Incorporating risk preferences in stochastic noncooperative games

ABSTRACT

Traditional game-theoretic models of competition with uncertainty often ignore preferences and attitudes toward risk by assuming that players are risk neutral. In this article, we begin by considering how a comprehensive analysis and incorporation of expected utility theory affect players’ equilibrium behavior in a simple, single-period, sequential stochastic game. Although the literature posits that the more risk averse a first mover is, the more likely she is to compete and defend her position as the “leader”, and that the more risk seeking a “follower” is, the more likely he is willing to participate and compete, we find that this behavior may not always be true in this more general setting. Under simple assumptions on the utility function, we perform sensitivity analyses on the parameters and show which behavior changes when deviations from risk neutrality are introduced into a model. We also provide some insights on how risk preferences influence pre-emption and interdiction by looking at how these preferences affect the first mover’s advantage in a sequential setting. This article generates novel insights when a confluence of factors leads players to deviate or change their behavior in many risk analysis settings where stochastic games are used.

KEYWORDS:

• risk analysis
• risk aversion
• competition
• homeland security
• attacker-defender games

Funding

This research was partially supported by the United States Department of Homeland Security (DHS) through the National Center for Risk and Economic Analysis of Terrorism Events (CREATE) under award number 2010-ST-061-RE0001. This research was also partially supported by the United States National Science Foundation (NSF) under award numbers 1200899 and 1334930. However, any opinions, findings, and conclusions or recommendations in this document are those of the authors and do not necessarily reflect views of the DHS, CREATE, or NSF.

Additional information

Notes on contributors

Victor Richmond R. Jose

Victor Richmond R. Jose is an Associate Professor and the William and Karen Sonneborn Term Chair in the operations and information management area of the Robert Emmett McDonough School of Business at Georgetown University. His research interests include decision analysis, forecast evaluation, probabilistic forecasting, machine learning, and risk analysis.

Jun Zhuang

Jun Zhuang is an Associate Professor and Director of Undergraduate Studies, Department of Industrial and Systems Engineering, at the University at Buffalo. Dr. Zhuang’s long-term research goal is to integrate operations research, big data analytics, game theory, and decision analysis to improve mitigation, preparedness, response, and recovery for natural and man-made disasters. Other areas of interest include applications to health care, sports, transportation, supply chain management, sustainability, and architecture.