Are there strategies that survive iterated elimination of dominant strategoes?
Yes, there are strategies that survive iterated elimination of dominant strategies (IEDS). The main concept behind IEDS is to eliminate any strategy that is strictly dominated by another strategy in each round of elimination. However, even after applying this elimination process, there can still exist certain strategies that are not strictly dominated.
These non-dominated strategies that survive IEDS are known as "equilibrium strategies" or "rationalizable strategies." These strategies cannot be eliminated since there is no other strategy that strictly dominates them. They represent rational choices for players because there is no better alternative option available.
In simple games, such as the Prisoner's Dilemma or Battle of the Sexes, where strategies can be easily evaluated and compared, there might be no strategies surviving IEDS as all strategies would be eliminated. However, in more complex games, such as extensive-form games or games with imperfect information, there may be equilibrium strategies that survive IEDS.
It is important to note that IEDS is a process that helps in narrowing down the set of feasible strategies, but it does not guarantee the identification of a unique outcome. Game theorists use more sophisticated solution concepts, such as Nash equilibrium, to predict the outcome of a game when multiple equilibrium strategies exist.