Undefeated equilibria of the Shi-Trejos-Wright model under adverse selection

Decentralized markets where assets are useful as media of exchange are also usually subject to private information. To analyze the liquidity and prices of such assets, I adapt the Shi (1995), Trejos and Wright (1995) model with Lucas trees under adverse selection. While most studies focus on either a pooling or separating equilibrium, I apply the undefeated equilibrium refinement by Mailath et al. (1993) to make the selection based on fundamentals. Under pooling, the high-quality asset holder accepts a pooled price, and under separating signals quality through asset retention. Applying the refinement results in a regime switch from no-information (pooling) to information revelation (separating) following a negative shock to the quality or quantity of lemons. This change leads to a discontinuous fall in aggregate welfare.