Consider a 2-person non-zero sum game with payoff matrix for strategies 4 and B

Question

Consider a 2-person non-zero sum game with payoff matrix for strategies 4 and B M=((2,2) (01) a. Show that the strategies (4,4) and (B, B) are Nash equilibria and ESS (evolutionary stable strategies) 2 pts) b. Find the return functions for Players I and Il when Player I plays strategies 4 and 2 pts) B with probabilities p and 1- probabilities q and 1-q and Player Il plays these strategies with Show that there is a mixed strategy (o.g) where Player I plays strategy4 with probability p* and Player II plays strategy A with probability *. Show that this mixed strategy is a Nash equilibrium but not an ESS. c. (4 pts)

Explanation / Answer

a)

When Player 1 is asked to select a strategy and if he selects strategy A, then B will look for maximum gain and will also go for A to get a value of 2 for each. Similarly if player 2 is asked to select a stretegy and if he selects A then player 1 will also select A for geting maximum gain of 2.

In the same way if one selects strategy B then the other also selects strategy B and vice versa to maximise the profit. It is called as nash equillibrium when both players select the event profitable to them and land in a comman event.

b) By assigning the probabilities to each strategy we get the value of p as 0.8 and q as 0.75.

So the functions can be formulated in the manner.

Player 1

F1 = 2*q + 1*(1-q)

F2 = 1*q + 4*(1-q)

Player 2

F3 = 2*p + 0*(1-p)

F4 = 1*p + 4*(1-p)

0.8 0.2 p (1-p) Player 1 A B Player 2 A (2,2) (0,1) q 0.75 B (1,1) (4,4) (1-q) 0.25

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