Scandinavian Working Papers in Economics

Memorandum,
Oslo University, Department of Economics

No 15/2016: Epistemically robust strategy subsets

Geir Asheim (), Mark Voorneveld and Jörgen W. Weibull
Additional contact information
Geir Asheim: Dept. of Economics, University of Oslo, Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Mark Voorneveld: Department of Economics, Stockholm School of Economics,, Postal: Box 6501, SE-113 83 Stockholm,, Sweden
Jörgen W. Weibull: Department of Economics, Stockholm School of Economics, Postal: Box 6501, SE-113 83 Stockholm,, Sweden

Abstract: We define a concept of epistemic robustness in the context of an epistemic model of a finite normal game where a player type corresponds to a belief over the profiles of opponent strategies and types. A Cartesian product X of pure strategy subsets is epistemically robust if there is a Cartesian product Y of player type subsets with X as the associated set of best reply profiles such that the set Yi contains all player types that believe with sufficient probability that the others are of types in Y-i and play best replies. This robustness concept provides epistemic foundations for set-valued generalizations of strict Nash equilibrium, applicable also to games without strict Nash equilibria. We relate our concept to closedness under rational behavior and thus to strategic stability and to the best reply property and thus to rationalizability.

Keywords: Epistemic game theory; epistemic robustness; rationalizability; closedness under rational behavior; mutual p-belief

JEL-codes: C72; D83

25 pages, November 1, 2016

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