2022/02/23 by Endre Boros, Boros, Endre, Paolo Giulio Franciosa +4
Decision Sciences · Economics, Econometrics and Finance · #Computer Science and Game Theory (cs.GT) #Economic theories and models #FOS: Computer and information sciences #G.2.2 #Game Theory and Applications #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.2202.11554
openalex publication_date 2022/02/23 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We prove that a deterministic n-person shortest path game has a Nash equlibrium in pure and stationary strategies if it is edge-symmetric (that is (u,v) is a move whenever (v,u) is, apart from moves entering terminal vertices) and the length of every move is positive for each player. Both conditions are essential, though it remains an open problem whether there exists a NE-free 2-person non-edge-symmetric game with positive lengths. We provide examples for NE-free 2-person edge-symmetric games that are not positive. We also consider the special case of terminal games (shortest path games in which only terminal moves have nonzero length, possibly negative) and prove that edge-symmetric n-person terminal games always have Nash equilibria in pure and stationary strategies. Furthermore, we prove that an edge-symmetric 2-person terminal game has a uniform (subgame perfect) Nash equilibrium, provided any infinite play is worse than any of the terminals for both players.