Informationally Robust Equilibria

Informationally Robust Equilibria (IRE) are introduced in Robson (1994) as a refinement of Nash equilibria for e.g. bimatrix games, i.e. mixed extensions of two person finite games. Similar to the concept of perfect equilibria, basically the idea is that an IRE is a limit of some sequence of equilibria of perturbed games. Here, the perturbation has to do with the hypothetical possibility that the action of one the players is revealed to his fellow player before the fellow player has to decide on his own action. Whereas Robson models these perturbations in extensive form and uses subgame perfection to solve these games, we model the perturbations in strategic form, thus remaining in the class of bimatrix games. Moreover, within the perturbations we impose two possible types of tie breaking rules, which leads to the notions optimistic and pessimistic IRE. The paper provides motivation on IRE and its definition. Several properties will be discussed. In particular, we have that IRE is a strict concept, and that IRE components are faces of Nash components. Specific results from potential games and matrix games are obtained. Possibilities to extend the definition of IRE to more-person games are proposed.