2025/03/17 by Boros, Endre, Gurvich, Vladimir, Makino, Kazuhisa
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Economics and business #Theoretical Economics (econ.TH)
paper · doi:10.48550/arxiv.2503.17387
We consider finite n-person deterministic graphical games and study the existence of pure stationary Nash-equilibrium in such games. We assume that all infinite plays are equivalent and form a unique outcome, while each terminal position is a separate outcome. It is known that for n=2 such a game always has a Nash equilibrium, while that may not be true for n > 2. A game is called \em play-once if each player controls a unique position and \em terminal if any terminal outcome is better than the infinite one for each player. We prove in this paper that play-once games have Nash equilibria. We also show that terminal games have Nash equilibria if they have at most three terminals.