Thus far this summer, the discussions here at ZIA have focused on two general topics: modeling extreme events, and the value of game theory in understanding these events. In continuing this theme, a very interesting paper arrived in my inbox this morning that attempts to use game theory to investigate the dynamics of emergency response teams during a multi-event crisis (e.g., natural disasters, or a coordinated terrorist attacks). In “A Game Theory Approach for Evaluating Terrorist Threats and Deploying Response Agents in Urban Environments,” the authors make the subtle—but profound— assumption that emergency response teams are self-interested actors attempting to coordinate a response that maximizes their individual utility. As the authors note:
…we model the interaction process between a multi-emergency event (which includes terrorist attacks, fires, riots, and traffic accidents) and a district response agent as a two-person strategy, which is a noncooperative finite and zero-sum game. The proposed payoff functions depend upon the threat measures for the multi-emergency events and the response agent resources of the two players. The mixed strategy Nash equilibrium is derived from these functions and is applied to assign a unique terrorist threat value (TTV) for the response agents in each alarm district.
The execution of model is muddled by unnecessary over-complication, as the authors attempt to model both the perceived threat-level of an emergency as well as the response, though I encourage those interested to read through the paper as there are many intriguing ideas scattered throughout the text. The notion that emergency response teams engage in competitive behavior during a crisis, however, is fascinating and well worth further consideration. It is generally assumed that emergency response teams play a cooperative game because their utility is based on the shared level of success, however, it may be considerably more interesting to consider the competitive dynamics that occur at the micro-level.
Large multi-event incidents eliminate the jurisdictional restrictions of smaller-scale emergencies, where response teams are assigned to incidents based on geographic proximity. In the large-scale cases, resources are stretched beyond their normal areas of responsibility due to a sudden rise in demand. We could, therefore, model this as a repeated coordination game, in the vein of a prisoner’s dilemma, in the following way. Before the game is played, Nature endows each team with a limited and expendable “ability” resource, which is spent in every emergency response. Then, assume a matrix of emergencies varying in severity (i.e., the amount of ability needed to dispel them); in each stage of the game, teams must attempt to coordinate with all other teams as to where they will use this resource. When an emergency has been successfully dispelled, teams share the utility of success, and likewise the reduction in utility when they fail. This game is repeated indefinitely until all emergencies have ended (total success), or all teams have expended their resources (total failure).
Highly endowed teams have an incentive to “go it alone,” as their relative ability allows them the luxury of not having to share their success utility with anyone, however, weak teams must seek out stronger teams in order to associate themselves with success. Without formalizing this any further, we can consider how these dynamics would result in undesirable outcomes. First, highly endowed teams may seek out smaller emergencies where the weaker teams are less likely to congregate, as they will easily be able to end them and will not have to share utility. Second, weak teams may move to larger emergencies with the hope that a strong team will be there so they have higher relative gains. Weak teams they seek out strong teams for success, so they may be attracted to large emergencies where they believe the strong teams will be. The result of this failed coordination is that resources become misplaced, as strong teams should go to large emergencies and weak team the small ones, however, the incentive structure induces the opposite behavior.
This idea is admittedly very raw (it’s my blog and I’ll spew if I want to), and rife with assumption. The primary assumption made is that there is no central player coordinating the assignment of teams, which as we all know is in fact a large part of emergency response. My counter to communication failures are often observed in large-scale emergency events of the type the model attempts to address (e.g., the loss of cellular and radio communication on 9/11). Second, those involved in emergency response may argue that there is little, if any, discernible difference in ability among teams, as they are all provided with the same training and relative resources. I would argue, however, that these differences are inherent to a system where the primary resource—the human actor—enters with a high level of variance in their physical and mental attributes, which in turn affords for high levels of variance among teams.
I am interested in your thoughts on modeling emergency response in this way, as I think it is novel and brings much to the study of these dynamics. What is missing from the proposed model above, or how would you alter it to better model these events? More to the point, do you believe there is value in modeling emergency responses as a non-cooperative game, and if not, why?
Photo: ABC Goldfields WA
Automatically Generated Related posts:
you should look into Robert Powell’s papers. He has a really good game theoretic treatment of homeland defense dilemmas.
[Reply]
Anna, does he look at response as non-cooperative? What papers do you recommend?
[Reply]
In his APSR August 2007 paper he discusses allocation dilemmas and compares allocation in strategic (terrorism) and non-strategic situations (natural disasters).
In his APSR November 2007 he analyzes an interesting tradeoff between secrecy and security. He has a signaling model in which he shows that in some cases the defender is better off allocating equal amounts of resources to protect all sides (secrecy about which site is most vulnerable is more important than allocating more to the most vulnerable sites), and in some cases it makes sense to allocate based on vulnerability.
Both papers are of course non-cooperative models (they are based on the logic of Colonel Blotto games which are zero sum). His solution concept is Bayesian perfect eq’m. Besides, Powell is one of the best modelers in political science, so you definitely have to know his models if you want to build your own games regarding homeland defense.
[Reply]
I know Powell’s older stuff, mostly his critics of previous game theoretic approaches to IR. I will have to check out these papers and give them some thought.
It seem from your description, though, that these models are still trying to get at the macro-dynamics of these situations, while I think the micro has much more value.
[Reply]