arXiv subjects
Publications and source records attributed to Songzi Du.
A Nash equilibrium is learnable if there exists a myopic adjustment dynamic for which it is asymptotically stable. In generic symmetric two-player games, a Nash equilibrium is learnable if and only if it has index +1.
We study robust mechanisms to sell a common-value good. We assume that the mechanism designer knows the prior distribution of the buyers' common value but is unsure of the buyers' information structure about the common value. We use linear programming duality to derive mechanisms that guarantee a good revenue among all information structures and all equilibria. Our mechanism maximizes the revenue guarantee when there is one buyer. As the number of buyers tends to infinity, the revenue guarantee of our mechanism converges to the full surplus.
We study how information perturbations can destabilize two-sided matching markets. In our model, agents arrive on the market over two periods, while agents in the first period do not know the types of those arriving later. Agents already present in the market may match early or wait for the small group of new entrants. Despite the lack of discounting or risk aversion, this perturbation creates incentives to match early and leave the market before the new agents arrive. These incentives do not disappear as the market gets large. Moreover, we identify a new adverse phenomenon in this setting: as markets get large the probability of \emph{chaos} -- where no early matching scheme for existing agents is robust to pairwise deviations -- approaches 1. These results are independent of the distribution of agents' types and robust to asymmetries between the two sides of the market. Our findings thus suggest that matching markets are extremely sensitive to institutional details and uncertainty.
This paper works out the rate of convergence of two "natural" random walks on the dicyclic group.