Layers of noncooperative games

We model and analyze classes of antagonistic stochastic games of two players. The actions of the players are formalized by marked point processes recording the cumulative damage to the players at any moment of time. The processes evolve until one of the processes crosses its fixed preassigned threshold of tolerance. Once the threshold is reached or exceeded at some point of the time (exit time), the associated player is ruined. Both stochastic processes are being “observed” by a third party point stochastic process, over which the information regarding the status of both players is obtained. We succeed in these goals by arriving at closed form joint functionals of the named elements and processes. Furthermore, we also look into the game more closely by introducing an intermediate threshold (see a layer), which a losing player is to cross prior to his ruin, in order to analyze the game more scrupulously and see what makes the player lose the game.