Nash in Najaf: Game Theory and Its Applicability to the Iraqi Conflict

Nash in Najaf: Game Theory and Its Applicability to the Iraqi Conflict
Brightman, Hank J. 2007. "Nash in Najaf: Game Theory and Its Applicability to the Iraqi Conflict." Air & Space Power Journal 21, no. 3: 35-41. Military & Government Collection, EBSCOhost (accessed April 20, 2009).

* Actual article was accessed through Mercyhurst College's EBSCOhost subscription - link to article was found as a Google cached site.

Summary:
The 2007 article written by Dr. Hank Brightman, an associate Criminal Justice professor at Saint Peter's College and a USN Information Warfare Officer at the US Naval War College's War Gaming Department, posits that game theory suggests that US and Coalition forces stationed in Iraq will suffer an increasing rate of casualties the longer they remain in Iraq. The reasoning behind this statement is that both Domestic Insurgents (DI) and Indigenous Security Forces (ISF) will "turn away from attacking each other towards a point of mathematical corruption." It is at this theoretical point that US and Coalition forces will be the target of ISF intelligence-fed DI attacks. ISF refers to Iraqi military as well as state and local police; DI refers to various domestic insurgent groups within Iraq.

Brightman reviews the "prisoner's dilemma" and zero-sum game theory, and states that the prisoner's dilemma is an example of a simple form game (SFG). SFGs have two players that strive for the highest payoff at the end of a move or event (known as the Pareto Optimal position). As SFG applies to the Iraqi conflict, ISFs and DIs are the two players.
Extensive Form Games (EFG) are more complex than SFGs as they feature two or more players that are engaged in move-for-move exchanges, leaving the players less concerned with intermediate payoffs and focused on the ultimate payoff. EFGs are typically not zero-sum games and are distinguished by multiple moves, leaving players not only focused on broad strategy, but also smaller sub-strategies that counter the other players' moves. However, as time progresses in EFGs, the model becomes susceptible to "strange attractors" that "affect the players' willingness to adhere to previously stated rules and therefore decrease the overall stability of the game." US and Coalition forces would be considered strange actors in both the SFG and EFG models.

As time elapses the players (ISF & DI) become more frustrated and ultimately begin to reduce their expectation for the ultimate payoff. As this happens, each player considers negotiating with the opponent as a means of reducing losses - this is known as bargaining toward equilibrium, or a Pareto Improvement). "When both players have reached a point at which they can achieve the highest aggregate payoff, the game ends in preferred equilibrium."

"However, the influence of strange attractors in a model that will become increasingly unstable (bifurcated) over time often induces the players to hasten their desire for a Pareto Improvement position instead of a superior (Pareto Optimal) position - even though doing so may lessen their ultimate payoff." The strange attractors cause frustration which preempts the players from achieving the preferred equilibrium (the point in the prisoner's dilemma where both prisoners remain silent and gain the most) and instead yield the inchoate or Nash equilibrium (the point in the prisoner's dilemma where both prisoners confess to the crime).

*Author's note: the article delves further into the SFG and EFG situations as they relate to the Iraq Conflict, however, due to length they have been cut from this summary.