The Prisoner’s Dilemma of (Not) Attacking Trump

This is a pretty obvious point, but one I haven’t heard made before: it can be individually rational for candidates not to attack Trump directly, even if the non-Trump candidates as a whole would be better off if Trump were attacked. The conditions for this don’t require a complicated or unlikely story like the one Jeb Bush’s idiotic advisers were telling him, that Trump would draw votes away from other candidates in Bush’s “lane,” allowing Bush to emerge unscathed. All that is required is for Trump to be able to retaliate against the first candidate to go negative against him sufficiently effectively that the costs outweigh the benefits.

For example, consider the following simplified scenario, which is quite optimistic about the potential efficacy of attacks on Trump, but still results in a no-attack equilibrium:

Trump has 35 percent of GOP support.

Cruz and Rubio both have 25 percent of GOP support.

The first candidate to attack Trump draws off 10 percent of Trump’s support.  This support is allocated evenly among Cruz and Rubio. Trump and his followers can retaliate to draw off 8 percent of the support of whoever initiates the attack, which is allocated between, say, Kasich and Carson.

If the two candidates attack Trump simultaneously, they draw a total of 16 percent from Trump’s support. Trump’s  retaliation becomes less effective as it is directed against more candidates- if two candidates attack simultaneously, Trump can only draw off only 4 percent from each.

This results in the following payoff matrix:


This is the famous Prisoner’s Dilemma, of course, usually framed in terms of prisoners who are induced to confess to a crime (and implicate their accomplice, the other prisoner) rather than stay silent and be convicted of a lesser crime.


The key characteristic of the Prisoner’s Dilemma is that even though the two Prisoners would both be better off if they remained silent, relative to both confessing, it is in the individual interest of each one to confess, since whatever the other prisoner does, they are better off confessing.

Similarly, in the scenario above, even though Cruz and Rubio might be better off if both of them attacked Trump than if neither did, it still is individually rational for each of them not to attack. Whether Cruz attacks or does not attack, Rubio is better off not attacking; whether Rubio attacks or does not attack, Cruz is better off not attacking.

Everything depends on your assumptions, of course, but the conditions are easier to meet, in general, with multiple players (or more candidates involved) than with fewer. And if somehow you ended up with only Trump and one other candidate, the Prisoner’s Dilemma, if it was one, would disappear.

Of course, by then, Trump might well have secured the nomination.



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