorithms that are lossless (i.e., equilibriumpreserving), as well as algorithms that are lossy, but which can yield much smaller games while still retaining the most important features of the original game. In a second stream of research, we develop specialized optimization algorithms for finding ɛequilibria in sequential games of imperfect information. The algorithms are based on recent advances in nonsmooth convex optimization (namely the excessive gap technique) and provide significant improvements
Games Computers Play: Simulating Characteristic Function Game Playing Agents with Classifier Systems
 In Proceedings of the 1994 IEEE Conference on Evolutionary Computation, IEEE
, 1994
"... * Many game theorists are turning to evolutionary simulations to model the behavior of boundedly rational agents. This new methodology allows researchers to observe purely adaptive behaviors in games, to observe differences of behavior due to changes in the games' parameters, to discover equil ..."
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Cited by 5 (3 self)
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* Many game theorists are turning to evolutionary simulations to model the behavior of boundedly rational agents. This new methodology allows researchers to observe purely adaptive behaviors in games, to observe differences of behavior due to changes in the games' parameters, to discover equilibria in games that are too complex to calculate analytically, and to discover new strategies for playing the games. In this paper, I extend this methodology to a more complex class of games than had previously been attempted. I create a coevolutionary environment in which three agents, represented by classifier systems, play a characteristic function game. Although the agents have no computational capabilities, they learn to adapt reasonably intelligent behavior. INTRODUCTION Cooperative game theory attempts to model how groups should and do act in cooperative situations. This consists of determining what equilibria exist in a cooperative game, and determining which equilibrium agents in the g...
Static Stability in Symmetric and Population Games
, 2011
"... Static stability in strategic games differs from dynamic stability in only considering the players ’ incentives to change their strategies. It does not rely on any assumptions about the players ’ reactions to these incentives and it is thus independent of the law of motion (e.g., whether players mov ..."
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Cited by 3 (1 self)
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Static stability in strategic games differs from dynamic stability in only considering the players ’ incentives to change their strategies. It does not rely on any assumptions about the players ’ reactions to these incentives and it is thus independent of the law of motion (e.g., whether players move simultaneously or sequentially). Examples of static notions of stability include evolutionarily stable strategy (ESS) and continuously stable strategy (CSS), both of which are meaningful or justifiable only for particular classes of symmetric and population games, such as games with multilinear payoff functions or with unidimensional strategy spaces. This paper presents a general notion of static stability in symmetric (player) games and population games and with nondiscrete strategy spaces, of which ESS and CSS are essentially special cases. JEL Classification: C72.