91影视

• When Firm 1 chooses to go for the low end of the market, Firm 2 will get a higher profit by choosing the high end of the market (600 > -30).
• Further, if Firm 1 chooses to go for the high end of the market, Firm 2 will get a higher profit by choosing the low end of the market (800 > 50).

Thus, Firm 2 does not have a dominant strategy that exists regardless of Firm 1鈥檚 decision.

• Similarly, when Firm 2 chooses to go for the low end of the market, Firm 1 will get a higher profit by choosing the high end of the market (100 > -20).
• If Firm 2 chooses to go for the high end of the market, Firm 1 will get a higher profit by choosing the low end of the market (900 > 50).

Thus, even Firm 1 does not have a dominant strategy regardless of Firm 2鈥檚 decision.

As neither of the firms has a dominant strategy, a pure-strategy Nash equilibrium is absent.

However, mixed-strategy Nash equilibria exist at two points in the market:

• When Firm 1 chooses to Low, and Firm 2 chooses High.
• When Firm 1 chooses High, and Firm 2 chooses Low.

Neither of the firms has an incentive to deviate from these points as they can earn comparatively higher payoffs by adopting these strategies.

Thus, there are two mixed-strategy Nash equilibria at the points (Low, High) and (High, Low).

If both firms are conservative and each follows a maximin strategy, the payoff will be as follows:

• The lowest payoff that Firm 1 will receive on choosing Low is -20, and the lowest payoff on choosing High is 50. To minimize losses, Firm 1 will choose High.
• Similarly, the lowest payoff that Firm 2 receives on choosing Low is -30, and the lowest payoff on choosing High is 50. Firm 2 will also choose High to minimize losses.

Thus, using a conservative maximin strategy, both firms choose High and obtain profits worth 50 each.

If the firms opt for a cooperative outcome, they will decide to maximize the total profit earned by both firms; that is, they will be concerned with joint payoff maximization.

The total payoff earned when Firm 1 opts for Low, and Firm 2 opts for High is: \({\rm{900 + 600 = 1500}}\).

The total payoff earned when Firm 1 opts for High, and Firm 2 opts for Low is: \({\rm{100 + 800 = 900}}\).

Thus, the cooperative outcome will be for Firm 1 to choose Low and Firm 2 to choose High as the joint payoff will be maximum for that outcome.

When the firms opt for the cooperative outcome, Firm 1 benefits the most from it.

Had Firm 1 chosen High and Firm 2 chosen Low, Firm 1 would have gained 100, whereas Firm 2 would have gained 800.

However, when the firms choose the cooperative outcome, Firm 1 gains 900 (900>100), and Firm 2 gains 600 (600<800).

Thus, Firm 1 benefits from the cooperative outcome, whereas Firm 2 is at a comparative disadvantage.

As Firm 1 benefits from the cooperative outcome, it must offer Firm 2 some of its yields to persuade it to collude. Firm 2 loses profit worth 200\(\left( {{\rm{800 - 600 = 200}}} \right)\).

Thus, Firm 1 must atleast provide 200 units of its profit to Firm 2.

Firm 1 gains profit worth 800 \(\left( {{\rm{900 - 100 = 800}}} \right)\).

Thus, Firm 2 might not be happy with just 200 additional yields and will try to obtain the maximum possible gains of Firm 1 to enter into the collaboration.