Consider a game in which, simultaneously, player 1 selects a number x ∈ [0, 6] and player 2 selects a number y ∈ [0, 6]. The payoffs are given by

(a) Calculate each player's best-response function as a function of the opposing player's pure strategy.

(b) Find and report the Nash equilibrium of the game.

(c) Suppose that there is no social institution to coordinate the players on an equilibrium. Suppose that each player knows that the other player is rational, but this is not common knowledge. What is the largest set of strategies for player 1 that is consistent with this assumption?