### Nash equilibrium

To start with nash equilibrium, let us revise the dominant strategy first.

A dominant strategy is the strategy that remains the same, irrespective of the behavior of its competitor’s. In a 2 x 2 game, either both or single player have a dominant strategy.

Nash equilibrium is a situation in which a player will choose the strategy he can, knowing the competitor’s reaction and does not have any incentive to deviate.

Example

Production decision problem
 Firm B Firm A Produce x Don’t produce Produce x -6,-6 10,10 Don’t produce 10,10 -6,-6

We know, that in nash eqilibriom, one company knows its competitor’s policy and does not deviate from its decision.

1. If Firm A gets to know that firm B is producing a particular commodity X.
2. Firm A will chose “not to produce” as it gives maximum profits
3. Or the Firm B gets to know that firm A is not producing the particular commodity X.
4. Firm B will chose to produce x as it gives maximum profits(10). if it also choses “not to produce” it will have losses.
5. (Don’t produce, produce) or (10,10) is a nash equilibrium situation.( both the firms will not deviate from their decision)
6. There is 1 more nash eqilibrium in the above matrix, ie (10,10)(produce ,don’t produce)

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