Finding Pure Bayes Nash Equilibria of the Game

Question

Suppose players 1 and 2 have to jointly decide whether to go to a BC Lions (L) or Canucks (C) game.

Table 1:

a) What are the Nash equilibria of this game (pure and mixed)?

b) Let’s turn this game into a Bayesian game. Now let’s assume that player 2 might be a friend or a foe to player 1. If player 2 is a friend he has exactly the same payoff as in item (a). If he is a foe, then he does not like to be together with player 1!. So player 2 gets a payoff of 4 if he goes to a Canucks game alone, a payoff of 1 if he goes to a BC Lions game alone, and a payoff of zero if he ends up in the same place as player 1. Player 2 is either a friend or foe with probability 12.

Player 1 is always a friend, and so has payoffs identical to the one presented in item (a). Formally describe the Bayesian game described (present all the elements that constitute a Bayesian Game).

c) What are the pure Bayes-Nash equilibria of this game?

Summary

This question belongs to game theory of economics and discusses about nash equilibria and Bayesian game.

Word count: Answer is in image format