Results 1  10
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22
Rational Learning Leads to Nash Equilibrium
 Econometrica
, 1993
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Cited by 217 (13 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
AWESOME: A general multiagent learning algorithm that converges in selfplay and learns a best response against stationary opponents
, 2003
"... A satisfactory multiagent learning algorithm should, at a minimum, learn to play optimally against stationary opponents and converge to a Nash equilibrium in selfplay. The algorithm that has come closest, WoLFIGA, has been proven to have these two properties in 2player 2action repeated games— as ..."
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Cited by 81 (5 self)
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A satisfactory multiagent learning algorithm should, at a minimum, learn to play optimally against stationary opponents and converge to a Nash equilibrium in selfplay. The algorithm that has come closest, WoLFIGA, has been proven to have these two properties in 2player 2action repeated games— assuming that the opponent’s (mixed) strategy is observable. In this paper we present AWESOME, the first algorithm that is guaranteed to have these two properties in all repeated (finite) games. It requires only that the other players ’ actual actions (not their strategies) can be observed at each step. It also learns to play optimally against opponents that eventually become stationary. The basic idea behind AWESOME (Adapt When Everybody is Stationary, Otherwise Move to Equilibrium) is to try to adapt to the others’ strategies when they appear stationary, but otherwise to retreat to a precomputed equilibrium strategy. The techniques used to prove the properties of AWESOME are fundamentally different from those used for previous algorithms, and may help in analyzing other multiagent learning algorithms also.
On the Global Convergence of Stochastic Fictitious Play
 ECONOMETRICA
, 2002
"... We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stocha ..."
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Cited by 52 (10 self)
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We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stochastic process to the limit behavior of a differential equation defined by the expected motion of the process. The key result in our analysis of supermodular games is that the relevant differential equation defines a strongly monotone dynamical system. Our analyses of the other cases combine Lyapunov function arguments with a discrete choice theory result: that the choice probabilities generated by any additive random utility model can be derived from a deterministic model based on payoff perturbations that depend nonlinearly on the vector of choice probabilities.
On the Impossibility of Predicting the Behavior of Rational Agents Dean P. Foster
 Proceedings of the National Academy of Sciences of the USA
, 2001
"... A foundational assumption in economics is that people are rational  they choose optimal plans of action given their predictions about future states of the world. In games of strategy this means that each players' strategy should be optimal given his or her prediction of the opponents' strategies. ..."
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Cited by 20 (3 self)
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A foundational assumption in economics is that people are rational  they choose optimal plans of action given their predictions about future states of the world. In games of strategy this means that each players' strategy should be optimal given his or her prediction of the opponents' strategies. We demonstrate that there is an inherent tension between rationality and prediction when players are uncertain about their opponents' payoff functions. Specifically, there are games in which it is impossible for perfectly rational players to learn to predict the future behavior of their opponents (even approximately) no matter what learning rule they use. The reason is that, in trying to predict the nextperiod behavior of an opponent, a rational player must take an action this period that the opponent can observe. This observation may cause the opponent to alter his nextperiod behavior, thus invalidating the first player's prediction. The resulting feedback loop has the property that, in almost every time period, someone predicts that his opponent has a nonnegligible probability of choosing one action, when in fact the opponent is certain to choose a different action. We conclude that there are strategic situations where it is impossible in principle for perfectly rational agents to learn to predict the future behavior of other perfectly rational agents, based solely on their observed actions. 3 Rationality vs predictability Economists often assume that people are rational: they maximize their expected payoffs given their beliefs about future states of the world. This hypothesis plays a crucial role in game theory, where each player is assumed to choose an optimal strategy given his belief about the strategies of his opponents. In this setting, a belief amounts to a forec...
A Learning Approach to Auctions
, 1998
"... We analyze a repeated firstprice auction in which the types of the players are determined before the first round. It is proved that if every player is using either a beliefbased learning scheme with bounded recall or a generalized fictitious play learning scheme, then after sufficiently long time, ..."
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Cited by 20 (3 self)
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We analyze a repeated firstprice auction in which the types of the players are determined before the first round. It is proved that if every player is using either a beliefbased learning scheme with bounded recall or a generalized fictitious play learning scheme, then after sufficiently long time, the players' bids are in equilibrium in the oneshot auction in which the types are commonly known.
On the convergence of fictitious play
 Mathematics of Operations Research
, 1998
"... We study the continuous time BrownRobinson ctitious play process for nonzero sum games. We show that, in general, ctitious play cannot converge cyclically to a mixed strategy equilibrium in which both players use more than two pure strategies. 1 ..."
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Cited by 17 (0 self)
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We study the continuous time BrownRobinson ctitious play process for nonzero sum games. We show that, in general, ctitious play cannot converge cyclically to a mixed strategy equilibrium in which both players use more than two pure strategies. 1
Generalised weakened fictitious play
, 2004
"... A general class of adaptive processes in games is developed, which significantly generalises weakened fictitious play [Van der Genugten, B., 2000. A weakened form of fictitious play in twoperson zerosum games. Int. Game Theory Rev. 2, 307–328] and includes several interesting fictitiousplaylike ..."
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Cited by 14 (3 self)
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A general class of adaptive processes in games is developed, which significantly generalises weakened fictitious play [Van der Genugten, B., 2000. A weakened form of fictitious play in twoperson zerosum games. Int. Game Theory Rev. 2, 307–328] and includes several interesting fictitiousplaylike processes as special cases. The general model is rigorously analysed using the best response differential inclusion, and shown to converge in games with the fictitious play property. Furthermore, a new actor–critic process is introduced, in which the only information given to a player is the reward received as a result of selecting an action—a player need not even know they are playing a game. It is shown that this results in a generalised weakened fictitious play process, and can therefore be considered as a first step towards explaining how players might learn to play Nash equilibrium strategies without having any knowledge of the game, or even that they are playing a game.
Simple forecasts and paradigm shifts
 Journal of Finance
, 2007
"... Abstract: We study the implications of learning in an environment where the true model of the world is a multivariate one, but where agents update only over the class of simple univariate models. If a particular simple model does a poor job of forecasting over a period of time, it is eventually disc ..."
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Cited by 14 (0 self)
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Abstract: We study the implications of learning in an environment where the true model of the world is a multivariate one, but where agents update only over the class of simple univariate models. If a particular simple model does a poor job of forecasting over a period of time, it is eventually discarded in favor of an alternative—yet equally simple—model that would have done better over the same period. This theory makes several distinctive predictions, which, for concreteness, we develop in a stockmarket setting. For example, starting with symmetric and homoskedastic fundamentals, the theory yields forecastable variation in the size of the value/glamour differential, in volatility, and in the skewness of returns. Some of these features mirror familiar accounts of stockprice bubbles.
Evolution of Beliefs and the Nash Equilibrium of Normal Form Games," mimeo
, 1992
"... The paper formulates a simple twoperson model of learning with pattern recognition and discusses its implications. In particular, it focuses on the asymptotic behavior of players ' beliefs when the game has a mixedstrategy Nash equilibrium. ..."
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Cited by 11 (0 self)
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The paper formulates a simple twoperson model of learning with pattern recognition and discusses its implications. In particular, it focuses on the asymptotic behavior of players ' beliefs when the game has a mixedstrategy Nash equilibrium.