Relationship to Rationality Is Common Knowledge
Relationship to Rationality Is Common Knowledge To explore the relationship between those strategies which survive the itera- tive deletion of strictly dominated strategies (IDSDS) and Nash equilibria, let’s start with an example. Consider a Nash equilibrium for a three-player game in which player 1 uses strategy x, player 2 uses strategy y, and player 3 uses strat- egy z. Do these strategies survive the IDSDS? It’s pretty easy to argue that none are eliminated on the first round: Since x is a best reply against player 2’s using y and player 3’s using z, x is most definitely not strictly dominated. Analogously, since y is a best reply for player 2 when player 1 uses x and player 3 uses z, y is not strictly dominated. Finally, since z is a best reply for player 3 when players 1 and 2 use x and y, respectively, z is not strictly dominated. Thus, x, y, and z are not eliminated in the first round of the IDSDS.