We propose a mechanism of interactions between agents that are dynamically connected. The agents play two-person symmetric game. The payoff from each encounter depends on the payoff matrix and on the weights of connections between players. In our model the weights are dynamical variables. Their evolution depends on the difference of the agent payoffs from the considered type of encounters and their average payoff. We construct two models: one, in which the agents are placed on network, and a mean field model with continuous population of players. Symmetric and asymmetric weights are considered. Solutions of the resulting systems of differential equations and numerical simulations are discussed. Structure of equilibrium states of the systems and their stability are investigated. In particular we show that starting from the Prisoner's Dilemma game we get long run coexistence of both strategies.

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