Donald Trump and the GOP’s Nash Equilibrium

Why is Donald Trump continuing to go from strength to strength in the GOP presidential primary? Why on earth can’t any of the other nine or so at least semi-viable candidates seem to slow his momentum, no matter how many vile or idiotic things he says? One popular explanation is that a large percentage of the GOP base is — in their worst and most self-indulgent moments — delighted by his vileness and idiocy, and I don’t deny that explanation a measure of plausibility.

But attending to the Republican base doesn’t explain the candidates’ behavior: why don’t the other candidates join forces in a coordinated effort to take Trump out of the race? If they all spent a week shining a floodlight on his insanity, repeating every nonsense promise he makes and offering plausible alternatives, and insisting that none of them want to have any part of a party that will nominate someone like him, he’d be out of the race in no time. He’s still in the race because the other candidates haven’t gone after him with the fury with which he’s gone after them.

Why isn’t that happening? Well, there’s a “solution concept” in game theory called a “Nash Equilibrium,” which says that each player in a game (the presidential primary) is likely to adopt a playing strategy that minimizes her losses in the event that no other player cooperates with her. In other words, it’s a solution “in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.” A classic example of this is the “prisoner’s dilemma”: John and Jane are both arrested for a crime they didn’t commit, and then individually told that they’ll receive one of four sentences: 20 years’ imprisonment for John if Jane confesses to the crime but he doesn’t, in which case Jane will receive a sentence of two years (or vice versa); a sentence of eight years if both confess to the crime; and a sentence of three years for both if neither confesses to the crime. The “Nash Equilibrium” in this case is that both confess — you have the possibility of just two years, and are guaranteed no more than eight, whereas by not confessing, you risk twenty years. The optimal solution (with a total of only 6 years of jail time) is simply too risky to be worth trying. (Spengler recently offered an interesting application of this concept to Iran’s and Turkey’s interests in the war in Syria.)

How does this apply to the presidential primary? All the non-Trump candidates surely know that the best possible outcome is for them to cooperate in eliminating Trump. But all of the non-Trump candidates also know that if they move aggressively on Trump and the other don’t, they risk looking petty and vindictive — maybe they’ll knock Trump out of the race, but they’ll likely be too damaged themselves to beat the remaining candidates. (It doesn’t help that political rivals are probably the only group of people on earth less likely to cooperate than a random assortment of rival gang-members.) If you have to choose between death right now and death in two weeks, of course you choose two weeks — and so the candidates slowly allow their poll numbers to be bled by Trump’s vitriol and bombast, because they fear that acting alone will mean swift and certain demise. It’s a Nash Equilibrium, folks.

That doesn’t mean, of course, that Trump is definitely going to be the nominee — hopefully he’ll still find a way to do something that even Mississippians won’t be able to stomach, and that will be that. But it looks increasingly likely that if he goes out of the race, it will have to be his own doing, not that of the other candidates.

This entry was posted in Donald Trump, Game Theory, GOP, Nash Equilibrium, Presidential Race 2016, Republican Primary and tagged , , , , . Bookmark the permalink.

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