Question

Question 1. н E F TOT 9 G 2 4. | 2 | 3 | 6 a.) Define a pure-strategy Nash equilibrium both mathematically and in words. b.) Find all pure-strategy Nash equilibria of the above game. c.) Find all strict Nash equilibria of the above game.

Answer 1

a>A strategy profile s ∈ S is a pure Nash equilibrium if ∀t and ∀si ∈ St, / Ut(st, s−t) ≥ Ut(st, s−t).

In simple  terms, a pure Nash equilibrium is a strategy profile in which there is no reason for players to deviate, given that all other players don’t deviate. Both play their mutual best response in response to each other.

blage 2 A 1,029) 3,2 3;'s player1 B 9,2 8,6 4,0 16. c3, 767/2, 16,8 D/2,4 |-336, 25, I Au Nash equilibrium pure - Strategy is (A,F) AU equilibrium Strict - Strategy Nash (AF) for player I if he plays a player 2 plays & player 2 would not cleant to deviate from f. (gets less pay off thang) for players 2, if he blays fi player I plays A not want to deviates) (get less pay off thang) attatet y 8, 6053 Thus, by playing (A,F) both players plays their mutual best response given other blays best response e also