# Game theory often looks silly

From Tim Harford’s blog:

“Game theorists know all about the centipede game:

One instance of the centipede game is as follows. A pile of \$4 and a pile of \$1 are lying on a table. Player I has two options, either to “stop” or to “continue.” If he stops, the game ends and he gets \$4 while Player II gets the remaining dollar. If he continues, the two piles are doubled, to \$8 and \$2, and Player II is faced with a similar decision: either to take the larger pile (\$8), thus ending the game and leaving the smaller pile (\$2) for Player I, or to let the piles double again and let Player I decide. The game continues for at most six periods. If by then neither of the players have stopped, Player I gets \$256 and Player II gets \$64. Figure 1 depicts this situation. Although this game offers both players a very profitable opportunity, all standard game theoretic solution concepts predict that Player I will stop at the first opportunity, getting just \$4.

Except, nobody really thinks this is the way players would behave in reality. The optimal strategy seems sociopathic; isn’t it worth playing cooperatively in the hope that the other player will do the same thing? (Unlike much real human interaction, standard game theory does not accomodate the “hope” that someone else will play suboptimally: optimal play is to be expected at all times. )”

Game theory is very clever and very useful, but often seems very naive. When it’s used in economics, it’s arguably the part of economics most hamstrung by the scattershot application of the “money=utility” fallacy. If you want your game theoretic result to be predictive or descriptively powerful, you must (must must) try really hard to make the payoffs reasonably accurate; in Harford’s quoted example the assumption is that the players care only about cash and that, as Harford says, they aren’t willing to take a shot on the other player prolonging the game. At the risk of being tautologically critical: can you read the setup of that game and not entertain the idea of waiting? I remember being taught the centipede game in David Myatt’s excellent game theory course as an undergrad; he showed us the ‘crazy centipede’ variant, which wondered exactly that: what chance of you choosing to continue the game is enough to make me also want to continue?

The kicker to me is that ‘game theoretic predictions’ are overwhelmingly often not as successful for the players as alternative strategies, even when we’re just measuring ‘success’ in the same cash-payoff terms as the theory. This is just what Harford goes on to describe:

But Ignacio Palacios-Huerta (best known to Undercover Economist readers as discovering that strikers and goalkeepers play optimal strategies in penalty-taking) and Oscar Volij gave the centipede game to skilled chess players. They found that the chess players were far more likely to play optimally; grandmasters always played optimally and took the \$4. Hyper-rationality can be a disadvantage. (Or did the experiment discover something else: that chess grandmasters are sociopaths?) Palacios-Huerta and Volij don’t speculate. My guess is that they have discovered something about the rationality rather than morality or empathy of chess players, but I may be wrong.

It really does just beg for the ‘behavioral economics’ explosion: if predictions aren’t great, and in any case are less profitable than reality, we’re up the creek without a paddle or a boat.

# Happy happy joy joy

Via the wondrous fark.com comes ‘How Rich People Spend Their Time‘ from the Washington Post – it’s about an article in Science written by a battery of psychologist/economist types, including Daniel Kahneman. Very relevant to the question of what motivates people; my first instinct was to assume that it might reveal what people with the time to do what they want do with their time, if you see what I mean, and while the actual intention of the article is somewhat different it’s still full of fun.

The original article is behind the Science subscriber wall, but via the wonders of institutional access, I can get access to metaphysical nuggets like this:

Schkade and Kahneman noted that, “Nothing in life is quite as important as you think it is while you are thinking about it.”

Perhaps some intriguing fact about human nature; perhaps not. The article goes on to talk about some well-known results in the burgeoning ‘happiness’ literature, like the importance of relative rather than absolute income, and adaption to circumstances. I think a great article about this stuff, for the terminally interested, is Richard Layard’s ‘Happiness and Public Policy’.

But the thing that hooked me on this particular Science article is the following piece of weird:

“In a representative, nationwide sample, people with greater income tend to devote relatively more of their time to work, compulsory nonwork activities (such as shopping and childcare), and active leisure (such as exercise) and less of their time to passive leisure activities (such as watching TV).”

Let me get this straight: richer people work more and buy more stuff, and poor schmucks watch a lot of TV? Stop those presses. The point of the article is well-made (from the the title, ‘would you be happier if you were richer’, right on down), and that is to say that people with higher incomes aren’t necessarily engaging in relatively more ‘fun’; however, there are a bunch of unasked questions. Does ‘TV’=’fun’? Is this really evidence that the rich are wasting their time, or are there other reasons why they endure work to get money?

The happiness literature is desperate to find an answer to the question of whether money buys happiness; an eerie similarity to the oft-(mis?)perceived economists’ equation of money with happiness when modeling people, and surely as deserving of the same retort: we know people care about more than money. The obvious question is, well, obvious. What does motivate people?

# Looking at brains

A related question to what people want is what makes people happy. The answers aren’t necessarily the same, but in thinking about one, especially as a modeler, it helps to think about the other.

I saw Andrew Caplin talk a couple of months ago about this paper, in the growing neuroeconomics field. My layperson’s understanding of neuroeconomics is that it looks at the brain to try and figure out what’s going on while we make choices. It seems to be concerned at least as much with “what makes people happy” (or at least what makes their brain light up on the machines) as it is with what people actually choose, a point that separates it somewhat from other economic fields that take preferences as given and observe only choices. The argument, presumably, is that knowing more about what motivates people might shed more light on their choices.

Caplin described a paper titled, excellently, “Responses of monkey dopamine neurons to reward and conditioned stimuli during successive steps of learning a delayed response task” (link) which described a Pavlovian experiment on monkeys. First the monkeys were given food, which set off a dopamine response in their brains, supposedly a sign of pleasure. Then the researchers started to ring a bell before giving the food, and the dopamine response shifted from the food to the bell. Finally, they rang the bell and withheld the food, and the dopamine measure showed pleasure at the bell and disappointment at the time when the food was expected.

The upshot is that this physical measure of pleasure in the brain seems to show that news was just as important as the tangible outcome: the monkeys don’t just care about the food. People, too, clearly care about more than just money, goods or tangible outcomes: perhaps I am happy to see a good weather forecast for tomorrow even though I didn’t actually get anything.

It’s related to the great loss and rediscovery of preferences in economics. At some point (to grossly oversimplify the history) the profession settled on making abstract simplifications of people’s motivations. Then a while went by and someone said “people don’t conform to your economic theory, they must be irrational!”, when of course the more obvious explanation is that people’s motivations are more complex than the simplification. If people care only about money, then according to some theory I should see this. If I see that instead, I have not disproved the theory independently from the assumption on preferences.

The potentially exciting thing about neuroeconomics is that, even allowing for inexactness, it might tell us more about the actual hedonic motivators of people. Ambitious, yes, but not unimaginable. Of course, to an economist who wasn’t under the mistaken impression that simplified preferences are supposed to be realistic, it might just amount to saying “your simplification is a simplification”, which is slightly less exciting news. Or not news at all.

In fact, one interpretation of the monkey result might be that new information – or expectations – matters to people’s decisions. Macroeconomists – Nobel memorial winners, Phelps and Friedman – incorporated expectations into their models forty years ago. If anything, what we’re seeing is individual-level (or at least individual monkey-level) evidence that, yes, expectations are important. That might be another way of saying that evidence from experimental/behavioral/neuroeconomics like this is fun, but it doesn’t materially change what economists are up to: if more complexity makes our modeling more accurate, we often end up doing it.

# Who was Pareto anyway?

Students of economics will hear about “Pareto efficiency” very early in Econ 101. It’s a tool to compare outcomes. Sadly, poor Pareto now has his name attached to a disastrously misunderstood concept – Pareto efficiency is everywhere used and frequently abused.

From a biography of the man himself, Vilfredo Pareto:

“Like Irving Fisher (1892), Pareto stumbled on the idea that cardinal utility could be dispensed with. Preferences were the primitive datum, and utility a mere representation of preference-ordering. With this, Pareto not only inaugurated modern microeconomics, but he also demolished the “unholy alliance” of economics and utilitarianism. In its stead, he introduced the notion of Pareto-optimality, the idea that a society is enjoying maximum ophelimity when no one can be made better off without making someone else worse off.”

Two reasons to be cheerful: apart from featuring the excellent word “ophelimity” (n., economic satisfaction), this could not be clearer on the definition of Pareto optimality (now synonymous with Pareto efficiency). A situation is Pareto optimal if no one can be made better off without making someone else worse off.

Why, then, is this type of statement easily the most common mistake in economics (not intended to pick on the source, which is certainly not unique):

“There is no connection between Pareto efficiency and equity! In particular, a Pareto efficient outcome may be very inequitable. For example, the outcome in which I have all the goods in the world is Pareto efficient (since there is no way to make someone better off without making me worse off).” [Emphasis mine]

To get the cheapest criticism out of the way first, saying “there is no connection between Pareto efficiency and equity” is a bit like saying “there is no connection between Pareto efficiency and the color of my shoes”; why should there be? It’s just a definition. It is, or it isn’t. The criticism that’s actually important is that the bit in bold is a logical falsehood.

The true statement would be “the outcome in which I have all the goods in the world can be Pareto efficient”. In fact, equally true: “outcome _____ can be Pareto efficient”. Why? The missing link is that Pareto efficient is, inherently, a concept built on utility. The “better off” part implies that our test of Pareto efficiency centers on the relative satisfaction enjoyed under alternative outcomes. This is, again, not the same as the relative levels of income, consumption or stuff enjoyed under alternative outcomes.

A simple proof by contradiction: I have all the goods in the world. I am also ascetic and thus get more satisfaction from having less goods. You always like more goods. The outcome in which I have all the goods in the world is Pareto inefficient.

Simple, no? Again, it’s a case of confusing utility with goods or money, a case that would probably have irritated Pareto himself. The hidden assumption in the mistake quotation is the assumption on what the preferences of the person with all the goods are. We can imagine many ways in which that person’s preferences would result in the falsehood of the assertion of Pareto optimality, yet we are anyway confronted with this manifestation of the prejudice that the concepts used by economists to compare outcomes are evil manifestations of an imagined money-centric, capitalist doctrine.

So is Pareto efficiency a normatively loaded term? Is the concept of Pareto efficiency part of positive economics or normative economics? Those who would argue that the boundary between the two is fuzzy frequently point to the Pareto efficiency tool as evidence. It’s a concept that is, however, firmly positive, at least up to the scale of the interpretation of language. It either is raining, or it isn’t. An outcome either is Pareto efficient, or it isn’t. This cannot be a normative statement.

Perhaps the problem arises because, like all concepts that rely on assessing utility or satisfaction, Pareto efficiency might be inherently untestable. Unless it’s actually possible to know or deduce preferences, we can’t make physically true statements about Pareto efficiency or the like; the best we can do is to say “if these people have these preferences, this outcome is or is not Pareto efficient”. To do better than conditional truth we somehow have to know preferences, and whether that’s possible is, to me, a huge open question. Pareto efficiency might then seem normatively loaded because the assumption on what preferences people hold is folded into the statement of Pareto efficiency, as in the mistake above that omitted “if people only care about their own material possessions”.

The irony is that Pareto, the man, for whom “Preferences were the primitive datum, and utility a mere representation of preference-ordering”, might perhaps be the first to object to the misuse of his most famous concept.

# Economics is not about money

“The most common misunderstanding about economics is that it is only about money and commerce.”

The beginning seems like a good place to start, and the beginning of the misperception of economics is surely the popular notion that it’s all about money. Where did that arise?

The quotation is from “What Economics Is Not” by Llewellyn Rockwell. Unfortunately, the essay also says:

“This is a confusion sown by economists themselves, who postulate something called “economic man” who possesses a psychological propensity to always behave in ways that maximize wealth.”

Economics is social science, so we have to include an idea of how people behave. One way we do this is to suppose people have some likes and dislikes that their choices seek to satisfy. We suppose our “economic man” will behave in ways that maximize satisfaction.

That seems better than having “economic man” behave randomly: who could argue that we don’t, in fact, try to make the best of what we have? Our problem is that it’s very difficult to decide what people like or dislike. We know that many things affect the way we feel – a new car, sunshine, helping a stranger, being smiled at – and, of course, no two people are exactly alike.

To make matters worse, how would we even know if our “economic man” is striving to maximize satisfaction if we don’t really know what makes him tick? What a huge philosophical question it is, and what an obstacle for economics to have to work with something so elusive as human satisfaction!

How can we recover? Economists often tried to make life much simpler by assuming that people only cared about wealth. Most people probably care about wealth to some degree, and wealth is, mercifully, more measurable than satisfaction, so this assumption shouldn’t be way off the mark. Sadly, once we use the wealth proxy for satisfaction, our “economic man” looks like Rockwell’s, and the misperception deepens.

Why was it deemed necessary to make the wealth-maximizer assumption? That is a question for another day. So, too, is how “economics” came to mean money, wealth or finance in its popular usage. Economics is to the stock market as physics is to your electricity bill – it’s not unrelated, but it’s a big stretch…