For any game, trembling hand perfect equilibria are a subset of sequential equilibria. What is a simple example where a sequential equilibrium is not a trembling hand perfect equilibrium? Is it possible to create a normal form example? Solution Yes. In a normal form game, every Nash equilibrium is also a sequential equilibrium. But not every Nash equilibrium is trembling hand perfect. Consider the game in which each of two players has two strategies, A and B. Both players get payoff 0 except in one case: they achieve positive payoffs if they both choose A. Then (A,A) and (B,B) are two Nash equilibria of this game. Both are therefore also sequential equilibria. However, (B,B) is not trembling hand perfect. If there is even the smallest tremble in player 2\'s choice, player 1 has a strict preference for A. Only (A,A) is trembling hand perfect. The generalization of this is that Nash equilibria in which some players play weakly dominated strategies are not trembling hand perfect..

1. For any game, trembling hand perfect equilibria are a subset of sequential equilibria. What is a
simple example where a sequential equilibrium is not a trembling hand perfect equilibrium? Is it
possible to create a normal form example?
Solution
Yes. In a normal form game, every Nash equilibrium is also a sequential equilibrium. But not
every Nash equilibrium is trembling hand perfect. Consider the game in which each of two
players has two strategies, A and B. Both players get payoff 0 except in one case: they achieve
positive payoffs if they both choose A. Then (A,A) and (B,B) are two Nash equilibria of this
game. Both are therefore also sequential equilibria. However, (B,B) is not trembling hand
perfect. If there is even the smallest tremble in player 2's choice, player 1 has a strict preference
for A. Only (A,A) is trembling hand perfect. The generalization of this is that Nash equilibria in
which some players play weakly dominated strategies are not trembling hand perfect.