Syria: Does game theory tell us everything?
http://www.wired.com/dangerroom/2012/09/syria-weapons/
The ongoing civil war in Syria pits two very different forces against one another. On higher ground, there are Assad‘s forces. I say higher ground because their weaponry is more advanced (cluster and thermobaric bombs), their soldiers are better trained, and their supply lines are much more robust. On the obviously lower ground, there are the rebels. Judging from the article‘s title, they’re a ragtag bunch, using digital cameras as scopes for their guns, wielding handmade pipe bombs, and firing artillery with a paltry two kilometer range and a not-so-paltry chance of blowing up a rebel. It’s interesting to consider that, while the Syrian civil war is extremely uneven, it is still going on nonetheless. To further explore this, we can model the Syrian civil war as a game. The war of attrition game is the closest type of canonical game that I could find. In an actual war of attrition (such as the last stages of the [American] Civil War in the South), the losing side either surrenders or runs out of resources, is completely scorched by the opponent, and goes down in flames.
The war of attrition game is different from the games that we have learned about in several respects. For example, the war of attrition game is not simultaneous, instead occurring in discrete rounds. In addition, a player’s strategy is defined not only by what all of the other players are doing, but by their stock of resources as well. Using these ideas, I’ll put together a simplified model of the Syrian civil war. There are two players, A and R, A being Assad’s forces and R being the rebel forces. The game is divided into different weeks of battle. It costs another one million Syrian pounds for a side to keep up the fight for a week. So, A and R have identical strategies each week: either pay another one million pounds (P), or surrender (S). Lets consider the payoff corresponding to each case. If both A and R choose strategy P in the same week, the payoff to each player is zero, since the game will continue without a winner. If both A and R choose strategy S in the same week, then the game is over, and the payoff to each player is again zero. The final case is that one player chooses P and the other player chooses S. Then, the payoff to the player who chose P will be positive, say +5, and the payoff to the player who chose S will be negative, say -5. The last two cases cause the game to end. In each case, the cost of the game to each player is equal to 1000000 * W (in pounds), where W is the number of weeks that have passed. As the rounds go on, the players will begin to exhaust their resources, and they become more likely to choose strategy S. But what if one player runs completely out of pounds? The game ends in this case as well, probably in a more violent, more total fashion. The payoff to the winner will be +10 and the payoff to the loser will be -10. In either case, the cost to each player is equal when the game ends. A final insight about the game is this: this game is an all-pay auction, where the winner is the player who is willing and able to spend the most pounds. The leadership of Syria depends on the outcome of an auction.
From this analysis, it seems a wonder that the rebels are still fighting. Their digital camera scopes have nothing on Assad’s cluster bomb supply chain. They’re outmatched in terms of resources. But there’s more than just game theory at work here. The rebels have at least two things going for them, the United States, which has recently stepped up its sanctions against Assad’s allies, links in his supply chain, and their own enduring belief in their cause. So, does game theory tell us everything?
-ras578