Zero-sum games with charges

Zero-sum games with charges

We consider two-player zero-sum games with countably infinite action spaces and bounded payoff functions. The players’ strategies are finitely additive probability measures, called charges. Since a strategy profile does not always induce a unique expected payoff, we distinguish two extreme attitudes of players. A player is viewed as pessimistic if he always evaluates the range of possible expec...

A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS

In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...

Perturbed zero - sum games with appli ations

Zero - Sum Games with Vector - Valued Payoffs

In this lecture we formulate and prove the celebrated approachability theorem of Blackwell, which extends von Neumann's minimax theorem to zero-sum games with vector-valued payoffs [1]. (The proof here is based on the presentation in [2]; a similar presentation was given by Foster and Vohra [3].) This theorem is powerful in its own right, but also has significant implications for regret minimiz...

Repeated zero-sum games with budget

When a zero-sum game is played once, a risk-neutral player will want to maximize his expected outcome in that single play. However, if that single play instead only determines how much one player must pay to the other, and the same game must be played again, until either player runs out of money, optimal play may differ. Optimal play may require using different strategies depending on how much ...