The effect of risk aversion on the outcomes of inspection games

Abstract

In this work, we study how risk aversion behavior affects the final outcomes of inspection games. We formulate two nonzero-sum parametric games between an inspector and an agent, which are distinguished by the players’ risk behaviors: risk aversion or risk neutrality. Both games are solved efficiently, and closed-form equilibria solutions are provided. The solutions of the two games are compared with each other and with a third game where both players are risk neutral. Analysis of the results reveals that the risk aversion of the agent has a stronger effect than that of the inspector, since the equilibrium strategies and utilities of both players depend on the risk aversion of the agent, whereas only the agent’s equilibrium strategies and the inspector’s equilibrium utility depend on the risk aversion of the inspector. Analysis of an incomplete information game version, when the agent has a private risk attitude, reveals that in order to know how to act in equilibrium, the inspector must know the probability that the agent is risk averse.

Keywords:

• Game theory
• inspection games
• risk aversion
• risk neutrality

Notes

Please note this paper has been re-typeset by Taylor & Francis from the manuscript originally provided to the previous publisher.

1. Separability implies that all nonlinear functions of the problem can be written as $f(x)={\sum }_{j=1}^n{f}^j\left(x_j\right).$