Game Theory

Discussion on “Game Theory for Swingers: What states should the candidates visit before Election Day?” by Jordan Ellenberg (Slate Magazine, October 2004).

The 2004 article by Jordan Ellenberg, an associate professor of mathematics at the University of Wisconsin, uses the real-world example of the Bush v. Kerry presidential race to how game theory applies to politics. Specifically, Jordan discusses the three swing states, Pennsylvania, Florida, and Ohio and how Bush and Kerry should go about campaigning in these states for the best chance to win. Each candidate’s decision depends in part on the other (interdependence, the key point to making this an example of game theory as we discussed in class). Kerry needs Pennsylvania to win, but focusing his assets there would leave Ohio and Florida up for grabs. Bush could go pick off Pennsylvania, but then it leaves Florida open for Kerry. Game theory helps solve this dilemma. Jordan simplifies the problem by narrowing it down to just the three states (rather than include the other 47), and sets the percent chance Bush has of winning each state’s electoral votes. The first scenario that Jordan discusses leaves Bush with a dominant strategy in which the option is clear: campaign in Ohio for the best chances to win. Because campaigning in Ohio is also the dominant strategy for Kerry, that result is a Nash equilibrium. The second scenario that Jordan discusses is a bit more complex, one with a much more subtle Nash equilibrium, this one dependent on chance. Because of that, the second scenario finds equilibrium through a mixed strategy (rather than a dominant one). Jordan sums up the example by reminding the reader that the true situation is not this simple, and that finding the actual percent chances of victory in the separate states is difficult. However, he successfully describes how game theory can be applied to politics. As previously mentioned, connections from this article to our class discussions come through Jordan’s mention and explanation of dominant strategies, mixed strategies, and the Nash equilibrium.

To look at game theory in a different light, let’s comment on a quote Jordan used in the article: “The key is that rational behavior tends to be predictable, and in a game of strategy, predictability will leave you with a decided disadvantage.” When interdependence determines what strategy should be used, predictability leads to a party’s demise. If a party’s actions are predictable, his opponent is allowed the opportunity to counteract his predictable move in order to strategically win. Randomness allows a “player” to conceal his strategy so that his opponent cannot absolutely anticipate his move and act accordingly. This decreases the opponent’s certainty of “winning.” Thus, it is strategically to a party’s advantage to act in a spontaneous function. Consider a shootout in soccer. A kicker can position the ball to the left, to the right, in the corner, on the ground, etc. If a kicker clearly positions his body in a way that is indicative of where he intends to position the ball, the goalie’s chance of blocking the ball is increased. However, if the kicker approaches the ball straight on or in a position that is not consistent with how he will actually place the ball, the goalie may not have any indication as to where he will kick it, or will be misled. Here, the kicker has used the element of surprise to his advantage.

While Jordan uses the party system as one real world example of game theory application, another real world application of game theory is the prisoner’s dilemma. This is a thought experiment essential to game theory. An example of the prisoner’s dilemma is this: prisoner A and prisoner B have both been arrested for robbing a bank. They have been placed in two separate cells. Each of the prisoners has been given two options; they can either confess or remain silent. They are both told the same thing by the police: “If you confess and your partner remains silent, then you will go free and your testimony will be used to make sure that your partner will serve 15 years in jail. On the other hand, if you remain silent and your partner confesses, then they will go free and you will serve 15 years. If you both confess, then you will get early parole after 10 years. If you both remain silent, you will each get 2 years or less.

There is a dilemma here because each of the prisoners is better off confessing than remaining silent. However, the result of them each remaining silent is much better than the result of the both confessing. This creates a dilemma and a clash between decision-making based on self-interest versus the best interest of the group. There are many conflicts of interest that arrive from this.

Posted by Maddie, Dalton, and Jed (Section 3)

Resources:

http://plato.stanford.edu/entries/prisoner-dilemma/

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