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Consider the following payoff matrix of a game with 3 strategies:

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Game Theory

Exam of 27/07/2018

Consider the following payoff matrix of a game with 3 strategies:

A =

a 1 2 0 1 1 3 0 2

where a ∈ R.

Answer to the following questions:

1. Find feasible pure, mixed and pure/mixed Nash equilibria by varying a in the given interval (Hint. For mixed equilibria fea- sibility can be verified by checking that x

1

> 0, x

2

> 0, and x

1

+ x

2

< 1).

2. Verify if the NE are also Evolutionary Stable for some values of a. Motivate theoretically the results.

3. Consider the replicator equation of the game: are the NE of the game also steady states of the replicator equation?

4. Report the flow of the replicator equation in the simplex for three different values of a.

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