On the Equilibria of Alternating Move Games [chapter]

Aaron Roth, Maria Florina Balcan, Adam Kalai, Yishay Mansour
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
We consider computational aspects of alternating move games, repeated games in which players take actions at alternating time steps rather than playing simultaneously. We show that alternating move games are more tractable than simultaneous move games: we give an FPTAS for computing an -approximate equilibrium of an alternating move game with any number of players. In contrast, it is known that for k ≥ 3 players, there is no FPTAS for computing Nash equilibria of simultaneous move repeated
more » ... unless P = P P AD. We also consider equilibria in memoryless strategies, which are guaranteed to exist in two player games. We show that for the special case of k = 2 players, all but a negligible fraction of games admit an equilibrium in pure memoryless strategies that can be found in polynomial time. Moreover, we give a PTAS to compute anapproximate equilibrium in pure memoryless strategies in any 2 player game that admits an exact equilibrium in pure memoryless strategies. 1 In section 5 we consider the special case of games with k = 2 players 805
doi:10.1137/1.9781611973075.66 dblp:conf/soda/RothBKM10 fatcat:z4nobnq4zfey7os27w3pejn6i4