Attainability in Repeated Games with Vector Payoffs

Details Attainability in Repeated Games with Vector Payoffs Attainability in Repeated Games with Vector Payoffs

2012-01-29

arxiv.org/abs/1201.6054v2

Mathematics

Optimization and Control

28 pages, 2 figures, conference version at NetGCoop 2011

Scientific paper

We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called {\em attainable} if player 1 can ensure that there is a finite horizon $T$ such that after time $T$ the distance between the set and the cumulative payoff is arbitrarily small, regardless of what strategy player 2 is using. This paper focuses on the case where the attainable set consists of one payoff vector. In this case the vector is called an attainable vector. We study properties of the set of attainable vectors, and characterize when a specific vector is attainable and when every vector is attainable.

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