Mechanism Design for Exchange Markets
Yusen Zheng, Yukun Cheng, Chenyang Xu, Xiaotie Deng
TL;DR
This paper studies mechanism design for exchange markets regulated by a market manager who sets per-agent trading limits and prices, introducing market liquid welfare $(\mathsf{MLW})$ and profitability as core objectives. It proves the existence of a profitable uniform-price mechanism that attains the optimal MLW but is not truthful, and then constructs a truthful uniform-price mechanism under a large-market regime that achieves a constant-approximation to the optimum (approaching $1/2$ as the market grows). For general—and not-necessarily-large—markets, it provides a truthful differential-pricing mechanism that also achieves a $1/2$-approximation with bounded unprofitability, extending to multi-parameter budgets under certain conditions. Overall, the work offers insights into truthful, profitable market-rule design for exchange economies and highlights the potential limits of achieving constant-approximation truthfulness in general markets.
Abstract
Exchange markets are a significant type of market economy, in which each agent holds a budget and certain (divisible) resources available for trading. Most research on equilibrium in exchange economies is based on an environment of completely free competition. However, the orderly operation of markets also relies on effective economic regulatory mechanisms. This paper initiates the study of the mechanism design problem in exchange markets, exploring the potential to establish truthful market rules and mechanisms. This task poses a significant challenge as unlike auctioneers in auction design, the mechanism designer in exchange markets lacks centralized authority to fully control the allocation of resources. In this paper, the mechanism design problem is formalized as a two-stage game. In stage 1, agents submit their private information to the manager, who then formulates market trading rules based on the submitted information. In stage 2, agents are free to engage in transactions within these rules, ultimately reaching an equilibrium. We generalize the concept of liquid welfare from classical budget-feasible auctions and use market liquid welfare as a measure to evaluate the performance of the designed mechanism. Moreover, an extra concept called profitability is introduced to assess whether the market is money-making (profitable) or money-losing (unprofitable). Our goal is to design a truthful mechanism that achieves an (approximate) optimal welfare while minimizing unprofitability as much as possible. Two mechanisms for the problem are proposed. The first one guarantees truthfulness and profitability while approaching an approximation ratio of 1/2 in large markets. The second one is also truthful and achieves 1/2 approximation in general markets but incurs bounded unprofitability. Our aim is for both mechanisms to provide valuable insights into the truthful market design problem.