Attainability in Repeated Games with Vector Payoffs

• 成果类型: Article
• 署名作者: Bauso, Dario; Lehrer, Ehud; Solan, Eilon; Venel, Xavier
• 署名单位: University of Palermo; Tel Aviv University; INSEAD Business School
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0693
• 发表日期: 2015
• 页码: 739-755
• 关键词: robust optimization approach; INVENTORY CONTROL; unknown inputs; approachability; systems; strategies

摘要

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.