The following payoff matrix shows the profits to two firms, A and B, that need to decide whether

Question

to set a high or a low price for identical products produced by both firms:
B’s campaign focused on:
Low High
A’s price:
Low 20, 30
50, 20
High 10, 60
40, 50
(a) Identify the Dominant Strategy Equilibrium for this game, and justify your answer.
(b) Is there an alternative cooperative solution that could offer both firms a higher return than
they achieve at the Dominant Strategy Equilibrium?
(c) What factors might be helpful in allowing the firms to adhere to the cooperative solution?

Answer 1

To analyze the given payoff matrix for firms A and B, we can follow these steps:

(a) Identify the Dominant Strategy Equilibrium

From the given payoff matrix:

| | B's Low Price | B's High Price | |-----------|---------------|----------------| | A's Low Price | (20, 30) | (50, 20) | | A's High Price | (10, 60) | (40, 50) |

We will look for the dominant strategies for both firms.

For Firm A:

• If B chooses Low: A's payoffs are 20 (Low) and 10 (High). A should choose Low since 20 > 10.
• If B chooses High: A's payoffs are 50 (Low) and 40 (High). A should choose Low since 50 > 40.

Thus, Firm A's dominant strategy is Low.

For Firm B:

• If A chooses Low: B's payoffs are 30 (Low) and 20 (High). B should choose Low since 30 > 20.
• If A chooses High: B's payoffs are 60 (Low) and 50 (High). B should choose Low since 60 > 50.

Thus, Firm B's dominant strategy is also Low.

Dominant Strategy Equilibrium: When both firms play their dominant strategies (A chooses Low, B chooses Low), they end up at the payoff (20, 30).

(b) Is there an alternative cooperative solution that could offer both firms a higher return?

The current equilibrium (20, 30) can be compared to other combinations in the matrix:

• (50, 20): If A chooses Low and B chooses High.
• (40, 50): If A chooses High and B chooses High.

Both (50, 20) and (40, 50) offer higher payoffs for Firm A than (20, 30), but (50, 20) is particularly better for A. The alternative cooperation could lead A to choose Low and B to choose High if they can coordinate.

The cooperative solution (if agreed upon) of having A choose Low and B choose High results in (50, 20), which is better for A.

(c) What factors might be helpful in allowing the firms to adhere to the cooperative solution?

Several factors can help firms adhere to the cooperative solution:

1. Communication: If both firms can communicate and negotiate effectively, they can reach an agreement on pricing that benefits both, like A pricing low while B prices high.

2. Trust: A mutual trust built through past interactions can help firms maintain cooperation. Trust would reduce the incentive to defect from the cooperative deal.

3. Repeated Interaction: If this is a repeated game, firms might be more inclined to cooperate, knowing that future actions will be influenced by current decisions. Future payoffs may encourage cooperation to avoid retaliation.

4. Contracts: Formal agreements that outline pricing strategies or revenue sharing might provide a legal basis for cooperation and performance guarantees.

5. Regulatory Environment: If there are industry regulations that encourage cooperative behavior or penalties for cutthroat competition (like price wars), firms may be more likely to adhere to cooperative pricing strategies.

Overall, while the dominant strategy's equilibrium provides a set outcome, cooperative solutions can yield higher returns and require alignment through various facilitating factors.