Trump: can game theory explain the inexplicable?

Trump: can game theory explain the inexplicable?

We like to think of ourselves as pleasant people rationally thinking through our actions ­- so it’s a shock to our psyche when confronted with a system failing as alarmingly as the 2016 Republican Nomination contest. Betting markets -­ believed by many economists to be the best predictors of election results ­- give Donald Trump as much as an 60% likelihood of becoming the Republican Nominee. A man who has advocated a ban on Muslim immigration and entertained the theory that Supreme Court Justice Antonin Scalia was murdered is now being described by The Economist as ‘almost unstoppable’. It’s almost too bizarre to understand.


Fortunately, economists have developed game theory as an apparatus to explain the inexplicable ­- and two simple insights from game theory explain much of Trump’s success. Less fortunately, game theory gives hints to the future as well as explaining the past ­ and its predictions are far from reassuring.


1. The Candidate’s Dilemma: To Drop Out or Bat On?


One way to understand the Nomination process is as a simple volunteer’s dilemma-­style collective action problem. Most voters dislike Trump, but their votes have (until recently) been split three ways between the remaining candidates: ‘establishment’ Republicans Marco Rubio and John Kasich and Tea Party darling Ted Cruz. The longer the vote is split, the more states Trump wins, so each candidate wants his competitors to drop out; yet each places their self-­interest in potentially winning the nomination first, and stays in the race ­ to the group’s collective detriment.


This view of the race has been featured in The New York Times and endorsed by Rubio and Cruz. It now looks to have resolved itself: though candidates will put self-­interest first while there’s some chance of winning the nomination, they should pull out to save face when the odds of success fall to essentially zero ­- as was the case recently for Marco Rubio, after his loss to Trump in his home state of Florida. But meanwhile, Trump’s been able to amass a large delegate count ­- and our second insight from game theory suggests it may be hard to surmount.


2. Trump and the Joys of Irrationality


Game theory gives Trump an advantage in winning states, but this itself won’t secure the nomination. The Republican Party establishment holds power over the eventual nominee: it could organise popular Governors to denounce Trump; it could encourage delegates who Trump has nominally won to ignore the decisions of primary voters; even if Trump won a plurality of delegates, it could refuse him the Nomination at a brokered convention.


At first glance, Republicans seem to have every reason to use those tools: Trump is hated by many Republicans and considered an election­-losing candidate who’d do a world of harm to the party’s image. But it’s unlikely that they’ll go for broke in their attempts to defeat Trump ­- and game theorist Thomas Schelling explains why.


Economists are known for their dreary hypotheticals, but Schelling’s are more dramatic than most. He asks us to put ourselves into the following (adapted*) situation. Midway through a trip from home, an armed robber bursts into our house hoping to access our life’s savings, which, rather anachronistically, are locked in a safe. The robber doesn’t know the code, but informs us that, if we don’t reveal it immediately, they will torture our family until we do so. We seem trapped: any rational person would give over the code to avoid the worse alternative the robber is threatening.


But Schelling sees a way out. If we could drink a potion to make ourselves irrational, and prove to the robber that we had done so, there would be no need to reveal the code. The robber would have no reason to torture our family; such an action would be unpersuasive to us, in our irrational state. Our blindness to the robber’s threats has turned out to be in our interests: it’s blunted the threat’s power entirely.


It’s a strategy Trump’s been exhibiting in spades. Don’t get me wrong; I have no doubt that Trump is genuinely irrational, rather than affecting it for strategic purposes. But, in game theory terms, the result is the same. Trump’s been able to deter the Republican Party from taking strong action against him, by threatening that he would respond by running as an independent in the general election. Though Trump pledged last September not to do so, he’s since clarified that an independent bid will be back on the cards if he is treated unfairly by the Republican Party.


This is a threat no rational politician could credibly make. An independent would find it almost impossible to win the Presidency: she would lack endorsements, funds and a campaign infrastructure; in some states, she would be prevented from even appearing on ballots; and even in the best­-case scenario, she would split the Conservative vote between herself and the eventual Republican nominee, with the result that neither would win enough states to be competitive. The Republican establishment wouldn’t take seriously any rational candidate who threatened an independent run: they’d know that it wouldn’t be in her interests to do so.


The threat only becomes meaningful when it comes from an apparently irrational candidate like Trump, who would be willing to run an almost inevitably doomed independent Presidential bid for the sole purpose of punishing the Republican party.


Paradoxically, Trump’s most obvious liability ­- his apparent irrationality -­ could be his greatest asset as his campaign for the Nomination continues.


It’s a result only an economist ­- or a realty­-billionare­turned­-Presidential­-candidate -­ could dream up.


*The example is adapted from Dodge, R 2012, Schelling’s Game Theory: How to Make Decisions, Oxford University Press, Oxford.