Reciprocity and Trust

Essential Questions

• What do trust games teach us about reciprocity?
• How do reciprocity and trust change optimal contracts?
• How can institutions cultivate trust to improve outcomes?

Overview

Picture a supply-chain partnership. A manufacturer must decide whether to invest in quality before a retailer commits to future orders. Contracts cannot specify every detail, so trust matters. Behavioral game theory studies reciprocity—the tendency to reward kindness and punish betrayal—even when it is costly.

This lesson explores trust games, summarizes empirical findings on reciprocity, and shows how relational contracts and reputation sustain cooperation.

The Trust Game

In the trust game, Player A (investor) receives $10$ and can send any amount $x$ to Player B (trustee). The amount sent is tripled. Player B then chooses how much to return. Standard theory predicts A sends $0$ because B has incentives to keep everything. Experiments prove otherwise: average transfers are over half the endowment, and B typically returns a fair share. Reciprocity emerges because B rewards trust, and A anticipates it.

Modeling Reciprocity

Economists capture reciprocity by augmenting utility with kindness terms. Rabin's fairness equilibrium model defines a "kindness" function $\kappa_i(a_j)$ measuring how player $i$ perceives player $j$'s action relative to a fair reference. Player $i$'s utility becomes $U_i = u_i(a_i, a_j) + \theta_i \kappa_i(a_j) \kappa_j(a_i)$, where $\theta_i$ measures reciprocity strength. Positive $\theta$ implies mutual kindness yields extra utility, sustaining cooperative outcomes.

In incomplete contracts, relational models assume future interactions and reputation. Suppose effort $e$ increases joint surplus $S(e)$ but is costly to the agent. The principal promises a discretionary bonus $b$ if effort appears high. If trust is broken, future cooperation ends, giving both parties incentives to reciprocate. The trigger strategy payoff is $\frac{S(e) - w - c(e)}{1 - \delta}$, where $\delta$ is the continuation probability. Cooperation holds if the present gain from cheating is less than the discounted future loss.

Institutions of Trust

Microfinance relies on group lending, where peers monitor each other. Reciprocity ensures timely repayment. Online platforms use ratings to build trust. Public policy invests in legal infrastructure and anti-corruption measures to reduce the cost of trusting strangers.

Designers can signal trustworthiness through transparency, warranties, and shared governance. Understanding reciprocity helps you predict when economic relationships thrive on goodwill and when formal enforcement is required.

Further Reading

• Berg, Dickhaut, and McCabe Trust Game
• Rabin's Incorporating Fairness into Game Theory
• Gibbons and Henderson on Relational Contracts