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Game Theory and Republicans

In light of the upcoming [note: this was written before the debate] Republican presidential debate, I thought it’d be apt to highlight an interesting dimension of the event: the game theory behind the political jostling. It makes sense that each candidate’s actions would be predicated on the actions of others, and that each presidential hopeful would want to pick a the strategy most conducive to his or her political success.

As said by Steven Brams in a recent article in the guardian (linked below), “Candidates could be aggressive in general, aggressive against a particular candidate, try to appease the rest of the field, try to look moderate – those are the strategies I think we’ll see.” And one candidate’s adoption of these strategies is dependent on what all the others choose. For example, if one candidate is aggressive and another is moderate, the exchange might look good for the aggressive candidate. However, two aggressive candidates might enter into a heated argument that could reflect poorly on both of them. And with stakes as high as they are during an election, the candidates don’t want any additional heat.

It’s not certain whether there will be any Nash equilibria involved in the debate, but it’s possible to conceive of some scenarios that might be fecund for equilibrium. If the topic of the debate is a politically charged issue, and two candidates are chosen to speak on it, then we might see a “hawk and dove” Nash equilibrium: one candidate will be aggressive (hawk), and the other will be more passive (dove). Should this occur, the aggressive candidate might look better on the national stage, but the candidate playing the passive role is not incentivized to escalate his behavior. Two aggressive candidates could break into an exchange that could damage both of their careers.

This disinclination to engage in a scandalous argument doesn’t extend to the frontrunner, Donald Trump. The current leader of the republican presidential chase seems to thrive off of political controversy, and his lack of filter makes his intended “strategy” pretty obvious: he’ll be aggressive. As such, candidates will have to decide how much to placate him, knowing that he won’t hesitate to ignite an ugly fight. As such, a Nash equilibrium that is likely to form is a dominant trump and a passive group of other candidates.

One thing is clear: most candidates won’t have a dominant strategy. Being aggressive with the wrong candidate—or over the wrong issue—could spell disaster, but being entirely meek won’t win primary elections. These candidates need to distinguish themselves, but they can’t do it in volatile situations, and the way to determine the optimal strategy in a given situation is through game theory.


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