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46
Evolutionary Game Theory
, 1995
"... Abstract. Experimentalists frequently claim that human subjects in the laboratory violate gametheoretic predictions. It is here argued that this claim is usually premature. The paper elaborates on this theme by way of raising some conceptual and methodological issues in connection with the very def ..."
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Cited by 874 (12 self)
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Abstract. Experimentalists frequently claim that human subjects in the laboratory violate gametheoretic predictions. It is here argued that this claim is usually premature. The paper elaborates on this theme by way of raising some conceptual and methodological issues in connection with the very definition of a game and of players ’ preferences, in particular with respect to potential context dependence, interpersonal preference dependence, backward induction and incomplete information.
Fast Equilibrium Selection by Rational Players Living in a Changing World
 Econometrica
, 1996
"... We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk dominant equilibrium. More precisely, a continuum of fully rational players are randomly matched to play a symmetric 2 ..."
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Cited by 49 (9 self)
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We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk dominant equilibrium. More precisely, a continuum of fully rational players are randomly matched to play a symmetric 2 \Theta 2 game. The payoff matrix changes over time according to some Brownian motion. Players observe these payoffs and the population distribution of actions as they evolve. The game has frictions: opportunities to change strategies arrive from independent random processes, so that the players are locked into their actions for some time. We solve the game using only backwards induction. As the frictions disappear, each player ignores what the others are doing and switches at her first opportunity to the risk dominant equilibrium. History dependence emerges in some cases when frictions remain positive. As an application we show how frictions and aggregate cost shocks can lead to the selecti...
Dynamic interactive epistemology
, 2004
"... The epistemic program in game theory uses formal models of interactive reasoning to provide foundations for various gametheoretic solution concepts. Much of this work is based around the (static) Aumann structure model of interactive epistemology, but more recently dynamic models of interactive rea ..."
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Cited by 35 (1 self)
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The epistemic program in game theory uses formal models of interactive reasoning to provide foundations for various gametheoretic solution concepts. Much of this work is based around the (static) Aumann structure model of interactive epistemology, but more recently dynamic models of interactive reasoning have been developed, most notably by Stalnaker [Econ. Philos. 12 (1996) 133– 163] and Battigalli and Siniscalchi [J. Econ. Theory 88 (1999) 188–230], and used to analyze rational play in extensive form games. But while the properties of Aumann structures are well understood, without a formal language in which belief and belief revision statements can be expressed, it is unclear exactly what are the properties of these dynamic models. Here we investigate this question by defining such a language. A semantics and syntax are presented, with soundness and completeness theorems linking the two.
Rationalizability in Lexicographic Beliefs
 International Journal of Game Theory
"... Abstract. Proper consistency is defined by the property that each player takes all opponent strategies into account (is cautious) and deems one opponent strategy to be infinitely more likely than another if the opponent prefers the one to the other (respects preferences). When there is common certai ..."
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Cited by 22 (3 self)
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Abstract. Proper consistency is defined by the property that each player takes all opponent strategies into account (is cautious) and deems one opponent strategy to be infinitely more likely than another if the opponent prefers the one to the other (respects preferences). When there is common certain belief of proper consistency, a most preferred strategy is properly rationalizable. Any strategy used with positive probability in a proper equilibrium is properly rationalizable. Only strategies that lead to the backward induction outcome are properly rationalizable in the strategic form of a generic perfect information game. Proper rationalizability can test the robustness of inductive procedures. JEL Classification Number: C72. Key words: Rationalizability, backward induction, strategic form
Modeling Beliefs In Dynamic Systems
, 1997
"... tions beliefs. We say that an agent believes ' if she acts as though ' is true. As time passes and new evidence is observed, changes in an agent's defeasible assumptions lead to changes in her beliefs. Thus, the question of belief changethat is, how beliefs change over timeis a ..."
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Cited by 15 (6 self)
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tions beliefs. We say that an agent believes ' if she acts as though ' is true. As time passes and new evidence is observed, changes in an agent's defeasible assumptions lead to changes in her beliefs. Thus, the question of belief changethat is, how beliefs change over timeis a central one for understanding systems that can make and modify defeasible assumptions. In this dissertation, we propose a new approach to the question of belief change. This approach is based on developing a semantics for beliefs. This semantics is embedded in a framework that models agents' knowledge (or information) as well as their beliefs, and how these change in time. We argue, and demonstrate by examples, that this framework can naturally model any dynamic system (e.g., agents and their environment). Moreover, the framework allows us to consider what the properties of wellbehaved belief change should be. As we show, such a framework can g
Admissibility and common belief
, 2003
"... The concept of ‘fully permissible sets’ is defined by an algorithm that eliminates strategy subsets. It is characterized as choice sets when there is common certain belief of the event that each player prefer one strategy to another if and only if the former weakly dominates the latter on the set of ..."
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Cited by 12 (6 self)
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The concept of ‘fully permissible sets’ is defined by an algorithm that eliminates strategy subsets. It is characterized as choice sets when there is common certain belief of the event that each player prefer one strategy to another if and only if the former weakly dominates the latter on the set of all opponent strategies or on the union of the choice sets that are deemed possible for the opponent. The concept refines the Dekel–Fudenberg procedure and captures aspects of forward induction.
Checkmate: Exploring Backward Induction Among Chess Players. NBER Working Paper Series, http://www.nber.org/papers/w15610
 European Journal of Social Psychology
, 2009
"... It is difficult to overstate the profound impact that game theory has had on the economic approach and on the sciences more generally. For that reason, understanding how closely the assumptions that underpin game theoretic analysis conform to actual human decisionmaking is a question of firstorder ..."
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Cited by 11 (0 self)
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It is difficult to overstate the profound impact that game theory has had on the economic approach and on the sciences more generally. For that reason, understanding how closely the assumptions that underpin game theoretic analysis conform to actual human decisionmaking is a question of firstorder importance to economists. In this spirit, backward induction represents one of the most basic concepts in game theory. Backward induction played a prominent role in Reinhard Selten’s (1965) development of perfect equilibrium, and it has helped to shape the modern refinement literature. Although backward induction is a cornerstone of game theory, existing empirical evidence suggests that economic agents engage in backward induction less frequently than theorists might hope. Backward induction has fared especially poorly in the centipede game, which was introduced by Robert W. Rosenthal (1981) and has since been extensively analyzed
DEDUCTIVE REASONING IN EXTENSIVE GAMES
, 2003
"... We justify the application to extensive games of a model of deductive reasoning based on three key features: ‘caution’, ‘full belief of opponent rationality’, and ‘no extraneous restrictions on beliefs’. We apply the model to several examples, and show that it yields novel economic insights. The app ..."
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Cited by 9 (1 self)
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We justify the application to extensive games of a model of deductive reasoning based on three key features: ‘caution’, ‘full belief of opponent rationality’, and ‘no extraneous restrictions on beliefs’. We apply the model to several examples, and show that it yields novel economic insights. The approach supports forward induction, without necessarily promoting backward induction.
Rationalizability and minimal complexity in dynamic games
, 2003
"... This paper presents a formal epistemic framework for dynamic games in which players, during the course of the game, may revise their beliefs about the opponents' utility functions. We impose two key conditions upon the players ' beliefs: (a) throughout the game, every move by the opponent ..."
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Cited by 5 (1 self)
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This paper presents a formal epistemic framework for dynamic games in which players, during the course of the game, may revise their beliefs about the opponents' utility functions. We impose two key conditions upon the players ' beliefs: (a) throughout the game, every move by the opponent should be interpreted as a rational move, and (b) the belief about the opponents' relative utilities between two terminal nodes should only be revised if you are sure that the opponent has decided to avoid one of these nodes. Common belief about these events leads to the concept of persistent rationalizability. It is shown that persistent rationalizability implies the backward induction procedure in generic games with perfect information. We next focus on persistently rationalizable types having beliefs with "minimal complexity", resulting in the concept of minimal rationalizability. For twoplayer simultaneous move games, minimal rationalizability is equivalent to the concept of Nash equilibrium strategy. In every outside option game, as defined by van Damme (1989), minimal rationalizability uniquely selects the forward induction outcome.
Conservative Belief and Rationality
, 2012
"... Brandenburger and Dekel have shown that common belief of rationality (CBR) characterizes rationalizable strategies, which are also characterized by a refinement of subjective correlated equilibrium called a posteriori equilibrium. It is possible that players ’ beliefs are incompatible, in the sense ..."
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Cited by 3 (3 self)
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Brandenburger and Dekel have shown that common belief of rationality (CBR) characterizes rationalizable strategies, which are also characterized by a refinement of subjective correlated equilibrium called a posteriori equilibrium. It is possible that players ’ beliefs are incompatible, in the sense that player i can assign probability 1 to an event E to which player j assigns probability 0. One way to block incompatibility is to assume a common prior. We consider here a different approach: we require players ’ beliefs to be conservative, in the sense that all players must ascribe the actual world positive probability. Aumann has shown that, under the common prior assumption (CPA), common belief of rationality characterizes strategies in the support of an objective correlated equilibrium. Under the CPA, without loss of generality, all players ’ beliefs can be assumed to be conservative. We consider the consequences of common convervative belief of rationality (CCBR), without the common prior assumption. We show that CCBR characterizes strategies in the support of a subjective correlated equilibrium where all players ’ beliefs have common support. We also In the Bayesian view of the world, each player has a subjective probability distribution (describing her