TY - GEN

T1 - Game theory with translucent players

AU - Halpern, Joseph Y.

AU - Pass, Rafael

N1 - Publisher Copyright:
Copyright 2013 by the authors.

PY - 2013

Y1 - 2013

N2 - A traditional assumption in game theory is that players are opaque to one another - if a player changes strategies, then this change in strategies does not affect the choice of other players' strategies. In many situations this is an unrealistic assumption. We develop a framework for reasoning about games where the players may be translucent to one another; in particular, a player may believe that if she were to change strategies, then the other player would also change strategies. Translucent players may achieve significantly more efficient outcomes than opaque ones. Our main result is a characterization of strategies consistent with appropriate analogues of common belief of rationality. Common Counterfactual Belief of Rationality (CCBR) holds if (1) everyone is rational, (2) everyone counterfactually believes that everyone else is rational (i.e., all players i believe that everyone else would still be rational even if i were to switch strategies), (3) everyone counterfactually believes that everyone else is rational, and counterfactually believes that everyone else is rational, and so on. CCBR characterizes the set of strategies surviving iterated removal of minimax dominated strategies: a strategy σi is minimax dominated for i if there exists a strategy σ'i for i such that minμ'-r μi (σi, μ'-i) > maxμ-r ui(σi, μ-i).

AB - A traditional assumption in game theory is that players are opaque to one another - if a player changes strategies, then this change in strategies does not affect the choice of other players' strategies. In many situations this is an unrealistic assumption. We develop a framework for reasoning about games where the players may be translucent to one another; in particular, a player may believe that if she were to change strategies, then the other player would also change strategies. Translucent players may achieve significantly more efficient outcomes than opaque ones. Our main result is a characterization of strategies consistent with appropriate analogues of common belief of rationality. Common Counterfactual Belief of Rationality (CCBR) holds if (1) everyone is rational, (2) everyone counterfactually believes that everyone else is rational (i.e., all players i believe that everyone else would still be rational even if i were to switch strategies), (3) everyone counterfactually believes that everyone else is rational, and counterfactually believes that everyone else is rational, and so on. CCBR characterizes the set of strategies surviving iterated removal of minimax dominated strategies: a strategy σi is minimax dominated for i if there exists a strategy σ'i for i such that minμ'-r μi (σi, μ'-i) > maxμ-r ui(σi, μ-i).

KW - Counterfactuals

KW - Epistemic logic

KW - Rationality

UR - http://www.scopus.com/inward/record.url?scp=85087097437&partnerID=8YFLogxK

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AN - SCOPUS:85087097437

T3 - Proceedings of the 14th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2013

SP - 216

EP - 221

BT - Proceedings of the 14th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2013

A2 - Schipper, Burkhard C.

PB - Institute of Mathematical Sciences

T2 - 14th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2013

Y2 - 7 January 2013 through 9 January 2013

ER -