Modelling ‘contracts’ between a terrorist group and a government in a sequential game

Abstract

In this paper, we apply a sequential game to study the possibility of ‘contracts’ (or at least mutually beneficial arrangements) between a government and a terrorist group. We find equilibrium solutions for complete and incomplete information models, where the government defends and/or provides positive rent, and the terrorist group attacks. We also study the sensitivities of equilibria as a function of both players’ target valuations and preferences for rent. The contract option, if successful, may achieve (partial) attack deterrence, and significantly increase the payoffs not only for the government, but also for some types of terrorist groups. Our work thus provides some novel insights in combating terrorism.

Keywords:

• contracts
• game theory
• homeland security
• preferences for rent
• sequential game
• target valuations

Acknowledgements

This research was supported by the United States Department of Homeland Security through the National Center for Risk and Economic Analysis of Terrorism Events (CREATE) under award number 2010-ST-061-RE0001. However, any opinions, findings, and conclusions or recommendations in this document are those of the authors and do not necessarily reflect views of the United States Department of Homeland Security, or CREATE. We thank the Editor and two anonymous referees for their helpful comments. We also thank Ms. Elizabeth Newell (University at Buffalo) for editorial help.

Notes

1 Although Table 2 provides technical solution for this theoretical paper, and one of the contribution of this paper is to provide some novel insights in combating terrorism, instead of summarizing real-world scenarios, we still observe some real-world examples corresponding to each of the seven cases in Table 2: (Case 1): since the desert has little valuation to both the terrorist and government, we observe no attack, defense, and rent for desert targets; (Case 2): in many developing countries receiving foreign aid (rent), there is no attack or defense activities; (Case 3): after the 11 September 2001 attacks to the World Trade Center, there was no attack from Al Qaeda following the original attack, and no rent provided to Al Qaeda from the US government, although the US government is still defending from Al Qaeda; (Case 4): before the recent 2010 Korean peninsula crisis, South Korea provided rent to, and defended from, North Korea, and no attack happened; (Case 5): the government may have no incentive to defend from, and provide rent to, terrorists that are active in other countries; (Case 6): there is no (known) rent provided from the US government to Taliban recently, but the two players are still attacking and defending from each other in Afghanistan; and (Case 7): there might be no direct defense for oversea targets, while rent is still provided and attacks still occur.  For Case 8, which is not possible at equilibrium for complete information model, we still observe multiple real-world examples. For the Iraq example, we simultaneously observe insurgent attacks, US defense, and US rent to the Iraq government. For the North Korea case over the past 10 years, South Korea provided rent to, defended from, and was recently attacked by North Korea.  Note that as a building block, this paper focuses on a one-government-one-terrorist, one-period, contract game; extensions to multiple-government, multiple-terrorist, multiple-period models could be developed in the future, to better model the complex real-world scenarios.