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75
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 642 (9 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.
Hypothetical Knowledge and Games with Perfect Information
, 1996
"... This paper, in a nutshell, disputes the adequacy of the standard model for describing games with perfect information and proposes a model which is adequate for this purpose. We show that standard models fail to capture an important structural aspect of strategic thinking and therefore leave unformal ..."
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Cited by 35 (3 self)
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This paper, in a nutshell, disputes the adequacy of the standard model for describing games with perfect information and proposes a model which is adequate for this purpose. We show that standard models fail to capture an important structural aspect of strategic thinking and therefore leave unformalized many intuitive arguments that depend on it. The model we propose captures this aspect by giving a fuller and more faithful account of strategic thinking. Using this model we reexamine the relation between rationality and backward induction and give formal expression to statements about the reasoning of players in games with perfect information }statements that cannot be formalized in the standard model
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 29 (7 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...
The power of paradox: some recent developments in interactive epistemology
 International Journal of Game Theory
, 2007
"... Abstract Paradoxes of gametheoretic reasoning have played an important role in spurring developments in interactive epistemology, the area in game theory that studies the role of the players ’ beliefs, knowledge, etc. This paper describes two such paradoxes – one concerning backward induction, the ..."
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Cited by 25 (2 self)
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Abstract Paradoxes of gametheoretic reasoning have played an important role in spurring developments in interactive epistemology, the area in game theory that studies the role of the players ’ beliefs, knowledge, etc. This paper describes two such paradoxes – one concerning backward induction, the other iterated weak dominance. We start with the basic epistemic condition of “rationality and common belief of rationality ” in a game, describe various ‘refinements ’ of this condition that have been proposed, and explain how these refinements resolve the two paradoxes. We will see that a unified epistemic picture of game theory emerges. We end with some new foundational questions uncovered by the epistemic program. 1
Substantive Rationality and Backward Induction
 Games and Economic Behavior
, 1998
"... Aumann has proved that common knowledge of substantive rationality implies the backwards induction solution in games of perfect information. Stalnaker has proved that it does not. Roughly speaking, a player is substantively rational if, for all vertices v, if the player were to reach vertex v, then ..."
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Cited by 18 (2 self)
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Aumann has proved that common knowledge of substantive rationality implies the backwards induction solution in games of perfect information. Stalnaker has proved that it does not. Roughly speaking, a player is substantively rational if, for all vertices v, if the player were to reach vertex v, then the player would be rational at vertex v". It is shown here that the key difference between Aumann and Stalnaker lies in how they interpret this counterfactual. A formal model is presented that lets us capture this difference, in which both Aumann's result and Stalnaker's result are true (under appropriate assumptions). Starting with the work of Bicchieri [1988, 1989], Binmore [1987], and Reny [1992], there has been intense scrutiny of the assumption of common knowledge of rationality, the use of counterfactual reasoning in games, and the role of common knowledge and counterfactuals in the arguments for backward Supported in part by NSF under grant IRI9625901. induction in games of ...
Evolutionary dynamics and backward induction
 Games and Economic Behavior
"... The backward induction (or subgameperfect) equilibrium of a perfect information game is shown to be the unique evolutionarily stable outcome for dynamic models consisting of selection and mutation, when the mutation rate is low and the populations are large. ..."
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Cited by 16 (0 self)
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The backward induction (or subgameperfect) equilibrium of a perfect information game is shown to be the unique evolutionarily stable outcome for dynamic models consisting of selection and mutation, when the mutation rate is low and the populations are large.
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 central one for ..."
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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
Hypothetical Knowledge and Counterfactual Reasoning
 International Journal of Game Theory
, 1999
"... Abstract: Salmet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypothetical knowledge and the extended informatio ..."
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Cited by 15 (3 self)
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Abstract: Salmet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypothetical knowledge and the extended information structures used to model it bear some resemblance to the way philosophers have used conditional logic to model counterfactuals, hypothetical knowledge cannot be reduced to conditional logic together with epistemic logic. Here it is shown that in fact hypothetical knowledge can be captured using the standard counterfactual operator "> " and the knowledge operator "K", provided that some assumptions are made regarding the interaction between the two. It is argued, however, that these assumptions are unreasonable in general, as are the axioms that follow from them. Some implications for game theory are discussed. 1
Keep ‘Hoping’ for Rationality: A solution to the Backward Induction Paradox
, 2009
"... Aumann has proved that common knowledge of substantive rationality implies the backward induction solution in games of perfect information. Stalnaker has proved that it does not. (Halpern, 2001) The jury is still out concerning the epistemic conditions for backward induction, the “oldest idea in gam ..."
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Cited by 12 (0 self)
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Aumann has proved that common knowledge of substantive rationality implies the backward induction solution in games of perfect information. Stalnaker has proved that it does not. (Halpern, 2001) The jury is still out concerning the epistemic conditions for backward induction, the “oldest idea in game theory ” (Aumann, 1995, p. 635). Aumann (1995) and Stalnaker (1996) take conflicting positions in the debate: the former claims that common “knowledge ” of “rationality ” in a game of perfect information entails the backwardinduction solution; the latter that it does not. 1 Of course there is nothing wrong with any of their relevant formal proofs, but rather, as pointed out by Halpern (2001), there are differences between their interpretations of the notions of knowledge, belief, strategy and rationality. Moreover, as pointed out by Binmore (1987; 1996),
Modal logic and game theory: two alternative approaches, Risk Decision and Policy
, 2002
"... Two views of game theory are discussed: (1) game theory as a description of the behavior of rational individuals who recognize each other’s rationality and reasoning abilities, and (2) game theory as an internally consistent recommendation to individuals on how to act in interactive situations. It i ..."
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Cited by 8 (1 self)
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Two views of game theory are discussed: (1) game theory as a description of the behavior of rational individuals who recognize each other’s rationality and reasoning abilities, and (2) game theory as an internally consistent recommendation to individuals on how to act in interactive situations. It is shown that the same mathematical tool, namely modal logic, can be used to explicitly model both views. 1.