On multivariate antagonistic marked point processes

This paper investigates two bivariate “antagonistic” processes in the framework of noncooperative games that find applications in economics, engineering, and warfare. These processes represent two players with entirely opposite interests. Hostile actions, associating with one of the components (such as deliberate sellout of stocks of the opponent), take place at random times having a random effect to various vital areas. A consequence of these actions is material damage (such as financial losses) which is associated with the second component. So, in general, each player has two (dependent) ways of striking, while his opponent can sustain multiple damages (of two kinds and interdependent) until his threshold of endurance is reached. Then, the player is ruined. One of the goals is to predict the ruin time of each player as well as the collateral damage to the loser and winner at the ruin time. Furthermore, it is also of vital interest to relate these random elements to the continuous time parameter processes referred to as time sensitive analysis. We succeed in these goals by arriving at closed form joint functionals of the named elements and processes.