Consider the rock-paper-scissors game shown below. Let us assume that the initial belief of each player is (0.5,0.25,0.25) for the other players two pure strategies. Show how the players actions change as they engage in fictitious play of the rock-paper-scissors game. Please draw a table showing the round of play, each players action and each players belief. Does the empirical distribution of the players joint actions converge to any Nash equilibria of the game? If so, which one? Please show your steps.

Rock Paper Scissors Rock 0,0 -1,1 1,-1 Paper 1-1 0,0 -1,1 Scissors -1,1 1,-1 0,0