Repeated Games and Credible Commitments

When firms interact repeatedly, today's action changes expectations and future payoffs. Cooperation that is unstable in a one-shot game may become sustainable if a short-term deviation triggers sufficiently costly future responses.

Let mutual cooperation pay $R$ each period, one-time deviation pay $T$, and punishment pay $P$ thereafter. With discount factor $\delta$, cooperation under a grim-trigger strategy requires

A larger $\delta$ means firms value future profit more, making discipline easier.

What supports repeated cooperation?

Frequent interaction, transparent actions, stable membership, and an uncertain ending make deviations easier to detect and future losses more important. Demand shocks, noisy data, hidden discounts, and likely market exit make punishment harder to target and can trigger mistaken retaliation.

Repeated cooperation is not automatically desirable. It may support quality and trust between trading partners, or sustain anticompetitive high prices. Welfare and legality depend on what behavior is being supported.

Credible threats and promises

A threat is credible if carrying it out is optimal when the threatened decision point arrives, or if a prior commitment makes execution unavoidable. A firm may announce ruinous price cuts against entry, but after entry occurs it may prefer accommodation. A rational entrant anticipates that reversal.

Contracts, deposits, reputation, capacity choices, organizational rules, and irreversible investments can create commitment. They can improve trust, but can also deter competition or lock parties into harmful actions. Evaluate whether commitment changes incentives, whether it can be observed and enforced, and whether it is legal.

In a known finite game, backward induction can unravel cooperation from the final period. Real relationships may avoid this result when endings are uncertain, players change, behavior is noisy, or reputation affects other interactions.

Solve the cooperation threshold

Suppose cooperation pays 8 each period, deviation pays 12 now, and punishment pays 4 forever after. Cooperation is worth $8/(1-\delta)$. Deviation is worth $12+4\delta/(1-\delta)$. Requiring cooperation to be at least as valuable gives $\delta\ge0.5$.

At $\delta=0.3$, future punishment is too weak. At 0.8, losing future cooperation is costly enough to discourage the one-time gain. The threshold changes when detection is imperfect, punishment lasts only a few periods, or players make mistakes.

Test credibility at the future node

A firm may threaten a below-cost price war against entry. Once entry occurs, however, accommodation may be more profitable. Without an irreversible commitment, the threat is not credible because the firm will want to reverse it later.

Capacity investment, contracts, deposits, or reputation can alter future incentives, but a commitment is not valuable merely because it is irreversible. It can lock a firm into a costly mistake or harm competition. Ask whether the mechanism is observable, enforceable, worthwhile when activated, and legal.