Factors Affecting Sustainability of Cooperation
In this note, we will consider how the ability of firms to collude under the grim trigger strategy is altered by these factors:
- market concentration
- difficulty of detection
- extent of consumer lock-in
- asymmetry of payoffs
Market Concentration
The more firms in an industry, the more difficult it is to sustain cooperation.
Consider an industry with N identical firms. The firms can compete or collude. If the firms collude, they evenly divide the monopoly profit (the profit that would be earned if a single firm controlled the market). If a firm wishes to cheat, it can charge a price just slightly below the monopoly price and capture all of the consumers. The punishment after such a deviation is based on the grim trigger strategy -- eternal severe price competition, driving all firms' profits down to zero. Denote the monopoly profit by Π.
| if the firm: | it earns: |
|---|---|
| cooperates | Π/N |
| cheats | Π |
| is being punished | 0 |
As the number of firms rises (N increases), the profit from cheating doesn't change, and neither does the punishment. But, with more firms, each firm is earning less from cooperating, or colluding. So, the more firms in an industry, the more incentive there is to cheat, and the less likely that collusion can be sustained.
Difficulty of Detection
The harder it is to detect cheating, the harder it is to sustain
cooperation.
In general, cooperation requires that the future payoffs from cheating are sufficiently low. For example, in the above market, a firm's present value of profits from cheating is (r is the interest rate):
Π + 0/(1+r) + 0/(1+r)2 + 0/(1+r)3 + ... = Π
Since after cheating, according to the grim trigger strategy, the firm will be punished forever.
However, say that it takes firms two periods to detect cheating. Then, I can "get away" with cheating for two periods, providing for a present value of:
Π + Π /(1+r) + 0/(1+r)2 + 0/(1+r)3 + ... = Π + Π /(1+r)
Obviously, the incentive to cheat is greater.
Extent of Consumer Lock In
The less consumer lock in, the more difficult it is to sustain cooperation.
Consumer lock-in refers to consumers who are unwilling or unable to switch away from a firm even if other firms offer advantageous prices. This can be due to loyalty, high costs of switching products, or other forces. If many consumers are "locked in" to a firm, then even if I cheat, I will not capture those consumers, so the incentive to cheat is small. However, by cheating and lowering its price, the firm is providing a discount to those consumers that are locked in to it, further lowering profitability.
At the extremes, consider an industry with no lock-in, so that every consumer always goes to the lowest price firm, and an industry in which almost every consumer is locked in to some firm, effectively making each firm a monopolist. In the first industry, collusion is quite difficult since, by cheating, a firm captures the entire market share, making the incentive to cheat large. In the second industry, cheating provides little benefit in terms of greater market share, but results in lower prices for the locked-in customers.
Asymmetry of Payoffs
When payoffs are asymmetric, we need to calculate each firm's incentives to cooperate
If the firms are not symmetric, so that some have a better product, more locked-in consumers, lower costs, etc., then the maximum interest rate to sustain cooperation will vary from firm to firm. In order to have cooperation, the actual interest rate has to be lower than every firm's maximum, in order to guarantee that no firm has incentive to cheat.
Effectively, we would need to calculate the range of interest rates required to sustain cooperation for each firm separately and make sure that both conditions are true.