Modeling Attacker-Defender Games with Risk Preferences

Principal Investigator: 
Performance Period: 
October 2013 to June 2014
Commercialization Status: 
N/A
Abstract: 
The objectives of this project are: (a) to study how the incorporation of alternative models of behavior (e.g., expected utility and cumulative prospect theories) affects the equilibrium behavior of players in attacker-defender games; (b) to validate the risk preferences and cumulative prospect theory utility functions using real data; (c) to transit the results to homeland security practitioners; and (d) to provide education and outreach to a large group of governmental agencies, students and communities. Traditional models of attacker-defender games generally assume that players are risk-neutral; i.e. they choose strategies that maximize their expected payoff or benefit. In practice, decision makers could be either risk seeking or risk averse, which has not been extensively studied in the attacker-defender game literature. For example, terrorists could have risk preferences (Yang et al. 2013); and Phillips (2013) even estimated the coefficient of relative risk-aversion for Al-Qaeda. Government could be risk averse: Standish (2002) argued that Western governments tend to be extremely risk-avers and constantly introduce disruptive risk-averse policies in many areas such as air travel security; Stewart et al. (2011) stated that the amount of government spending for “many homeland security measures would fail a cost-benefit analysis using standard expected value methods of analysis [suggesting] not surprisingly that policy makers within the US Government /DHS are risk-averse.” Unfortunately, the growing attacker-defender game literature has not rigorously studied the players’ risk preferences. To fill this gap, the research objective of this proposal is to study how the incorporation of alternative models of behavior (e.g., expected utility and cumulative prospect theories) affects the equilibrium behavior of players in attacker-defender games. Though Zhuang and Bier (2007) asserted that the more risk-averse a defender is, the more likely she is to defend and that the less risk-averse an attacker is, the more likely he is to attack, our preliminary results show that this behavior may not be true when other factors such as initial wealth, risk aversion/risk seekingness, loss aversion, and optimism are incorporated into a model. By studying these two commonly used paradigms outside the attacker-defender games literatures, we show that Nash equilibrium behavior in these games may change. This project results enrich our understanding of how players in attacker-defender games when a rich set of empirically recognized aspects of human behavior and decision making is introduced in analytic models, and help transform a large group of existing models which ignore player preferences. This project has been developing and transitioning models in integrating decision analysis, game theory and operations research for both terrorism and natural disasters, resulting in numerous peer-reviewed journal publications conference/seminar presentations, education and outreach, and internal/external awards. The research has interested agencies from DHS and other government organizations. All model parameters are tunable so that practitioners are able to customize and play with the software demos.