Michael Ummels wrote:The last decades have seen an immense amount of research on the algorithmic content of game theory. On the one hand, a new subject called algorithmic game theory has emerged that is concerned with the study of the algorithmic theory of finite games with multiple players. On the other hand, infinite and, in particular, stochastic two-player zero-sum games have become an important tool for the verification of open systems, which interact with their environment.

The aim of this work is to bring together algorithmic game theory with the games that are used in verification by extending the algorithmic theory of stochastic two-player zero-sum games to incorporate multiple players, whose objectives are not necessarily conflicting. In particular, this work contains a comprehensive study of the complexity of the most prominent solution concepts that are applicable in this setting, namely Nash and subgame-perfect equilibria.