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Quantal Response Equilibria For Normal Form Games
 NORMAL FORM GAMES, GAMES AND ECONOMIC BEHAVIOR
, 1995
"... We investigate the use of standard statistical models for quantal choice in a game theoretic setting. Players choose strategies based on relative expected utility, and assume other players do so as well. We define a Quantal Response Equilibrium (QRE) as a fixed point of this process, and establish e ..."
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Cited by 638 (27 self)
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We investigate the use of standard statistical models for quantal choice in a game theoretic setting. Players choose strategies based on relative expected utility, and assume other players do so as well. We define a Quantal Response Equilibrium (QRE) as a fixed point of this process, and establish existence. For a logit specification of the error structure, we show that as the error goes to zero, QRE approaches a subset of Nash equilibria and also implies a unique selection from the set of Nash equilibria in generic games. We fit the model to a variety of experimental data sets by using maximum likelihood estimatation.
Rationalizable Strategic Behavior and the Problem of Perfection
 ECONOMETRICA
, 1984
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Epistemic conditions for Nash equilibrium
, 1991
"... According to conventional wisdom, Nash equilibrium in a game “involves” common knowledge of the payoff functions, of the rationality of the players, and of the strategies played. The basis for this wisdom is explored, and it turns out that considerably weaker conditions suffice. First, note that if ..."
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Cited by 226 (6 self)
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According to conventional wisdom, Nash equilibrium in a game “involves” common knowledge of the payoff functions, of the rationality of the players, and of the strategies played. The basis for this wisdom is explored, and it turns out that considerably weaker conditions suffice. First, note that if each player is rational and knows his own payoff function, and the strategy choices of the players are mutually known, then these choices form a Nash equilibrium. The other two results treat the mixed strategies of a player not as conscious randomization of that player, but as conjectures of the other players about what he will do. When n = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures yields Nash equilibrium. When n ≥ 3, mutual knowledge of the payoff functions and of rationality, and common knowledge of the conjectures yield Nash equilibrium when there is a common prior. Examples are provided showing these results to be sharp.
Games of perfect information, predatory pricing and the chainstore paradox
 Journal of Economic Theory
, 1981
"... The thesis of this paper is that finite, noncooperative games possessing both complete and perfect information ought to be treated like oneplayer decision problems. That is, players ought to assign at every move subjective probabilities to every subsequent choice in the game and ought to make decis ..."
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Cited by 172 (1 self)
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The thesis of this paper is that finite, noncooperative games possessing both complete and perfect information ought to be treated like oneplayer decision problems. That is, players ought to assign at every move subjective probabilities to every subsequent choice in the game and ought to make decisions via backward induction. This view is in contrast with the gametheoretic approach of Nash equilibrium. After expanding on this view for games in the abstract in Sections 2 and 3, attention is turned in Section 4 to an example due to Reinhard Selten, called the chainstore paradox, which possesses the flavor of a situation involving a predatorypricing monopolist. It is argued that for the chainstore game the decisionanalytic approach leads, under certain assumptions, to more realistic outcomes than the standard Nashequilibrium approach. 2. AN ILLUSTRATIVE EXAMPLE Consider the game tree in Fig. 1 to be played only once in which the outcomes are assumed to be expressed in U.S. dollars and x and y are dollar values known to both players. In words, if Player 1 chooses Left, he receives x dollars and 2 receives y dollars; if Player 1 chooses Right, then the outcome is either (0,O) or (1 million, 1) depending on Player 2’s choice. Assuming that each player’s von NeumannMorgenstern utilities for the outcomes are ordered in the same way as the dollar values and assuming that the game is played under conditions of complete information (i.e., each player knows the rules, the dollar payoffs for both, von NeumannMorgenstern utility images of both players ’ payoffs, the fact that the other player knows all of this, the fact that the other knows that he knows, etc.) what should Player 1 do? More directly, for what values of x and y would you as Player 1 be indifferent between your two choices? For
COMPUTATION OF EQUILIBRIA in Finite Games
, 1996
"... We review the current state of the art of methods for numerical computation of Nash equilibria for nitenperson games. Classical path following methods, such as the LemkeHowson algorithm for two person games, and Scarftype fixed point algorithms for nperson games provide globally convergent metho ..."
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Cited by 149 (1 self)
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We review the current state of the art of methods for numerical computation of Nash equilibria for nitenperson games. Classical path following methods, such as the LemkeHowson algorithm for two person games, and Scarftype fixed point algorithms for nperson games provide globally convergent methods for finding a sample equilibrium. For large problems, methods which are not globally convergent, such as sequential linear complementarity methods may be preferred on the grounds of speed. None of these methods are capable of characterizing the entire set of Nash equilibria. More computationally intensive methods, which derive from the theory of semialgebraic sets are required for finding all equilibria. These methods can also be applied to compute various equilibrium refinements.