1. Dynamic Trading under Adverse Selection Maarten C.W. Janssen University of Vienna

2. Question(s) Adverse selection: high qualities cannot be traded in market equilibrium Dynamic perspective: what if trade possibilities open at different moments in time? – Choose when to sell When time is involved: – Given stock, or inflow of new products? – Resale allowed or not? Alternative view on adverse selection: high qualities need to wait (longer) to sell; what about welfare aspects of this?

3. Discrete Example Suppose there are two qualities with seller‘s reservation values θ of 10 and 20 (equal probability) Consumers value product vθ if they know θ. Suppose v=1.2 Both have same discount factor δ. Consider dynamic equilibrium where quality 10 trades at t=1 and 20 at t=2 (Max) price p1 = 12, price p2 = 24. Upper bound on δ. Welfare improvement Do these results hold true in continuous model?

4. Walrasian market model: sellers

5. Walrasian market model: buyers More buyers than sellers All buyers have unit demand and value quality θ at vθ No reselling (buyer leaves the market)

6. Walrasian market model: equilibrium

7. Continuous example

8. Kind of Results Characterization Result: In any dynamic equilibrium, consecutive intervals of qualities traded over time Existence result When is break in trading necessary Strategic re-interpretation of results

9. Related Literature Bilateral Bargaining and durable goods monopolist (…) – Intertemporal price discrimination – Independent values – Results depend on specific formulation Correlated values – Strategic manipulation of beliefs Dynamic auctions (Vicent, 1989) – Bidders bid in different periods; he assumes specific distribution and considers specific out-of-equilibrium beliefs Time on the market signals low quality (Taylor, 1999)

10. Characterization

11. Proof of characterization

12. When is break in trade not necessary

13. Strategic Interpretations Suppose that sellers set prices: signaling game – Any dynamic market equilibrium is outcome equivalent to a perfect Bayes-Nash equilibrium of the signaling model – Reverse is not true. For example, there is a signalling equilibrium where only the qualities that are traded in a static equilibrium are traded; pessimistic out-of- equilibrium beliefs – Intuitive criterion: who has most incentives to set price slightly above this static equilibrium price in t=2? Suppose buyers set prices: screening game

14. Final remarks Multiple equilibria are possible Welfare properties – Multiple equilibria can be Pareto-Ranked – Comparison with static equilibrium (total surplus?) If good is not perfectly durable, but decay is exponential, then analysis goes through