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Game Theory and the GOP debate

http://www.washingtonpost.com/blogs/monkey-cage/wp/2015/09/18/what-game-theory-tells-us-about-wednesdays-debate-and-the-republican-primary/

http://elections.huffingtonpost.com/pollster/2016-national-gop-primary

 

When Donald Trump was topping the polls in early July this year, many thought it was only a matter of time before he either self-destructed or grew disinterested. Over two months later, his lead has only grown more secure, owning a 17.2% advantage over his closest competitor as of September 19. Many are concerned with the prospect of Trump having a valid prospect of leading the United States and have made observations that, when put together, lead to a strategy for how those rivalling Trump can approach debates with maximum effectiveness.

The most important of these observations is that voters are strategic, meaning that they will vote for candidates who are slightly farther away from their ideals who have a better chance of winning over a candidate that fits the voter’s liking perfectly but doesn’t have a good chance of winning. Many of the candidates that are currently not supporting Trump would prefer another serious GOP candidate to Trump. Therefore, for a candidate to overtake Trump, the voting population that is currently not voting for him will have to converge on a candidate that they think will be able to properly overcome him. The problem is that, at the time of the article, it was not clear which candidate the people should rally behind. Here is where the game theory comes in. We can think of a payoff matrix such as this one to demonstrate the situation:

 

Carson supporters\Bush Supp. Carson Bush
Carson 10, 6 0, 0
Bush 0, 0 6, 10

 

The top-left and bottom-right options are (10,6) and  (6, 10), respectively because the supporters that get a 10 payoff will see their preferred candidate progress in the election. Meanwhile, the supporters that get a 6 payoff get the satisfaction of knowing that Donald Trump will not be president. Alternatively, if Donald Trump does move on, then both supporters of Carson and Bush are severely disappointed and get no benefit. The resulting matrix looks like a typical “Battle of the Sexes” payoff matrix. With this matrix, it can be very difficult to predict what will be chosen, and is typically decided by conventions between the two players.

The outstanding contribution of this article is to identify the convention that exists between the voters – speaking time. Patty declares that the more time a candidate spends speaking, the more they become a focal point of the debate, which will lead to a convergence of the non-Trump supporters on that candidate. This leads to a strategy in which these two candidates should not speak about each other for fear of letting the other candidate into the conversation and making that candidate more of a focal point.

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