A game-theoretic model of pollution control with asymmetric time horizons

In the contribution a problem of pollution control is studied within the game-theoretic framework (Kostyunin et al., 2013; Gromova and Plekhanova, 2015; Shevkoplyas and Kostyunin, 2011). Each player is assumed to have certain equipment whose functioning is related to pollution control. The $i$-th player's equipment may undergo an abrupt failure at time $T_i$. The game lasts until any of the players' equipment breaks down. Thus, the game duration is defined as $T=\min(T_1,\dots, T_n)$, where $T_i$ is the time instant at which the $i$-th player stops the game.
We assume that the time instant of the $i$-th equipment failure is described by the Weibull distribution. According to Weibull distribution form parameter, we consider different scenarios of equipment exploitation, where each of player can be in “an infant”, “an adult” or “an aged” stage. The cooperative 2-player game with different scenarios is studied.