The Evolution of Trust under Institutional Moral Hazard

TL;DR

The paper analyzes how a for-profit reputation platform shapes trust and market participation in a sequential trust game with moral hazard. By embedding payoff-biased imitation of seller types in an evolutionary framework and allowing the platform to choose reputation accuracy at a cost (or endogenize commissions), it demonstrates a unique interior equilibrium with coexisting good and bad sellers and reveals a robust incentive for rating inflation when signaling is inexpensive. However, higher accuracy is valuable for social welfare, and when commissions are controllable,profit-maximization can still align with accuracy under certain conditions. The work thus clarifies the tension between platform incentives and social utility in online marketplaces and provides a formal mechanism for rating distortion bounded by market participation. $\xi^{*}=\frac{1-\beta}{r(1-\alpha)+(1-\beta)}$ captures how signal accuracy shapes the equilibrium composition of sellers and market activity.

Abstract

We study the behavior of for-profit institutions that broadcast reputations to foster trust among market participants. We develop a theoretical model in which buyers and sellers are matched on a platform to engage in transactions involving a moral hazard: sellers can either faithfully deliver goods after receiving payment, or not. Although the buyer does not know a seller's true type, the platform maintains a reputation system that probabilistically assigns binary reputation signals. Buyers make purchase decisions based on reputation signals, which influence the payoffs to sellers who then adapt their type over time. These market dynamics ultimately shape the platform's profit from commissions on sales. Our analysis reveals that platforms inherently have an incentive for rating inflation, driven by the desire to increase commission. This introduces a second layer of moral hazard: the platform's incentive to distort reputations for its own profit. Such distortion is self-limited by the platform's need to maintain enough accuracy that trustworthy sellers remain in the market, without which rational buyers would refrain from purchases altogether. Nonetheless, the optimal strategy for the platform can be to invest in order to reduce signal accuracy. When the platform can freely set commission fees, however, maximum profit may be achieved by costly investment in an accurate reputation system. These findings highlight the intricate tensions between platform incentives and resulting social utility for marketplace participants.

Figures (11)

• Figure 1: An extensive-form trust game between buyer and seller, with incomplete information. Nature assigns the seller type and the reputation signal, and the buyer makes a purchase decision without observing the seller's true type. The dashed lines represent the buyer’s information sets, indicating that the buyer cannot distinguish the true type given a reputation signal. Terminal nodes show payoffs in the order (buyer, seller).
• Figure 2: Platform revenue $\Pi$ as a function of true-positive and false-positive rates, $\alpha$ and $\beta$. Revenue rises with the true-positive rate because more accurate recognition of good sellers increases their equilibrium share and boosts successful transactions. Revenue also increases with the false-positive rate, since bad sellers make more sales when they are mislabeled as good. However, this effect is bounded: beyond an upper threshold $\bar{\beta}$, buyer trust collapses and revenue falls to zero. The figure illustrates both the incentive for the platform to promote transactions by blurring distinctions between seller types, and the constraint that too much dishonesty undermines the stability of the market. Parameters: $r = 0.85, c = 0.72$ with $C(\alpha,\beta)\equiv 0$.
• Figure 3: The cost $C(\alpha,\beta)$ to a platform for maintaining a reputation system with true-positive rate $\alpha$ and false-positive rate $\beta$. The cost of the reputation system is zero in the convex hull of freely achievable pairs, which includes the "natural" values $(\alpha_0,\beta_0)$ as well as any pairs with $\alpha=\beta$. Outside the convex hull, the cost grows as the accuracy increases. Parameters: $\alpha_{0}=0.6,\beta_{0}=0.4,\kappa=0.5,p=2,q=0.5$.
• Figure 4: Maximal platform profit (top) and optimal true-positive (middle) and false-positive (bottom) rates. Dotted lines mark the baseline "natural" accuracy levels, ($\alpha_{0}, \beta_{0}$). Platform profit increases when good-faith transactions generate more value (higher $r$) but falls when the cost of improving accuracy ($\kappa$) is high. The platform’s optimal strategy generally involves investing to raise both $\alpha$ and $\beta$ above their natural levels. Notably, the optimal false-positive rate $\beta^{\ast}$ generally increases with $r$ and it can even exceed its baseline value $\beta_{0}$, meaning that the platform has a net benefit from paying to artificially inflate the ratings of bad sellers. When $r$ is low and $\kappa$ is high, the cost of improving signals dominates, and the platform refrains from investing in accuracy altogether, resulting in zero profit (black regions). Parameter: $c=0.45$, $p=2$, $q=0.5$$\alpha_{0}=0.6$, $\beta_{0}=0.4$.
• Figure 5: Maximal platform profit (top) and optimal true-positive (middle) and false-positive (bottom) rates, in response to the scaled commission fee $s \triangleq c/r$. Dotted lines indicate the natural accuracy $\alpha_{0}$ and $\beta_{0}$. When the platform can adjust the commission fee $c$, for a given value of $r$, it tends to obtain higher profit with a higher commission $s$, provided it does not approach the extreme case $s=1$. In the region with high $s$, the optimal value of $\beta$ is much lower than the optimal $\alpha$, indicating the incentive to maintain a somewhat accurate reputation system. The region where the platform incurs no cost and gains no profit is indicated in black. Parameter: $\kappa=0.2$, $p=2$, $q=0.5$, $\alpha_{0}=0.6$, $\beta_{0}=0.4$.