Dynamic Equilibrium with Randomly Arriving Players

There are real strategic situations where nobody knows ex ante how many players there will be in the game at each step. Assuming that entry and exit could be modeled by random processes whose probability laws are common knowledge, we use dynamic programming and piecewise deterministic Markov decision processes to investigate such games. We study these games in discrete and continuous time for both finite and infinite horizon. While existence of dynamic equilibrium in discrete time is proved, our main aim is to develop algorithms. In the general nonlinear case, the equations provided are rather intricate. We develop more explicit algorithms for both discrete and continuous time linear quadratic problems.