# Firm 2 LOW HIGH Firm 1 LOW \$40

 Firm 2 LOW HIGH Firm 1 LOW \$40,000     \$40,000 \$80,000     \$10,000 HIGH \$10,000     \$80,000 \$70,000     \$70,000

1) What is the pure strategy Nash equilibrium (outcome) of thegame?

2)Is the NE unique? If not, suggest a possible remedy to resolvethe redundancy.

In the above problem, let us think that firm-1 starts with thestrategy Low. Given firm-1’s strategy, firm-2 will select thestrategy Low as it gives him a higher pay off than the strategyHigh. Firm-1 will also stick to that strategy as deviating fromthat strategy to High will give him a lower pay off. So (40,00040,000) is a nash equilibrium of the game.

Again, if Firm-1 chooses the strategy High. Given his strategy,Firm-2 will choose the strategy Low since it gives him a higher payoff than the other strategy. Again, Firm-1 will deviate from thestrategy High to the strategy Low, which gives him a higher payoff. Thus Firm – 1 will move vertically upward to the strategy Low.Given Firm-1 chooses Low, Firm-2 will also choose low, sincedeviating from that strategy will give him a lower payoff.

Thus, both the Firms will choose the strategy Low with the payoff (40,000 40,000) finally, after starting from any of thestrategies.

Thus (40,000 40,000) is the only Nash Equilibrium of the gameand thus the Nash Equilibrium is unique.

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