2016/07/12 by Stéphane Le Roux, Arno Pauly
Computer Science · #cs.GT #cs.LO
paper · pdf · doi:10.4204/eptcs.218.3
published as EPTCS 218, 2016, pp. 27-40 · In Proceedings SR 2016, arXiv:1607.02694
arxiv created 2016/07/12 · arxiv updated 2016/07/13
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding class of multi-player multi-outcome games. This generalizes a previous result by Brihaye, De Pril and Schewe. For most of our conditions we provide counterexamples showing that they cannot be dispensed with. Our proofs are generally constructive, that is, provide upper bounds for the memory required, as well as algorithms to compute the relevant winning strategies.