• Antal Ertl

Game Theory and Behavior

Tim Harford in his recent blog told a joke about a pianist getting caught by the KGB in the Soviet Union. In his suitcase, the pianist was carrying a copy of Beethoven’s Moonlight Sonata, which the KGB thought was some sort of code western intelligence used. They put him into an interrogation room, where he waited. After an hour, the interrogation officer came in and said to the pianist: “You better start talking, comrade! Your partner, Beethoven, has already told us everything.”

This story aimed to serve as a demonstration to one of the great classics in economics – the Prisoner’s Dilemma. The background is: two thieves successfully complete a robbery; however, after a couple of days, both are caught by the police. Each of them is transported to their own separate cells, where they are disconnected from everyone and everything. Later, the interrogator offers each of them a deal: they can make a deal with the police and tell on the other thief, or they can stay silent. If they tell on the other thief while the other stays silent, they get to walk, and the other gets 5 years. If both of them tell on each other, they each get 4 years. If no one tells on the other, they only get charged for minor misdemeanor, each getting 1 year in prison.

Folsom Prison Blues

Classical Game Theory is a tool which aims to predict the outcomes of interactions between two (or more) parties. Mostly building on the Expected Utility Theory, developed by Neumann and Morgenstern (1947), it is founded upon a straightforward idea: how should I act towards someone in order to maximize my well-being? As such, the decision-maker evaluates the other person’s perspective, their choices, and, if applicable, identifies his or her dominant strategy. Based on that knowledge, our economic agent decides what their actions should be, and will act accordingly. However, it is important to note, that in order to evaluate other agents’ possible actions and make relevant judgements about them, an agent requires some information – which could be the outcome probabilities or perhaps some knowledge of their preferences.

In the Prisoner’s Dilemma – a simple and symmetric game – the model suggests that they will always tell on each other. This is depicted in the figure bellow: inside the boxes, the first and the second number defines payoffs for prisoner “A” and “B”, respectively. To see why we arrive at this conclusion, we can attempt to reason from the perspective of A:

  • If B chooses not to tell on me, then I should tell on them (because my payoff will be higher than if I do not tell on them)

  • If B chooses to tell on me, then I also should tell on them.

A possible interpretation of the Prisonner’s Dilemma: the arrows depict both player’s dominant strategies

As such, based on rational decisions, the outcome should always be both telling on each other. This is called a “Nash-equilibrium”, named after Robert Nash. However, if they both chose not to tell on the other, a better result could be achieved. How can this be achieved, if they do not have any means of communication at their disposal? Well, the answer is trust.

The battle of the sexes

Another case is “the battle of the sexes”. The situation is simple (and all-too familiar): a wife and a husband want to spend time together, but they have different activities in mind. The wife wants to go to the theatre, while the husband wants to go see a boxing match. If they can come to an agreement, they will both benefit from it – if they agree to go to the theatre, the wife obviously will be happier, but the husband is happy as well, as he gets to spend time with his significant other. If, however, they cannot come to an agreement, both will be worse off due to the absence of each other’s company. Traditional game theory declares that the latter would be the outcome in most cases.

However, Rabin (1993) considered an alternative. In the model outlined in his article (which incorporates fairness into decision-theory), economic agents, besides having their own interest, also have social interests and goals. In order to achieve more social acceptance, they are willing to sacrifice their intrinsic, individual well-being and help others. Applying this to the battle of the sexes: suppose that the husband chooses boxing. The wife then concludes that choosing the theatre would hurt both players, and is willing to choose boxing.

Alternatively, if she perceives going for a boxing match as unfair (as they went there for the past 5 weeks straight), she chooses theatre in order to agitate her husband. We covered this topic recently in our blog regarding unfairness. Rolling with this might not have the best outcome for the relationship – but barely anything, that is driven by our emotions, does.

Games we like to play

As you probably guessed by now, this blog-post is not strictly about behavioral economics, as it is more about how it applies methodology to validate or model its findings. In this blog, I wanted to give you a glance into the world of game theory, which can model a wide range of situations and agent interactions.

Camerer (2003) provides a great example of how behavioral economics got integrated to game theory, and thus creating “behavioral game theory”. For the vast majority, this is a formal alteration of classical, rational game theory, using validations from experiments provided by behavioral economics. If we take a look at the Trust Game mentioned a couple of weeks ago, the results from the experiments inspired parameterization of preferences, as well as the “new” homo reciprocus and homo equalis. As such, even institutional economics started to use these “calibrated” models as standards.

Why is game theory so interesting for us? Because it is exceptionally good at modelling things like uncertainty, environmental effects, as well as emotions and feelings in interpersonal settings. In the 18th and 19th century, these factors had a pivotal importance in the political economy. But later, general economics wasn’t really dealing with problems arising from the economy being interpersonal (while justifiably giving a very important role to uncertainty). With the rise of experimental economics, experiments conducted could and should be analyzed in game theoretic settings, cutting away some of the complexities, and decomposing the important factors. In order to do this, behavioral economists have to quantify the effects of these rather qualitative factors; and while it is very complex and difficult to do, there are examples – such as the Trust Game – where this has been successful.

References and Further Readings

Camezer, C. (2003). Behavioral game theory: Experiments in strategic interaction. Princeton, NJ: Princeton University Press.

Rabin, M, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.

von Neumann, J.& Morgenstern, O. (1947) Theory of Games and Economic Behavior Princeton, NJ: Princeton University Press, 194.

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