Game Theory and Military Planning

In “Game Theory: Can a Round of Poker Solve Afghanistan’s Problems?” Major Richard J.H. Gash creates a simple two player game to show how game theory can be used to influence military planning. Gash’s game involves two villages in Afghanistan with the choice to either support the “Coalition” or support the “Taliban.” The scoring of the game generates a payoff matrix that is similar to that of the Prisoner’s Dilemma with a non Pareto-optimal Nash equilibrium. Unfortunately, Gash oversimplifies the game to just one round. In reality, Afghan villages participate in multiple rounds of decision making, with the actual number of rounds unknown, leading to differing strategies and outcomes than those proposed by Gash.

In a single round game with a payoff matrix similar to that proposed by Gash there is a clear Nash equilibrium, representing the optimal strategy both parties will adopt. In this case, both villages choose to support the Taliban. But, supporting the Taliban or Coalition is not a single round game, it is continuous game, with significant but unknown number of rounds. Not only may villages switch allegiance at any time, but if the Taliban is defeated or cleared from the area, the game may abruptly end.

In his seminal work, “The Evolution of Cooperation,” Robert Axelrod explores how cooperation surprisingly trumps competition in a similarly styled prisoner’s dilemma game. Based on an iterated prisoner’s dilemma tournament, Axelrod found that strategies which always defected, (or in the case of Gash’s example, supported the Taliban) performed the worst. The best strategies were mixed, and tended to copy their opponents previous actions, leading to cooperative alliances.

Extending this theory of cooperation to the actions of Afghan villages, we can infer that over time they are likely to discover that cooperation and supporting the coalition is the best strategy. While Gash correctly concludes that changing the cost/benefit value (incentive) for supporting the coalition may speed up the process, it is not necessary to achieve the optimal cooperative solution.

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  • kevindick

    This is a very good point. To take it further, we might be better off focusing our efforts on “priming” the villager to think in terms of repeated interaction than changing the one-shot payoff matrix.

    This would include things like making regular visits to the village where our forces provide modest, but highly visible rewards for cooperation in that round. We should also make a highly visible commitment to keeping our forces there for a significant period of time.

    Of course, if we don’t think there’s anything we can do to get the villagers to think we’ll be around and consistent enough to treat this as a repeated game, then this won’t work.

  • DennisP

    Are you sure you’re looking at this in an unbiased way? A Taliban game theorist might say that supporting the Taliban is the “cooperation” strategy. The paper mentions that supporting the Coalition brings a “public benefit” to both villages, but that assumes that Coalition victory is what villagers actually want.

    Also, you mention “if the Taliban is defeated or cleared,” but don’t mention the possibility that Coalition forces may run out of patience/political support/money and leave the country. Given the history of Afghanistan (vs. the Soviets and the British), and of the U.S. (Vietnam), this is not all that unlikely.

    It appears to me that the situation is symmetrical, and neither side can be said to have a clear advantage in game-theoretic terms.

  • Tony-S

    I don’t see how you can infer that in a multiple round game, Afghan villagers would see cooperation with the coalition as the best strategy. Seems more like wishful thinking to me.

    That would be probably because you left out so many important elements in your analysis:
    - The general hostility of Afghan civilians towards foreign troops, no matter the amount of aid,
    - the fact that Talibans can be cleared off a region only on a short-term basis (basis of guerrilla warfare)
    - the fact that allegiances are temporary, favors the ones that are likely to be more permanent. The coalition will leave one day. The Talibans are there to stay.
    - The differences in the price paid for allegiance to the wrong side. Talibans have apparently no problem cutting away fingers and hands of collaborators
    - etc…

  • danielhorowitz

    Hi Tony -

    My analysis is based on the payoff matrix provided in the paper. You are correct that the “game” is actually far more complex than the simplified payoff matrix I am using, and thus my conclusions are not applicable to “real life.”

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