How Profitable Are Strategic Behaviors in a Market?

Abstract

It is common wisdom that individuals behave strategically in economic environments. We consider Fisher markets with Leontief utilities and study strategic behaviors of individual buyers in market equilibria. While simple examples illustrate that buyers do get larger utilities when behaving strategically, we show that the benefits can be quite limited: We introduce the concept of incentive ratio to capture the extent to which utility can be increased by strategic behaviors of an individual, and show that the incentive ratio of Leontief markets is less than 2. We also reveal that the incentive ratios are insensitive to market sizes. Potentially, the concept incentive ratio can have applications in other strategic settings as well.

The Incentive Ratio in Exchange Economies

“…If we impose the (common) restriction that all agents possess at least a little bit of every commodity and the market is strongly competitive, the utility gain in Cobb-Douglas markets is bounded by the number of commodities, but it may exceed the upper bound from Fisher markets, which we show by means of an example. The results obtained show a sharp contrast with the findings in [7], [6]: in the Fisher market setup, incentive ratios are bounded by the small constants 2, 2 and e 1/e ≈ 1.44 for linear, Leontief and Cobb-Douglas markets, respectively.…”

“…The results indicate that, without any further restrictions on the setup presented in [7], [6] incentive ratios in Leontief and Cobb-Douglas exchange economies are unbounded.…”

“…The incentive ratio is a concept introduced in [7]. It attempts to measure the (maximum) benefits of manipulating the equilibrium mechanism by strategically misreporting personal parameters.…”

“…In fact, in [7], [6], the following markets are considered, with arbitrarily many agents and commodities: The (tight) bounds proven in [7], [6] for Fisher markets are 2, 2 and e 1/e for linear, Leontief and Cobb-Douglas respectively.…”

“…Specifically, we ask how much any individual agent can gain from strategically misreporting some of his/her utility function. The primary tool for this will be the incentive ratio as introduced by [7], [6]. In a nutshell, when all agents report truthfully, an equilibrium will materialise, * I am grateful to Xiaohui Bei and Satoru Takahashi for discussions on the topic and many useful suggestions and comments on earlier versions of this manuscript.…”