Incentives for Strategic Behavior in Fisher Market Games

In a Fisher market game, a market equilibrium is computed in terms of the utility functions and money endowments that agents reported. As a consequence, an individual buyer may misreport his private information to obtain a utility gain. We investigate the extent to which an agent's utility can be increased by unilateral strategic plays and prove that the percentage of this improvement is at most 2 for markets with weak gross substitute utilities. Equivalently, we show that truthfully reporting is a 0.5-approximate Nash equilibrium in this game. To identify sufficient conditions for truthfully reporting being close to Nash equilibrium, we conduct a parameterized study on strategic behaviors and further show that the ratio of utility gain decreases linearly as buyer's initial endowment increases or his maximum share of an item decreases. Finally, we consider collusive behavior of a coalition and prove that the utility gain is bounded by 1/(1 - maximum share of the collusion). Our findings justify the truthful reporting assumption in Fisher markets by a quantitative study on participants incentive, and imply that under large market assumption, the utility gain of a buyer from manipulations diminishes to 0.

[1]  Xiaotie Deng,et al.  Can Bandwidth Sharing Be Truthful? , 2015, SAGT.

[2]  Marc Lanctot,et al.  Computing Approximate Nash Equilibria and Robust Best-Responses Using Sampling , 2011, J. Artif. Intell. Res..

[3]  Paul W. Goldberg,et al.  Learning equilibria of games via payoff queries , 2013, EC '13.

[4]  Ning Chen,et al.  How Profitable Are Strategic Behaviors in a Market? , 2011, ESA.

[5]  Faruk Gul,et al.  WALRASIAN EQUILIBRIUM WITH GROSS SUBSTITUTES , 1999 .

[6]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[7]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[8]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[9]  Artur Czumaj,et al.  Approximate Nash Equilibria with Near Optimal Social Welfare , 2015, IJCAI.

[10]  Koushik Kar,et al.  Envy-Free Pricing in Large Markets , 2015, ArXiv.

[11]  Ruta Mehta,et al.  Nash Equilibria in Fisher Market , 2010, SAGT.

[12]  Nicole Immorlica,et al.  Marriage, honesty, and stability , 2005, SODA '05.

[13]  Leif Johansen.  Price-Taking Behavior , 1977 .

[14]  Eric Budish,et al.  Strategyproofness in the large as a desideratum for market design , 2012, EC '12.

[15]  Y. Otani,et al.  Equilibrium allocations of Walrasian preference games , 1982 .

[16]  H. Scarf,et al.  How to Compute Equilibrium Prices in 1891 , 2005 .

[17]  Paul W. Goldberg,et al.  The Complexity of Computing a Nash Equilibrium , 2009, SIAM J. Comput..

[18]  Aranyak Mehta,et al.  Progress in approximate nash equilibria , 2007, EC '07.

[19]  Aviad Rubinstein.  Inapproximability of Nash Equilibrium , 2018, SIAM J. Comput..

[20]  Simina Brânzei,et al.  The Fisher Market Game: Equilibrium and Welfare , 2014, AAAI.

[21]  M. Jackson,et al.  Approximately competitive equilibria in large finite economies , 1997 .

[22]  E. Eisenberg.  Aggregation of Utility Functions , 1961 .

[23]  Ning Chen,et al.  Incentive Ratios of Fisher Markets , 2012, ICALP.

[24]  Ilya Segal,et al.  Solutions manual for Microeconomic theory : Mas-Colell, Whinston and Green , 1997 .

[25]  D. J. Roberts,et al.  THE INCENTIVES FOR PRICE-TAKING BEHAVIOR IN LARGE EXCHANGE ECONOMIES , 1976 .

[26]  Omer Reingold,et al.  Fault tolerance in large games , 2008, EC '08.

[27]  Xiaotie Deng,et al.  Settling the complexity of computing two-player Nash equilibria , 2007, JACM.