Question

4. [20] Answer the following. (a) [4] Explain the difference between a strategy that is a best response versus a strategy that is strictly dominant. (b) (6) Consider the following game: player 2 D E F G A 3,7 7,3 1,2 4,3 player 1 B 89 8,5 2,8 5,2 C | 0.10 | 7.0 | 1.9 | 2.2 Find the strictly dominant strategies solution and the iterated elimination of strictly dominated strategies solution, if any. (c) [10] Consider the following game: player 2 L C R T İ 10,4 | 1,2 1,0 player 1 M 6,4 2,0 3,0 B 9,0 3,3 4,8 Find all the Nash equilibria (including mixed strategy ones).

Answer 1

Ans (a) In game theory the best response is the strategy which produces the most favorable outcome of a player, taking other player's strategies given. It is not dominated. And every dominated strategy is never a best response to any belief and that if a strategy is never a best response it is dominated. There can be a game without having dominant strategy but without best response there can not be any game, according to game theory.

Ans (b) while calculating the dominant strategy in the game we have to see the payoffs of the players I.e for player 1 we will see the payoffs horizontally and for player 2 we will see the payoffs vertically and then marks the maximum payoff from the table. When we see the each player payoffs the B,E will be the dominant strategy (8,5) .

Ans (c) As we have seen the above how we calculated the dominant strategy in the same way we will calculate the Nash equilibrium of the game in the above table T,L (10,4) is the Nash equilibrium strategy.