Should Marco Rubio or Ted Cruz drop out? (Republican Primary Prisoner’s Dilemma)

Our friend and colleague Steve Landsburg makes the following two observations on his blog: (i) “for either Ted Cruz or Marco Rubio to become the Republican nominee, he must first consolidate the anti-Trump vote, which is to say that either can succeed only if the other drops out,” and (ii) “Cruz and Rubio have approximately equal chances of driving each other out” between now and the last primary. Given these premises, Professor Landsburg then proposes that Cruz and Rubio toss a fair coin to determine which man should drop out of the race. According to Landsburg (emphasis in original): “This [a coin toss] gives each of them only a 50% chance of survival. But if they’ve already each got only a 50% chance of survival, that’s no loss. And it substantially increases the value of survival, because it gets things over with now instead of a month from now.”

For our part, we like Landsburg’s proposal, but here is why we think neither Cruz nor Rubio will ever agree to let a coin decide their political fates. In brief, they are locked in a political version of the famous prisoner’s dilemma: both would be better off cooperating (i.e. agreeing to the coin toss), but the logic of defection (i.e. “I stay in; the other guy drops out”) results in mutual defection (both stay in and both lose).

Update (3/2): Ken B writes that our prisoner’s dilemma analogy does not apply here because Senators Cruz and Rubio “are not in a one time game [;] they have careers and future elections.” Ken B makes a good point. In our democracy, elections are really more like an iterated or repeat game since there are presidential elections every four years. But we think Ken B is wrong in this particular case because of the inherent uncertainty in future election cycles. Furthermore, unlike Kasich and Carson, both Cruz and Rubio are serious contenders, and both want to win their party’s nomination in this election cycle. As a result, this year’s election is for all practical purposes a one time game. Lastly, we would add that the payoff for mutual defection will occur very soon (i.e. both Cruz and Rubio will lose to Trump), as it now appears that Trump will wrap up the nomination in a matter of weeks unless either Cruz or Rubio drops out.


Which one should drop out?


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