Game Theory in Pokemon
http://bulbanews.bulbagarden.net/wiki/Crunching_the_numbers:_Game_theory
First, I’d like to qualify my choice of article. I don’t believe that this particular article holds any ground against any formal game theory paper, but I think it does offer a fantastic introduction to several topics we discussed in class. The author, Danielle Detering, first introduces payoff matrices through the prisoner’s dilemma problem with Pokemon characters. She walks the reader through the analysis, and then proposes a much harder, more involved problem involving the Pokemon video games.
Of course, this article explores a manifestation of game theory in everyday life, which is fun and exciting. But it goes deeper than that. Networks class today (Wednesday 9/7) ended with the notion that even two player games can have hundreds of possible strategies, making them impossible to analyze by hand. And this is the feature of the article that really interested me: the way the larger problem (the second one) was broken down. The original problem listed 6 strategies per player, leading to 36 possible “pure” Nash equilibria alone. Examining each of these would already prove difficult, and this is without even accounting for mixed equilibria. The author recognizes this, though, and starts to break down the problem into smaller parts. She recognizes that “some moves are just flat-out better than others” – perfect examples of strictly dominant strategies – in order to reduce the number of possible strategies. Of course, this leads to a parallel change in the other player’s strategy, since they will realize you will never use the sub-optimal strategies.
That being said, I think my biggest takeaway from this article is that this problem (and probably many like it) is still far more difficult than the author recognizes. I am convinced that the steps she uses to reduce the size of the payoff matrix, though useful, result in a loss of some properties of the original game. In other words, the problem she ends up solving doesn’t match up with the situation that she started with. I imagine this happens frequently in these types of problem, and the author herself mentions that “there could be outside influences that this model does not account for”.