On the partial cooperative games (Nonlinear Analysis and Convex Analysis)

Resume 1 Introduction.Considering the cooperative games in extensive form, we suppose that the coalition membership of players does not change during the game.In this paper we propose a model of dynamic conflict process where conflict participants (players) alter their coalition membership during the process evolution.Consider a finite non-cooperative game in extensive form with perfect information $\Gamma=$ $\langle K(X_{0}), P, h\rangle$ , where $K(X_{0})$ is the game tree with the initial point $x_{0},$ $P$ is the player partition $P_{1},$ $P_{2\cdot\cdot nn+1},.,$$P,$ $P$ ( $P_{n+1}$ is the set of endpoints), and $h'$ .$P_{n+1}arrow R_{+}^{n}$ is the terminal payoff function.Basing on $\Gamma$ we introduce a class of partial coopertive games where $\mathrm{p}\mathrm{l}|\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}\mathrm{s}$ use both cooperative and non-cooperative behavior.