Colonel Blotto, Game Theory, and the Election
Colonel Blotto, in essence a simple game, may actually be able to help us in predicting the election in November. A recent Forbes article summarizes the game and its applications. Put simply, the game describes a Colonel who is waging war. He must divide his troops into a number of regions, and his opponent must do the same. The region with the most troops wins the region, and the Colonel with the most regions takes the game.
The author describes the following example to illustrate the the game’s complexity: if the Colonel has 5 regions and 100 troops, he could take a seemingly reasonable approach and divide them evenly as such: (20, 20, 20, 20, 20). However, a slightly more clever opponent might in response divide as follows: (24, 24, 24 ,24, 4), taking four out of five regions in a landslide with a simple change.
As we discussed in class, we presumably should go about looking for a Nash equilibrium for this game. This is difficult for two reasons: 1) any strategy can dominate any other strategy, a la rock, paper scissors, and 2) the amount of strategies is staggeringly large. The scale of the numbers falls under the realm of partitions, which describes the ways of writing an integer as the sum of other integers. For only 100 troops, there’s already almost 200 million strategies. But according to the article, computer scientists from Stanford, the University of Maryland, and Microsoft have developed an algorithm to solve the game, involving reducing the staggering domain of strategies.
But how does this relate to the election? Fundamentally the game of Colonel Blotto is a very useful abstraction. The most interesting games are the ones that are so simple in rules, and yet so complex in emergent strategy, and these are the same types of games that tend to describe all manners of phenomena in real life. For Colonel Blotto in particular, the divisions of troops and the winning of regions is clearly analogous to winning voting districts and dividing resources, as the author mentions.
The author thinks that the true test of these new algorithms would be predicting a battle of the Blotto sort on the immense scale of a US election. While I’m not sure these algorithms will utilized as quickly and practically as the author seems to think, Colonel Blotto is still a fascinating puzzle that underpins our lives, whether we know it or not.
http://www.forbes.com/sites/kevinknudson/2016/02/23/solving-colonel-blotto-resource-allocation-and-game-theory/