Trust, Reputation, and the Market for Lemons: A Free-Energy Model of Endogenous Belief Refinement

This paper examines how internalized honesty and reputation can mitigate adverse selection when buyers lack an exogenous quality index. A privately informed seller probabilistically chooses whether to offer or withhold a product using a free-energy policy rule. Internalized norms enter as a prior policy bias, whereas reputation changes anticipated consequences. A buyer observing an offer updates beliefs about quality through Bayes’ rule and decides whether to purchase at an exogenous posted price. Seller payoffs specify reservation values, offering costs, and expected reputational losses. Seller policy incorporates the anticipated probability of purchase, and a behavioral consistency condition requires this anticipation to agree with the buyer’s optimal response. On the full-purchase branch, stronger honesty and reputation discourage lemon offers and increase the buyer’s posterior probability of high quality. I derive a threshold under which purchase after an offer is strategically consistent and high-quality trade occurs with positive probability. This is a result about posted-price trade rather than a complete Akerlof-type unraveling equilibrium. The framework shows how socially embedded behavior can generate informative seller actions without a physical quality index.