“It is not the case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree, where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth, and higher degrees.”
- John Maynard Keynes describing the stock market, The General Theory of Employment, Interest and Money
During a recent trip to New York, while I enjoyed a sandwich at Katz’s deli, I was reminded of the age old question so eloquently posed in the movie When Harry Met Sally, “can men and women be just friends?” Except as the marketing researcher that I am, that question quickly transformed into a nerdier (but equally age old) question, “can economics and psychology just be friends?” Since the inceptions of both disciplines, economists have been accused by psychologists of creating models with too many unrealistic assumptions about human behavior. Meanwhile economists have criticized psychologists for having too many diverse theories to make any meaningful quantitative predictions about human behavior.
One particular subfield of economics that I have often found myself attempting to defend is game theory. However, the truth is that game theory often does a poor job of predicting behavior because it assumes that humans have a limitless capacity to think. For example, take the famous “Nash Equilibrium,” a skinny mathematics dissertation that garnered John Nash a Nobel Prize. Though the concept of strategic pairings in which no player can improve his outcome by acting differently is practically gospel in the field of economics. Yet only in a prescriptive context or when describing players who are sufficiently sophisticated, can the actual predictions of Nash Equilibria be of real world relevance.
Despite this shortcoming, the basic framework of game theory can be easily adapted to accommodate many psychological principles and circumstances. For example, as Keynes observed, individuals often think in different degrees. The most naïve individuals have no strategic thinking. The next level of thinker reacts optimally to the actions of the naïve population. Individuals yet one level up can react optimally to the actions of all those who think less strategically. This typology of sophistication can be extended to infinite levels of thinking.
Behavioral economists have formalized a model of players with such bounded rationality in a game setting (Camerer, Ho, & Chong, 2004). Simply, the model assumes that individuals have different strategic abilities that, in aggregate, follow a known distribution. Additionally, each individual of level K sophistication is assumed to believe that the rest of the world contains only individuals of ability levels 0, 1, 2, …, K-1. Moreover, the believed relative frequency of these types is consistent with the actual relative frequencies in the population. Given these assumptions, behavioral economists are able to adapt the framework of game theory to model the interactions of players with more psychologically accurate capabilities.
One of the most commonly used examples of the inaccuracy of Nash Equilibrium is in the beauty contest game. In this game, every player is asked to pick a number between 1 and 100 in such a way that his number is closest to 2/3 of the average number picked by the rest of the players. The unique Nash Equilibrium solution to this game is that everyone will pick 0. The logic is straightforward. If everyone picks randomly, the average will be 50, and the optimal number would be 33. If everyone knows this, then everyone should pick 2/3 of 33. If everyone knows that, then all players would pick 2/3 of 2/3 of 33, and so on. As this logic gets extended infinitely, the ultimate equilibrium is that everyone picks 0. However, when real people play this game, the average number picked is generally much higher than 0. Can cognitive hierarchy theory better fit the real data?
Camerer and his colleagues ran a series of beauty contest studies with different subject pools to test their proposed model in order to estimate the average level of strategic thinking for each subgroup. The results are reported below and are ordered from lowest to highest average level of strategic thinking.
Several things seem particularly interesting. The estimated cognitive hierarchy level for CEOs is 1. This suggests that CEOs tend to think that everyone else is naïve. This is also almost precisely the case with German students and 80 year olds. As we move down the list, it appears that portfolio managers are on average half a level more sophisticated than PhD students in economics, but slightly less sophisticated than Caltech students. And of course, game theorists top the list with almost a 4th degree level of strategic deduction. These results provide some face validity for the idea of cognitive hierarchy and demonstrate an area of cross-disciplinary research that has kept the parsimony and quantitative predictive ability of economic models with more real world assumptions about human psychology.
So to answer the age old question, yes in this case econ and psych can be friends; it just takes a bit more work. The end results can help social scientists understand observed behavior of individuals in real world-contexts. Likewise (in case you were wondering), I suspect men and women can also be just friends.
 In this case, it uses what’s called a “Poisson distribution.” See the original paper for a detailed explanation of this assumption
Camerer, C., Ho, T.-H., & Chong, J.-K. (2004). A cognitive hiearchy model of games. Quarter Journal of Economics , 861-898.