Question

Game Theory: State whether it is true or false. If it is false, provide a counter-example:

In every dominance solvable game, every player is better off when players play the rationalizable action profile, than if they play any other action profile.

Answer 1

Solution:

The given statement is True.

A rationalizable action is the one which a person will take at least once given other players strategies. In other words, if there exists a strategy for a player which shall never be chosen as the best response action under any scenario (as in under any possibile strategy profile of other players).

When we talk of a dominance solvable game, in case of strict dominance, that is every player has a strict dominant strategy to play, that is a strategy which will be chosen every time for whatever the other player plays. Hence, that would be the only strategy left as the rationalizable action, and thus, playing this will result in an equilibrium where each player is playing the best and have no incentive to deviate.