Ing. Rostislav Horčík, Ph.D.

While there is an increasing number of practical applications of game theory, there are still severe computational limitations of the current models and algorithms used to find approximate optimal strategies. One such limitation is the high computational complexity of finding an equilibrium for games with large or even infinite sets of actions. Moreover, the strategy space in applications often has a complex inner structure, making equilibrium computations even more difficult. The thesis will advance the state-of-the-art theoretical understanding of the structure of equilibria in games with complex strategy spaces, develop novel iterative strategy-generating algorithms for finding approximate solutions, and investigate the computational complexity of equilibrium problems for special classes of games.