In 2014, ?the Bridgestone tire corporation admitted guilt in a U.S. ?Department of Justice price-fixing case that involved 26 ?suppliers of auto parts including Toyo Tires. Bridgestone, Toyo Tires, and other auto parts suppliers colluded in order to charge higher prices, and thus earn higher profits. Bridgestone alone was fined $425 ?million for their part in the price-fixing conspiracy. Consider the following payoff table Consider the accompanying payoff table.
\table[[,\table[[Bhyestone charges high prices],[(conspires)]],\table[[Bridgestone],[charges low prices],[(defects)]]],[\table[[Toyo],[charges high prices],[(conspires)]],\table[[Toyo receives],[$15 ?billion profit],[Bridgestone receives],[$15 ?billion profit]],\table[[Toyo receives],[$10 ?billion profit],[Bridgestone receives],[$18 ?billion profit]]],[\table[[Toyo],[charges low prices],[(defects)]],\table[[Toyo receives],[$18 ?billion profit],[Bridgestone receives],[$10 ?billion profit]],\table[[Toyo receives],[$12 ?billion profit],[Bridgestone receives],[$12 ?billion profit]]]]
a. ?If Bridgestone and Toyo were going to conspire to set prices for one period only, the Nash equilibrium for this game would be that Bridgestone and Toyo
b. ?The best way for Bridgestone and Toyo to ensure cooperation is to play game, following a
The correct answer and explanation is:
To answer the given questions:
Part a: Nash Equilibrium for One Period
If Bridgestone and Toyo are playing this pricing game for one period only, they face a classic Prisoner’s Dilemma scenario.
Payoff Table (for clarity):
| Toyo: High Prices (Conspires) | Toyo: Low Prices (Defects) | |
|---|---|---|
| Bridgestone: High Prices (Conspires) | Toyo: $15B, Bridgestone: $15B | Toyo: $18B, Bridgestone: $10B |
| Bridgestone: Low Prices (Defects) | Toyo: $10B, Bridgestone: $18B | Toyo: $12B, Bridgestone: $12B |
- If both companies conspire and set high prices, they each earn $15 billion.
- If one defects (low prices) while the other conspires (high prices), the defector earns $18 billion, and the other earns $10 billion.
- If both defect (low prices), they each earn $12 billion.
In a one-period game:
- Defection dominates for both companies, as it yields a higher payoff regardless of the opponent’s action:
- If Toyo charges high prices, Bridgestone earns $18 billion by defecting versus $15 billion by cooperating.
- If Toyo charges low prices, Bridgestone earns $12 billion by defecting versus $10 billion by cooperating.
The same logic applies to Toyo. Thus, the Nash equilibrium for a one-period game is for both companies to defect (charge low prices). They each earn $12 billion in this scenario.
Part b: Ensuring Cooperation
The best way for Bridgestone and Toyo to ensure cooperation is to play this game repeatedly, engaging in a repeated or infinitely repeated game framework. This scenario introduces the possibility of punishment strategies, such as trigger strategies or tit-for-tat, which encourage cooperation over time.
- Repeated Games and Payoff Optimization:
- In a repeated setting, the companies weigh short-term gains from defection against long-term losses if cooperation breaks down.
- Cooperation is sustainable if both parties value future profits highly (i.e., they have a high discount factor, reflecting patience and foresight).
- Trigger Strategy:
- A common strategy is for both firms to conspire (set high prices) initially.
- If one defects, the other punishes by charging low prices forever.
- This threat discourages defection, as the long-term loss outweighs the one-time gain.
- Tit-for-Tat:
- Each company mimics the other’s previous action.
- If one defects, the other defects in the next period. If both cooperate, they continue earning the higher payoff.
- Monitoring and Trust:
- Agreements to share market intelligence or self-monitor can also foster trust, ensuring that both firms adhere to high prices.
In summary, repeated interactions with credible threats of punishment (such as trigger or tit-for-tat strategies) are key to sustaining cooperation, allowing both firms to maximize long-term profits ($15 billion each per period). This cooperative behavior aligns their incentives and mitigates the temptation to defect.