## 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.

Original language | English |
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Pages (from-to) | 739-755 |

Number of pages | 17 |

Journal | Mathematics of Operations Research |

Volume | 40 |

Issue number | 3 |

DOIs | |

State | Published - 1 Aug 2015 |

## Keywords

- Approachability
- Attainability
- Continuous time
- Dynamic games
- Repeated games
- Vector payoffs