2. Consider the following variation to the Rock (R), Paper (P),Scissors (S) game:• Suppose that with probability p player 1 faces a Normal opponent and with probability 1-p, he faces a Simple opponent that will always play P. Player 2 knows whether he is Normal or Simple, but player 1 does not.• The payoffs are pictured in the payoff matrices below:Normal1\2RPSwith probability pSimple1\2RPSRPS0,0-1,11,-11,-10,0-1,11,-1-1,1 0,0P-1,10,01,-1 with probability 1-p.
Suppose p = 1/3, select all pure strategy Bayesian equilibria (there may be more than one):
(Form: 1's strategy; 2's type - 2's strategy)
a) (S; Normal - P, Simple - P)
b) (R; Normal - P, Simple - P)
c) (S; Normal - R, Simple - P)
d) (P; Normal - P, Simple - P)