The game rock paper scissors is a simultaneous move game each player chooses either rock, paper, or

The game rock paper scissors is a simultaneous move game each player chooses either rock, paper, or scissors. If they pick the same thing, it is a tie (payo zero for both players). If they pick dierent options, rock beats scissors, paper beats rock, and scissors beats paper. Let the payo from winning be 1 and the payo from losing be -1.(a) Write the game’s normal form (i.e. the usual grid of payos). Whatare the pure and mixed strategy Nash equilibria of this game? Whatis each player’s expected payo?(b) What are the pure and mixed strategy Nash equilibria of this game?(c) What is each player’s expected payo?