Shortest Path Games

Numerous finite games can be played on a directed graph, and the existence of a stationary (positional) equilibrium is always an interesting and challenging question. In shortest path games two players try to find a "shortest" path between two specified vertices of the given graph. However, the two players have their own, distinct ways of measuring distance. We prove the existence of a stationary equilibrium by using multiple potential transformations on the given graph, and arguing with the already known zero-sum case. 

Joint research with K. Elbassioni, V. Gurvich and M. Vyalyi.