Top Trump: The Game theory of the Trump endgame

pres15-001For those of us outside the US, the Trump entry into the US Presidential race so many months out from the actual election has been entertainment heaven. Sure, he is destroying the fabric of a great nation by bring horrific stereotypes and misinformation to the fore, but sometimes that is the price to pay for depravity.

But there is a strong sense that this will come to an end. There is no one who believes he will be the Republican nominee, let alone President. Our favourite prediction markets have the odds of the former at 7% and the latter at 3%; both actually higher than the priors of most. The real question is how long will he last. To be sure, as viewers our interests are in him lasting some time, but when we put our rational heads on, what prediction do we get?

To apply game theory to all this, we need to make some assumptions:

1. The GOP will not nominate Trump

2. For Trump, running and losing has more disutility than not running. I don’t know this for sure but I am willing to go with it. Trump doesn’t strike me as someone who wants to be tested.

3. For Trump, losing as a third party candidate involves less disutility than losing as the GOP nominee.

4. Trump could not stand to be at an event without being the centre of attention.

5. Trump is not really able to “work for it.” In other words, coming from behind isn’t in him.

That should do us to get some predictions.

First of all, let’s consider the actual primary race that starts early next year. The Iowa caucuses aren’t really that critical for leading candidates but New Hampshire is. The chances are, the field will have shrunk enough by then that, whomever is the alternative to Trump, will actually poll higher than Trump in New Hampshire. Thus, being at that race for Trump means losing.

Second, given this, he won’t run in that race. He has two options. First, to pull out for the GOP race prior to that and run as an independent. Second, to pull out of the race entirely for that citing medical reasons. This last one is appealing as a prediction as it satisfies Trump’s preference assumptions. If this is the case, however, he will want to do this when it was still the case that he had a chance in New Hampshire. That way he can claim “I was going to win, but what can you do?” Effectively, the Republican equivalent of Bobby Kennedy although with a healthier degree of endogeneity to the decision.

Third, what this means is that running as an independent isn’t likely to happen. When we get to just the point where the medical exit or mexit is feasible, the mexit option will be taken. So there will be no opportunity for the independent run at that stage.

Fourth, which brings us to now. The first Republican debate is next week. Trump and nine others will be on the stage for a couple of hours. Think about that for a moment. Trump will be on stage with nine other people presumably with rules that will require him to spend 80 to 90% of the time listening to others speak. We are all tuning in to watch it. But to be sure, we are doing so because we don’t think that can happen.

Fifth, in addition, there is a strategy available to the other candidates. We can term it “Top Trump” or alternatively the “Quayle Fail.” Remember when Quayle stood there like a stunned mullet against Lloyd Bentsen. If one of the other candidates can get that reaction or sometime equally embarrassing from Trump, not only will Trump be out of the race but that candidate will become the leader. Basically, the “vanquished Trump” title is a game winner. But it will take something big and if someone can do it, they deserve kudos up the wazoo.

Sixth, just before you get too excited, the game theorist in me has to tell you that Trump will surely know about the “Top Trump” possibility. He’ll be watching for it. Obviously, if someone can do it, it is too late for him.

Seven, points 4 – 6, suggest that there is a reasonable probability that Trump will pull out of the debate or, at the very least, be off the stage early to destroy it. He’ll claim “why am I on a stage with all you losers” and that will be it. It is a clear win-win for Trump. A debate does him no good and carries risks — especially at this stage.

Will that mean that he forms a third party then and there or that he pulls out altogether shortly after with a mexit? Sadly, this is as far as my game theorist’s predictive lens will take me. My point is: I hope I’m wrong but our entertaining run seems like it will come shortly to an end.

Gladwell misses some game theory

Re-published from Medium

Malcolm Gladwell has a new book out entitled David and Goliath. It is about underdogs and is based on the classic David vs Goliath setting in which a shepherd, David, defeats a giant, Goliath. I have yet to read the whole book — this isn’t a review — but in the very first chapter I was struck by logical flaws in Gladwell’s account of the original David and Goliath match-up. (If you don’t have the book you can watch Gladwell’s recent TED talk for an account).

In what you would expect from Gladwell, he argues that the original David and Goliath biblical account and, in particular, its interpretation is not what it seems. Indeed, he argues that David was, in fact, the giant and Goliath was the underdog and things played out as if the powerful struck down the weak. Suffice it to say that I expect that his revised account is somewhat likely to undermine the theme of the rest of the book but I won’t worry about that in what follows.

So the original story is that the Philistine and Israelite armies stared each other down across a valley. To resolve the impasse, the Philistines sent the armour-clad giant, Goliath down as their champion. The Israelites had no takers until David, then a shepherd boy,volunteered to fight Goliath. Armed with only a sling, David landed a stone between Goliath’s eyes, he fell and David decapitated him with his own sword. Then the Philistines fled in panic.

But Gladwell, and his revision is based on the work of others, suggests to us that things were not as they seemed. In fact, Goliath was not necessarily so strong. He was led to the field and likely suffered from a disorder that simultaneously accounted for his height but also likely left him with poor eyesight. That said, the potential weakness of Goliath probably wasn’t significant as Gladwell’s alternative account would be exactly the same if Goliath were the mighty and healthy warrior he was made out to be.

The focus is David. Was he really the underdog he seemed to be? Gladwell argues that, in fact, those soldiers who were skilled in projectiles were a key part of ancient warfare. A sling in skilled hands could have the power of a gun. In that respect, David outmatched Goliath and it wasn’t that surprising he was able, in short order, to fell the giant. In fact, Gladwell argues, everyone at the scene would have understood that.

Then he reaches into his shepherd’s bag for a stone, and at that point no one watching from the ridges on either side of the valley would have considered David’s victory improbable. David was a slinger, and slingers beat infantry, hands down. (emphasis added)

And therein lies the issue: if no one at the scene was surprised by the outcome, how did that outcome arise?

First, the Philistines would have known that slingers were powerful and would surely assume that the Israelites had some. So why send the giant down for such a key battle?

Second, perhaps Goliath could handle a slinger. But, in which case, why did he not act like it? Why not move around? Why not protect more of the head from stones with armour that was everywhere but his face? Even if he could not see well to see what he was facing, he saw enough to know it wasn’t a be-sworded foe. Goliath would have to be incredibly stupid as well as weak. And again, why would the Philistines place their bets on him.

Third, why did the Israelites send David? By all accounts he was not battle hardened. If you have experienced slingers and you see Goliath, you send one of those. No bravery required. Instead, apparently, no one else sees this opportunity but David. To be sure, as we later find out, he was a capable fellow but King Saul was in charge of military resource allocation and surely had other options.

In fact, the actions of everyone else — other than David who may have had private knowledge of his ability, exceptional courage or, let’s face it, it is a biblical story, something powerful on his side — suggests that they saw the game being played out as a classic David-Goliath battle where David was the underdog and was not expected to win.

We know, as Gladwell himself accounts for but does not consider, that no one at the scene thought David would win. The Israelites tried to arm him. The Philistines fled the scene after the battle apparently in total shock and thinking that there was an army of Davids on the other side of the valley. And Goliath himself had an unexpectedly bad day.

In accepting a revised account, Gladwell fails to consider that the two person battle was part of a larger game and the players in that game clearly do not agree with his revised account. Had they, this classic story would surely never had begun.

Instead, we are left with the plausible account that Goliath was formidable, was known to be so, only David knew he had a chance and everybody was surprised he won. And herein lies a key lesson of David and Goliath stories: for a real underdog to unseat a giant, underdogs, in general, must really be underdogs with little chance of victory and the few times they do win are because there was unexpected exceptionalism.

What is ‘face’?

I have been part of a research group looking into Chinese migration for about 5 years now (see, and the main cultural difference one has to get used to as a Westerner in interactions with the East is the notion of ‘face’. This Asian cultural trait has been written about for centuries, but I haven’t found a definition that makes sense to an economist used to the language of game theory and utility functions. So let’s look at ‘face’ from an economic perspective, allowing me to make statements on where it comes from and what will happen to it.

To set the scene, consider some examples of the way in which ‘face’ pervades everyday life in China, Japan, and much of South-East Asia. For one, the boss never gets contradicted directly and no-one tells a boss that he is wrong, even if behind his back things are done completely differently and everyone believes him to be wrong. It would thus be quite common for people to congratulate a boss about a decision he did not in fact take. Connected to this, decisions and opinions are obscured in secret codes. By this I mean that it is never said that ‘we dont care about this so we are not going to do it’ but rather the whole topic is avoided or some technical difficulty is fabricated to avoid a negative decision on something. You will thus be hard pressed to hear ‘no, we will not allow you to do X’ but instead will be told ‘we are still working on how to measure X’.

And loss of face is serious business for as soon as you are publicly contradicted and told you are useless, it means that no-one will protect you, help you, or trade with you. Losing face is thus being shut out from a community, which of course explains why keeping up face is a life-and-death thing for many people in Asian societies, even today.

Face thus means people are not directly contradicted; opinions and preferences are hardly ever asked for directly, but instead are inferred; and there is a whole language known to insiders via which to convey actual opinions and coordinate responses.

If you think about this from a game-theoretical perspective you might first naively think that ‘face’ is about people’s beliefs as to how good (or useful or important, etc.) that you are. To have face would then mean people believe you to be virtuous, valuable, important, etc.

This clearly does not fit most examples of face though: it is perfectly possible that someone has face and yet nothing he or she says gets done. What people hence actually think about you does not prevent you from having a ‘face’. As long as efforts are made to hide the truth from you, one still has ‘face’. Hence face is not just about beliefs.

Face is more about the willingness of others to go along with pretending you are good, important, useful, etc. It is only when that pretense becomes unsustainable that one has lost face.

Yet this as a definition is not useful enough because it begs the question why it would matter what others are willing to pretend about you. With well-defined property rights, it matters not what other people think about you since that in no way influences the trades and decisions you can make.

I would therefore venture that the rub behind the whole concept of face is imperfect property rights. With imperfect property rights, it becomes a matter of fluid group opinion as to what you actually own and what you dont. ‘Face’ is then connected to those implicit property rights. The willingness of others to go along with your ‘face’ then signals the degree to which they still respect your property rights and the moment you lose face is the moment all others can rob you of whatever you possess with social impunity.

Translated to a game-theoretical context, this means one should think of ‘face’ as the degree to which others see you as partaking of the social norm upholding a particular allocation of property rights. Their willingness to go along with your face is then nothing less but a social vote as to whether you are still in the club or not. This in turn relies upon a social game in which the accepted rule is that if any two (or more) people deny each other their face then social voting continues until either face is restored or face is lost completely, leading to a re-allocation of the property rights of the loser. Note that what is actually believed about anyone does not matter.

This kind of conception of face has many important implications. For one, it is clear that something like this is more likely to arise in economic systems where most property rights are ill-defined, such as in large bureaucracies where nominally all is owned by the collective (or the emperor who leads the collective) but where limitations of span of control imply that cliques can actually appropriate things for themselves though only to the degree they cover each other’s backs. This of course explains the importance of face for a country like China that has so long had a bureaucracy. It also fits the ‘all who remain in the clique have to stick up for each other’ aspect of face and why someone who has lost face must be killed or in some other way neutralised since there is an outside world who can be alerted to the degree to which these implicit property rights violate the official ones.

Yet, also in more primitive cultures that lack well-established property rights (understood here as allocations that can only be undone by voluntary trades), the same general idea would hold to some extent though one then more normally would call it ‘honour’, and indeed there is an anthropological literature saying that pastoralists (who dont have official lists of who owns what) are big on honour.

The second and perhaps more important implication is that ‘face’ should lose its meaning and value when an economy becomes more monetised and based on formal property rights. Hence the industrial revolution taking place in China right now should be strongly eroding the whole notion of face, at least within the business community. And indeed, if you meet an outspoken Chinese person who says what he wants and tells you what he thinks, it is most likely someone from the business community.

The third, and most worrying implication is that something like face should inevitably start to arise in any major organisation that survives for a long time, since it is in large organisations that property rights become less perfect. Hence the Western world, which has seen greatly expanding government bureaucracies in the last few centuries and where there are relatively large long-lived private enterprises with major span-of-control problems over what all the managers do should see an increase in the importance of face. Whilst ‘face’ thus becomes less important in the East, it is probably on the rise here……

Game Theory in Action: Sven Feldmann on Kindergarten Matching

My colleague Sven Feldmann presented a talk today on Game Theory in Action. The city council where he lives has been using a very common approach for matching children to kindergartens. The Boston Approach (see here for details) involves asking for a preference ranking and making several rounds of offers. This approach is fraught with problems including: inefficient matching, an incentive for parents to misrepresent their preferences, and “justified envy“, whereby a student prefers a school S that she was not admitted to, despite having a higher priority than another student who was in fact admitted to school S.

Sven has persuaded his City Council that they should implement the Gale-Shapley Mechanism instead (see here for details). In step 1, parents get to propose their first ranked kindergarten. Schools temporarily assign seats to proposers based on their expressed priority, others are rejected. In step 2, each rejected parent proposes her next choice. Schools then consider the pool of accepted students plus the proposer, and update their tentative offers based on expressed priorities. This repeats until a stable state is reached, at which point the tentative offers are finalized. So it is a pretty feasible approach to implement. One of its benefits is that it is strategy-proof so parents do not have an incentive to lie about their preferences. Theory also predicts that stable envy-free matching will always occur under the Gale-Shapley approach. So a few changes in behavior can make for a better matching system. But it takes a bit of work to explain this approach and its merits to city councils and parents, as Sven has apparently done with some success.

It is great to see that practical applications of game theory are making a difference in daily life. If you live in a school district that needs help, ask your city council to contact Sven who has a clear and concise explanation of how the different matching techniques work. Or move to Darebin City, Victoria, Australia.

Update: lots of good writeups on school choices are available at

Switching to the correct side

A coordination game is one where everyone benefits from choosing a similar strategy but there are many such strategies so the issue is how coordination occurs. Usually, we think of which side of the road you drive on as a legal issue but it is actually a coordination issue: we drive on the same side as everyone else otherwise things would be bad if we took liberty into our own hands.

With that it is really interesting when a country decides it is in the ‘wrong’ equilibrium and wants to change to another. Samoa has decided just that and will early morning on 7th September switch driving from the right to the left hand side of the road. Why?

The main reason for Samoa’s switch is that two of its biggest neighbors, Australia and New Zealand, drive on the left-hand side, whereas Samoa currently drives on the right, as in the U.S. By aligning with Australia and New Zealand, the prime minister says, it will be easier for poor Samoans to get cheap hand-me-down cars from the 170,000 or so Samoans who live in those two countries. It could also help more people escape tsunamis, says Mr. Tuilaepa.

Tsunamis? OK, that is just a reflection of clear dissent on this issue and political handwaving. There’s more.

In a TV address about the road change last week, the prime minister warned that “the only thing to fear is fear itself.”

The reasons for change seem weak (e.g., the ability to buy Australian cars!). Sweden switched in 1967 but at least you could drive somewhere.

Oh yes, and if you think that there wasn’t enough cost, 7th September is a Monday. It is hard to imagine a worse day of the week to switch things. That said, the Government did realise that and declared the Monday and Tuesday a holiday. It also has set up a training area now so Samoans can practice driving on the left. Of course, that has only illustrated the issue they face.

One recent Sunday morning, a bus was seen barreling down the right side of the road in the training area, the driver apparently oblivious to the fact that it was the wrong side. After nearly running head-on into a sport-utility vehicle, the bus driver swerved then returned to the wrong side of the road and chugged on.

I think the 7th September is the day to watch for South Pacific YouTube activity.

Open Course in Game Theory

It is free, online and from one of the world’s best, Yale’s Ben Polak. Click here for 24 lectures. That is over a day of footage. Download some of them to your iPhone. While you are at it, Barry Nalebuff is also on the ticket.

Solving the reality game

On the Freakonomics blog, a call to arms in solving for the Nash equilibrium of the Beauty and the Geek game. Basically, there is a bit of game theory all over it because you have the ability to pit two of your competing teams against each other for elimination. The question is: who should you send? The answer is, of course, simple: the two teams who are most likely to score well. You might be worried about retribution but in that case it will be a strong team doing the retribution and you won’t be competing against them in future elimination rounds. The hard part is predicting whether this will be a balanced team or one where one of the members is particularly strong.