Revealed Preference Implications of Backward Induction and Subgame Perfection (Forthcoming, AEJ: Microeconomics)
Frictions in Internet Auctions with Many Traders: a Counterexample, with Javier Donna and Gregory Veramendi (Economic Letters)
Identifying subjective beliefs in subjective state space models (Games and Economic Behavior, Vol. 95, (January 2016), Pages 59–72)
This paper uses networks to study price dispersion in seller-buyer markets where buyers with unit demand interact with multiple, but not all, sellers; and buyers and sellers compete on prices after they meet. Our approach allows for ex post indirect competition, where a buyer who is not directly linked with a seller affects the price obtained by that seller. Indirect competition generates the central finding of our paper: price dispersion depends on both the number of links in the network, and how these links are distributed. Networks with very few links can have no price dispersion, while networks with many links can still support significant price dispersion. We present three main theoretical results. First, for any given network we characterize the pairwise stable matchings and the prices that support them. Second, we characterize the set of all graphs where price dispersion is precluded. Third, we use a theorem from Frieze (1985)to show that the graphs where price dispersion is precluded arise asymptotically with probability one in random Poisson networks, even as the probability of each individual link goes to zero. We also provide quantitative results on the finite sample properties of price dispersion in random networks. Finally, we present an application to eBay to show that: (i) a calibration of our model reproduces the price dispersion documented in eBay quite well, and (ii) the amount of price dispersion in eBay would decrease substantially (35-45 percent as measured by the coefficient of variation) in a counterfactual analysis, where we change eBay’s network structure so that links are drawn with equal probability for all sellers and buyers.
We propose a decision-theoretic model akin to Savage (1972) that is useful for defining causal effects. Within this framework, we define what it means for a decision maker (DM) to act as if the relation between the two variables is causal. Next, we provide axioms on preferences and show that these axioms are equivalent to the existence of a (unique) Directed Acyclic Graph (DAG) that represents the DM's preference. The notion of representation has two components: the graph factorizes the conditional independence properties of the DM's subjective beliefs, and arrows point from cause to effect. Finally, we explore the connection between our representation and models used in the statistical causality literature (for example, Pearl (1995)).
This paper studies repeated games of incomplete information where each player knows his own payoffs and where the unknown state of the world can be identified by the combined private information of all players. We obtain a condition that is both necessary and sufficient for a Perfect Bayesian Equilibrium (PBE) folk theorem to hold. This contrasts with the existing literature where, due to the difficulty in keeping track of beliefs as play evolves, the analysis has focused on either Nash equilibrium for one-sided incomplete information or has dealt with various ex-post solution concepts. Finally, we also show the condition obtained is also necessary and sufficient to obtain Ex-Post folk theorems.