Game theory with translucent players

Joseph Y. Halpern, Rafael Pass

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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).

Original languageEnglish
Title of host publicationProceedings of the 14th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2013
EditorsBurkhard C. Schipper
PublisherInstitute of Mathematical Sciences
Pages216-221
Number of pages6
ISBN (Electronic)9780615747163
StatePublished - 2013
Externally publishedYes
Event14th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2013 - Chennai, India
Duration: 7 Jan 20139 Jan 2013

Publication series

NameProceedings of the 14th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2013

Conference

Conference14th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2013
Country/TerritoryIndia
CityChennai
Period7/01/139/01/13

Keywords

  • Counterfactuals
  • Epistemic logic
  • Rationality

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