Research
Working Papers
This paper studies the effect of transparency in negotiations in the presence of outsiders. I consider a game in which two players (negotiators) engage in bargaining, in the presence of a third player (outsider) who also cares about the negotiation. As the bargaining progresses, the outsider takes a single irreversible action that brings him a payoff that depends on the unknown gains from the bargaining game. This action imposes externalities on the negotiators who know the gains from the negotiation. However, they have misaligned incentives regarding the outsider's decision. When proposals are public (transparent negotiation), there is an equilibrium where negotiators engage in posturing behavior as a tactic to distort the outsider's action. This behavior reduces efficiency because the outsider makes a suboptimal decision, and sometimes, there is delay in the negotiation. Moreover, I show that these inefficiencies arise for a general class of equilibria. On the other hand, when proposals are private (non-transparent negotiation), the negotiators agree immediately, and the terms of the agreement are highly informative for the outsider. In this situation, I show that every equilibrium is approximately efficient.
Revenue Maximization with Heterogeneous Discounting: Auctions and Pricing with Jose Correa and Juan Escobar
Revise and resubmit, Theoretical Economics
We characterize the revenue maximizing mechanism in an environment with private valuations and asymmetric discount factors. The optimal mechanism combines auctions to encourage competition and dynamic pricing to screen buyers’ valuations. When buyers are ex-ante symmetric and the seller is more patient than the buyers, the optimal mechanism takes a remarkably simple form. The seller runs a modified second price auction and allocates the item to the highest bid buyer if and only if the second highest bid exceeds the reserve price. The winning buyer pays the second highest bid. If the item is not sold in the auction, the seller posts a price path that depends on the second highest bid. The item is then allocated to the highest bid buyer at a strictly positive time. Our results imply that, for a patient seller, auctions and pricing schemes are complements and caution against the presumption that it is ex-ante optimal to commit not to trade when an auction fails.
We provide a novel family of stochastic orders, which we call the α,[a, b]- convex decreasing and α,[a,b]-concave increasing stochastic orders, that generalizes second order stochastic dominance. These stochastic orders allow us to compare two lotteries, where one lottery has a higher expected value and is also riskier than the other lottery. The α, [a, b]-convex decreasing stochastic orders allow us to derive comparative statics results for applications in economics and operations research that could not be derived using previous stochastic orders. We apply our results in consumption-savings problems, self-protection problems, and in a Bayesian game.
Published
Optimal Continuous Pricing with Strategic Consumers with Luis Briceno and Jose Correa
Management Science, 63(8):2741--2755, 2017
An important economic problem is that of finding optimal pricing mechanisms to sell a single item when there are a random number of buyers who arrive over time. In this paper, we combine ideas from auction theory and recent work on pricing with strategic consumers to derive the optimal continuous time pricing scheme in this situation. Under the assumption that buyers are split among those who have a high valuation and those who have a low valuation for the item, we obtain the price path that maximizes the seller’s revenue. We conclude that, depending on the specific instance, it is optimal to either use a fixed price strategy or to use steep markdowns by the end of the selling season. As a complement to this optimality result, we prove that under a large family of price functions there is an equilibrium for the buyers. Finally, we derive an approach to tackle the case in which buyers’ valuations follow a general distribution. The approach is based on optimal control theory and is well suited for numerical computations.