Cooperative Control and Potential Games

Cooperative Benefit and Cost Games under Fairness Concerns

Solution concepts in cooperative games are based on either cost games or benefit games. Although cost games and benefit games are strategically equivalent, that is not the case in general for solution concepts. Motivated by this important observation, a new property called invariance property with respect to benefit/cost allocation is introduced in this paper. Since such a property can be regar...

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...

Cooperative Games

A coalitional (or cooperative) game is a model of interacting decision-makers that focuses on the behavior of groups of players. N denotes the set of players. A coalition is a group of players S ⊂ N . We refer to N as the grand coalition. Every coalition S has a set of available actions AS. An outcome consists of a partition of N (coalition structure) and one action associated with each coaliti...

Cooperative games

Non-Cooperative and Semi-Cooperative Differential Games

In this paper we review some recent results on non-cooperative and semicooperative differential games. For the n-person non-cooperative games in one-space dimension, we consider the Nash equilibrium solutions. When the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic, we show that the weak solution of a corresponding system of hyperbolic conservation laws deter...