Game Theory True, False, Why Questions 1. Say that Ann and Bob are playing a nor

Question

Game Theory

True, False, Why Questions

1. Say that Ann and Bob are playing a normal form game. If we observe that they do not play a Nash equilibrium, then at least one of them is not rational. [10 marks]

2. Ann and Bob are playing a mixed strategy Nash equilibrium of a normal form game. In this equilibrium, Ann is mixing over the strategies s 1 and s 2 . Ann can change her payoff by reducing the probability of playing s 1 and increasing the probability of playing s 2 .

3. Recall that the Backwards Induction procedure can be used in games of perfect information. There are games of perfect information for which Backwards Induction and Subgame Perfect Nash Equilibrium make different predictions.

Explanation / Answer

Ans 1)

Not playing Nash equilibrium strategy is an irrational behaviour because there is no other available strategy with which player can maximise its payoff

Hence True

Ans 2)

True

In Mixed strategy Nash equilibrium we have more than 1 Nash equilibrium that is we choose probability at which expected payoff from all the strategies is equal

Hence he can change its payoff by changing the probability

Ans 3)

True

In Perfect information game no player has any first mover advantage hence outcome remains the same even if backward induction process is used but in case of Subgame perect nash equilibrium there is a possibility of first mover advantage and hence change can be seen in predictions

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