Question

find any dominant strategies and any nash equilibrium

Player 2 X Y 3, 3 0, 5 Player 1 5, 0 1, 1 B

Answer 1

A dominant strategy of a player is the strategy that always makes the player better off, no matter what his opponent chooses.

In the given game, when player 2 plays X, it is best for player 1 to choose B because payoff 5 from choosing B is greater than payoff 3 from choosing A. And if, player 2 plays Y, then it will be the best for player 1 to choose B, because 1 from choosing B is greater than 0 from choosing A.

So it can be seen that, no matter what player 2 plays, player 1 is always better off by choosing B. So 'B' is player 1's dominant strategy.

Now for player 2, when player 1 plays A, player 2 will be better off by choosing Y (because 5>3) and when player 1 plays B, player 2 again will be better off by playing Y (because 1 > 0). So, 'Y' is Player 2's dominant strategy.

Therefore, the Nash equilibrium is (B,Y) : (1,1).