We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called attainable by a player if there is a positive integer such that the player can guarantee that in all finite game longer than that integer, the distance between the set and the cumulative payoff is arbitrarily small, regardless of the strategy Player 2 is using. We provide a necessary and sufficient condition for the attainability of a convex set, using the concept of B-sets. We then particularize the condition to the case in which the set is a singleton, and provide some equivalent conditions. We finally characterize when all vectors are attainable.

Attainability in repeated games with vector payoffs / Bauso, D; Lehrer, E; Solan, S; Venel, X. - In: MATHEMATICS OF OPERATIONS RESEARCH. - ISSN 0364-765X. - 40:3(2015), pp. 739-755. [10.1287/moor.2014.0693]

Attainability in repeated games with vector payoffs

Venel X
2015

Abstract

We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called attainable by a player if there is a positive integer such that the player can guarantee that in all finite game longer than that integer, the distance between the set and the cumulative payoff is arbitrarily small, regardless of the strategy Player 2 is using. We provide a necessary and sufficient condition for the attainability of a convex set, using the concept of B-sets. We then particularize the condition to the case in which the set is a singleton, and provide some equivalent conditions. We finally characterize when all vectors are attainable.
attainability, continuous time, repeated games, Vector payoffs, dynamic games, approachability
Attainability in repeated games with vector payoffs / Bauso, D; Lehrer, E; Solan, S; Venel, X. - In: MATHEMATICS OF OPERATIONS RESEARCH. - ISSN 0364-765X. - 40:3(2015), pp. 739-755. [10.1287/moor.2014.0693]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/197465
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