Econ 618 Rationalizable Sets, Iterated Elimination of Strictly Dominated Strategies (IESDS)

NE as a prediction for the outcome of a game requires that each player (1) know the equilibrium of the game and (2) correctly expects it to be played. Then and then only, will each player have no incentive to unilaterally deviate from his equilibrium strategy as he expects his rivals to play their equilibrium strategies. The two assumptions are sensible if a game has been played a number of times and a specific steady state of the game observed. Thus a NE equilibrium is a plausible prediction of the outcome of a game if the last statement is true, but in general not if such conditions are not satisfied (as in one shot games with players choosing actions simultaneously). Recall from previous discussions that even if each player knows the equilibria of a game, a problem of coordinating on one arises if there are multiple equilibria. Similarly, the issue of mistakes arise if an equilibrium is not strict. An area of game theory explores how far can we move towards predicting an outcome of a game assuming only that (1) strategy spaces and payoffs are common knowledge and (2) each player is rational and rationality of all players is common knowledge. A belief of player i about his opponents is a probability distribution σ−i on A−i, his rivals’ pure strategy space. A player is rational if he uses only those strategies (pure or mixed) in his strategy space which are BR to some belief σ−i about A−i. Define as level 1 knowledge of rationality, ”each player i thinks that each player j is rational”.