True or False: In any Nash equilibrium, if a player is paying two (or more) strategies...

True or False: In any Nash equilibrium, if a player is paying two (or more) strategies with positive probability, then she is indifferent between any of those strategies. (provide examples)

Expert Solution

Answer to the question:

The statement is true.

For example

A mixed strategy is a probability distribution over the set of actions.

The police chooses to set up checkpoints with probability 1/3

What should you do?

If you drink cola you get 0

◮ If you drink wine you get −2 with prob. 1/3 and 1 with prob. 2/3 ⋆

What is the value of this to you? ⋆

We assume the value is the expected payoff: 1/ 3 × (−2) + 2 /3 × 1 = 0

◮ You are indifferent between Wine and Cola

◮ You are also indifferent between drinking Wine and Cola with any probability

Rahul Sunny answered 2 years ago

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