Playing Off-Line Games with Bounded Rationality

Posted: 12 Mar 2012

See all articles by Jerome Renault

Jerome Renault

University of Toulouse 1 - Toulouse School of Economics (TSE)

Marco Scarsini

Luiss University Dipartimento di Economia e Finanza

Tristan Tomala

HEC Paris - Economics & Decision Sciences

Date Written: 2008

Abstract

We study a two-person zero-sum game where players simultaneously choose sequences of actions, and the overall payoff is the average of a one-shot payoff over the joint sequence. We consider the maxmin value of the game played in pure strategies by boundedly rational players and model bounded rationality by introducing complexity limitations. First we define the complexity of a sequence by its smallest period (a nonperiodic sequence being of infinite complexity) and study the maxmin of the game where player 1 is restricted to strategies with complexity at most n and player 2 is restricted to strategies with complexity at most m. We study the asymptotics of this value and a complete characterization in the matching pennies case. We extend the analysis of matching pennies to strategies with bounded recall.

Keywords: Zero-sum games, Periodic sequences, Bounded recall, de Bruijn graphs, Oblivious strategy

JEL Classification: C72, C73

Suggested Citation

Renault, Jerome and Scarsini, Marco and Tomala, Tristan, Playing Off-Line Games with Bounded Rationality (2008). Mathematical Social Sciences, Vol. 56, No. 2, 2008, Available at SSRN: https://ssrn.com/abstract=2019686

Jerome Renault

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

Place Anatole-France
Toulouse Cedex, F-31042
France

Marco Scarsini (Contact Author)

Luiss University Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

Tristan Tomala

HEC Paris - Economics & Decision Sciences ( email )

1 rue de la Liberation
Paris, 78351
France

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