Since some Nash equilibria can be considered as irrational, we are interested here in refinements of Nash equilibria, i.e. concepts of solutions associating to each game a subset of Nash equilibria of this game. Considering only finite games with normal form, we first define the most desirable...

In strictly competitive games, equilibrium mixed strategies are invariant to changes in the ultimate prizes. Dixit & Skeath (1999) argue that this seems counter-intuitive. We show that this invariance is robust to dropping the independence axiom, but is removed if we drop the reduction axiom.

In a carrot game for a player, that player must help his opponent in order to get a desired response. In a stick game for a player, that player must hurt his opponent to get a desired response. We show that most all smooth monotonic two player games can be classified as: carrot for both, carrot...