Optimal robust bilateral trade: Risk neutrality

Abstract

A risk neutral seller and buyer with private information bargain over an indivisible item. We prove that optimal robust bilateral trade mechanisms are payoff equivalent to non-wasteful randomized posted prices.

A Theory of Simplicity in Games and Mechanism Design

“…35 In environments without transfers, however, even SOSP mechanisms-serial dictatorships-can achieve efficient outcomes. Building on the results of the present paper, in single-unit demand allocation problems without transfers, Pycia and Troyan (2023) and Pycia (2019) 32 Prior economic studies on the focal role of posted prices in mechanism design-for example, Hagerty and Rogerson (1987) and Copic and Ponsati (2016)-focused on bilateral trade, while our analysis is applicable to any economic environment satisfying our richness assumption. 33 Building on these results, Pycia and Troyan (2023) showed that every obviously strategy-proof, Pareto efficient, and symmetric mechanism is equivalent to Random Priority.…”

“…32 32 Prior economic studies on the focal role of posted prices in mechanism design—for example, Hagerty and Rogerson ( 1987 ) and Copic and Ponsati ( 2016 )—focused on bilateral trade, while our analysis is applicable to any economic environment satisfying our richness assumption. …”

A dominant strategy double clock auction with estimation‐based tâtonnement

“…Vickrey (1961) first noted that developing mechanisms for two‐sided allocation problems that minimize inefficiencies, do not run a deficit and require no prior information about the true equilibrium price is “extremely difficult.” For a bilateral trade setting à la Myerson and Satterthwaite (1983) with the buyer and seller drawing their value and cost independently from distributions with overlapping support, Hagerty and Rogerson (1987) showed that the best the market maker can do subject to dominant strategy incentive compatibility, ex post individual rationality and budget balance is to post an exogenously given price and let the buyer and seller decide if they want to trade at that price. With only one agent on each side of the market, there is simply no way of endogenizing the price at which trade occurs without giving up on dominant strategies (see also Copič and Ponsatí 2016, and Copič 2017).…”

“…For a bilateral trade setting à la Myerson and Satterthwaite (1983) with the buyer and seller drawing their value and cost independently from distributions with overlapping support, Hagerty and Rogerson (1987) showed that the best the market maker can do subject to dominant strategy incentive compatibility, ex post individual rationality and budget balance is to post an exogenously given price and let the buyer and seller decide if they want to trade at that price. With only one agent on each side of the market, there is simply no way of endogenizing the price at which trade occurs without giving up on dominant strategies (see also Copič andPonsatí 2016, andCopič 2017). McAfee (1992) proposed a double auction that embeds this insight in a setup with multiple single-unit traders, whose values and costs are elements of the [0 1] interval, and that endogenizes the posted price of Hagerty and Rogerson.…”

Robust double auction mechanisms

“…A special instance of the robust double auction mechanisms is the robust bilateral trading mechanism for the environments in which there is one seller who initially owns one indivisible good and there is one buyer who is interested in obtaining the good. Hagerty and Rogerson (1987) and Čopič and Ponsatí(2016) have shown that the only robust bilateral trading mechanism is the posted price mechanism, i.e., the mechanism in which a price is posted in advance and the seller and the buyer either trade at this price or do not trade at all. The purpose of this paper is to obtain a similar characterization for the general robust double auction mechanisms.…”