4 5 A game Kermit and Miss Piggy are separately deciding whi

4. (5) A game Kermit and Miss Piggy are separately deciding which of two bars to go to, Bar A or Bar B. Miss Piggy would like to go the bar that Kermit goes to. Kermit would like to go to the bar that Miss Piggy does not go to. a) Depict the normal (box) form of the game, where each of the cells gives the payoff of first Kermit and then Miss Piggy. b) Are there pure strategy Nash equilibria of the game? If there are, what are they? If there are not, explain why.

Solution

A pure strategy Nash equilibrium is a strategy is one in which each player uses a pure strategy .  In a pure strategy each player chooses a strategy without randomizing. When a player uses a rule to randomize over the choice of strategy , we say the player is choosing a mized strategy . In this game there is no pure strategy because Piggy\'s strategy to select the bar is dependent on which Bar Kermit would go and similarly the Bar which Kermit chooses to go is dependent on the Bar which Peggy goes . Kermit chooses a bar which Peggy does not go and Peggy chooses a bar which Kermit . This is a game of mixed strategy and therefore pure strategy Nash equilibria of this game does not exist.