The Incentive Ratio in Exchange Economies

TL;DR

This paper investigates the incentive ratio in exchange economies, revealing unbounded utility gains through strategic misreporting in linear, Leontief, and Cobb-Douglas markets, with bounds established under certain restrictions.

Contribution

It demonstrates that the incentive ratio can be unbounded in general exchange markets and provides bounds for specific cases, contrasting with Fisher market results.

Findings

Unbounded incentive ratios in linear, Leontief, and Cobb-Douglas markets.

Bounded incentive ratios in restricted Cobb-Douglas markets.

Exceeding known Fisher market bounds in exchange economies.

Abstract

The incentive ratio measures the utility gains from strategic behaviour. Without any restrictions on the setup, ratios for linear, Leontief and Cobb-Douglas exchange markets are unbounded, showing that manipulating the equilibrium is a worthwhile endeavour, even if it is computationally challenging. Such unbounded improvements can be achieved even if agents only misreport their utility functions. This provides a sharp contrast with previous results from Fisher markets. When the Cobb-Douglas setup is more restrictive, the maximum utility gain is bounded by the number of commodities. By means of an example, we show that it is possible to exceed a known upper bound for Fisher markets in exchange economies.