Response Dynamics, Nash Equilibria and Random Games

Pure Nash equilibria are foundational to the field of game theory. We use a "random games" approach to understand both how likely Nash equilibria are to exist, and also how effective various iterative procedures are at locating them. We address games with many players that can each choose from two actions (and introduce a novel connection between game theory and percolation theory), and games with two players that can choose from many actions. We also allow for ties in the scores that players can earn in these games, which yields many different game behaviours.