Making the Best of Limited Memory in Multi-Player Discounted Sum Games

Anshul Gupta
(University of Liverpool)
Sven Schewe
(University of Liverpool)
Dominik Wojtczak
(University of Liverpool)

In this paper, we establish the existence of optimal bounded memory strategy profiles in multi-player discounted sum games. We introduce a non-deterministic approach to compute optimal strategy profiles with bounded memory. Our approach can be used to obtain optimal rewards in a setting where a powerful player selects the strategies of all players for Nash and leader equilibria, where in leader equilibria the Nash condition is waived for the strategy of this powerful player. The resulting strategy profiles are optimal for this player among all strategy profiles that respect the given memory bound, and the related decision problem is NP-complete. We also provide simple examples, which show that having more memory will improve the optimal strategy profile, and that sufficient memory to obtain optimal strategy profiles cannot be inferred from the structure of the game.

In Javier Esparza and Enrico Tronci: Proceedings Sixth International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2015), Genoa, Italy, 21-22nd September 2015, Electronic Proceedings in Theoretical Computer Science 193, pp. 16–30.
Published: 23rd September 2015.

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