Last year in August I was warning the media was underestimating Trump. I suggested his strategy of retaliation, his threat to run as a third party, and his railing against political correctness were surprisingly effective tactics. Nate Silver, who predicted Trump did not have a realistic chance, was wrong, and eventually admitted so: “we basically got the Republican race wrong.”

How did Trump manage to beat out 16 other Republican candidates? Many point out that Trump dominated the media coverage. Every news station was showing his rallies live and opinion shows even let Trump phone in many interviews. Although voters may have wanted more equal coverage of candidates, the media had a financial incentive to cover Trump. It played out a lot like the equilibrium of Hotelling’s location competition game.

Now Trump is the presumptive Republican nominee. I have been seeing more articles that analyze Trump’s actions using game theory. In this post I want to share a couple that I enjoyed. RollingStone explains the game theory of Trump’s strategy and suggests how a rival could exploit his weakness. Another article comes from Justin Wolfers, on New York Times Upshot blog, who explain what to deduce from Trump’s unreleased tax returns.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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What Game Theory Tells Us About Donald Trump

We typically characterize successful leaders as smart people employing sophisticated strategies. The best sports coaches are said to engage in the mind games of a chess match to outthink the opponent. The best companies today are said to use big data analysis to predict future trends. The best artists will experiment thousands of variations to find the words or the colors to evoke a specific emotion.

We may forget that sometimes it’s best to keep it short and simple. Trump’s frequent and spontaneous outbursts suggest he did not craft a master plan to outthink 16 other candidates. Rolling Stone points out his strategy was about as complicated as a “four-line computer program.” And the maddening part is the strategy has been working.

The article makes an interesting argument that Trump is using a tit-for-tat strategy. If you are nice to him, he will be nice in return. If you are mean to him, he will be mean in return. And after a small feud, everyone will make up and start over, playing nice again. In 1980 there was a famous tournament where computer programs faced off in a repeated prisoner’s dilemma. Many people submitted complicated strategies. But in the end, the strategy that had the highest average payoff was surprisingly only four lines long: it was the tit for tat strategy.

The narrative seems to fit Trump well. He has often responded in kind to others, and mostly he has started off playing nice. Whereas the other 16 candidates had complicated strategies, it was Trump that ended up with the highest average payoff to outlast everyone else.

However, the media often calls tit for tat the best strategy. This is not true. The key is that tit for tat does well on average against many other strategies. If you put tit for tat against a program playing a random move, then its performance sinks. Also, it is possible that tit for tat can end up with both sides retaliating and that will continue forever. This kind of death spiral means a more forgiving strategy could do better.

Rolling Stone argues that knowing Trump’s simple strategy should offer insights on how to defeat him.

For example, someone could confront Trump on something from his past. The Washington Post reports Donald Trump masqueraded as publicist to brag about himself. As predicted, Trump responded in kind. He first denied it was him. Then he retaliated by continuing to take shots at the Washington Post.

But will this really be an effective strategy? The story has a twist: the reporter who did the interview claimed she did not leak the tape, and since there were only 2 copies of the recording, she suggests it could have been Trump who leaked it!

It may not be so easy to beat the “Tit for Trump” strategy after all.

Check out their article: What Game Theory Tells Us About Donald Trump

What We Can Learn From Donald Trump’s Unreleased Tax Returns

Justin Wolfers applies game theory reasoning to Trump not releasing his tax returns. Is there anything we can infer about his tax returns, even if we cannot see them?

He uses the analogy of the market of lemons, which I have written before as follows:

Imagine you’re buying a used car using online car listings. You investigate the market and find listings ranging from $17,000 to $23,000. You’re in email contact with the owners and you’re trying to get the best deal. You’re participating in a marketplace with smart buyers just like you. Which car are you likely to buy?

The seller of the car knows the quality of his car.

However, you, as a buyer, cannot distinguish good quality cars from bad quality cars. This means your best estimate of a car is an average level of quality. You and other buyers reasonably will not offer more than an average price for cars of average quality.

The most buyers are willing to pay for a car is the average price $20,000. In the marketplace of cars, the range of offers shrinks in half.

The key part is what now happens to sellers. A seller that has a high quality car is not willing to sell the car for an average price. So a seller of a high quality car removes his car from the market.

In this new market, there are cars listed that range in quality, and the listings go from $17,000 to a maximum of $20,000.

What happens now? Pretty much the same thing happens again! You, as a buyer, cannot distinguish between the average cars and the worst cars, so you are at most willing to pay the new average price of $18,500. The market for offers shrinks again. But then even more sellers of high quality cars are unable to find suitable buyers. This means even more sellers leave the market.

The process can repeat over and over until the only sellers that remain offer the lowest quality cars–it’s a market full of lemons.

What does this have to do with Trump’s tax returns?

Trump is kind of like a used car seller in this game. He knows private information about his tax return. We, as uninformed voters, can at best make an educated guess about the quality of his return.

At the start we would estimate that all politicians have an average quality of tax return: somewhere between shady and honest. As politicians campaign, however, each has a chance to reveal the tax return and let voters learn information.

Candidates with sparkling tax returns will want to immediately release their returns. They want to separate themselves from other candidates who have less honest returns.

Once this happens, there is a cascading effect. The candidates with the next most honest returns will want to release their returns. Although they do not have the best returns, it is better to show they are of higher quality than those with unreleased returns.

The process continues. If a candidate dodges and delays releasing a tax return, then a voter may want to infer the candidate’s tax return is below the average of the other unreleased returns. Is Trump trying to hide something?

Then again, this process assumes that voters are rational and can use k-level logical reasoning. Assuming rational voters may not be the best way to analyze this particular election which has defied all kinds of logic.

Read the article on New York Times: What We Can Learn From Donald Trump’s Unreleased Tax Returns