Colonel Blotto Game
In this article, researchers study the Colonel Blotto game. The game provides each of two players the same starting number of troops, and each player must decide how to allocate these troops among five territories. A player wins a territory by allocating more troops to that territory than does the other player, and a player wins the game by winning at least three of the five territories.
As we learned about in class, the researchers note that the optimal strategy is actually a randomized (mixed) strategy. However, they bring up the important point that game theory sometimes ignores biases and effects that come up in practice. In particular, they say, “the agents in classical game theory are assumed to be fully rational: they base their decisions solely on maximizing utility, are capable of performing very complex reasoning and assume that their adversaries are equally rational.” I found this interesting because it slightly limits the applicability of the proof that a Nash equilibrium always exists.
To see what kinds of biases affect the behavior of players in the Blotto game, the researches implemented it as a Facebook game and collected data about each round. One of the biases they discovered was that the geographical position of the territories affected how players allocated troops. They even found that the relationship between the two players of the game affects the distribution of troops among territories. So, although classical game theory provides a base from which to reason about the likely outcome of the Blotto game, it is important to be aware that it cannot always take into account social and psychological biases.
http://research.microsoft.com/en-us/um/people/pkohli/papers/waterloo_analysis.pdf