Nash Equilibrium and Mutual Knowledge of Preferences – (Oct. 2020)

What is a "Nash Equilibrium" and why is it relevant?

The Nash equilibrium concept was introduced by John Forbes Nash in the 1950s. Nowadays, it is the most commonly used solution concept in the analyses of non-cooperative strategic interaction. These are situations in which two or more interacting individuals choose actions that jointly affect the payoff of each party. Most economic, political and social situations involve strategic interaction. As a consequence, the Nash equilibrium concept has a broad scope of applications, e.g., auctions, bargaining situations, political competition and public good provision. This makes it a powerful concept. It is furthermore one of the few theoretical concepts that made it into a Hollywood movie. "A beautiful mind" is definitely worth watching.

Can you explain the idea of this solution concept?

Yes. A Nash equilibrium is a strategy combination meaning a list of strategies – one for each player – where no player has an incentive to deviate. In other words, no player can be better off by selecting a different strategy.

What has the Nash Equilibrium to do with preferences?

In a situation with strategic interaction, commonly called game, every strategy combination leads to material outcomes. The interacting parties need to have preferences over these outcomes. If they didn't care about the outcomes, they would have no "goals". Hence, analyses of strategic behavior would be pointless.

Ok but why do we need to do research here?

Well, the empirical results on game theory stem largely from laboratory experiments. In the analyses of these experiments, it is frequently assumed that the monetary payments in the experiments represent subjects' utilities, i.e. their preferences. However, research on social preferences shows that people frequently have other-regarding preferences. That is, they do not only care about their own monetary payments but also about the payments of other agents. This suggests that the games subjects actually play are often different from the games being analyzed. Our research attempts to shed some light on the implications of this discrepancy.

Why is it important that preferences are mutually known?

Nash Equilibrium relies on a couple of rather strict requirements. One of which is that there is mutual knowledge about preferences. This means that agent A knows the preferences of agent B and agent B knows the preferences of agent A. Often, Nash Equilibrium even requires common knowledge of preferences meaning that agent A knows the preferences of agent B, agent B knows that agent A knows her preferences, agent A knows that agent B knows that A knows the preferences of B and so on down the line. Apparently, common knowledge implies mutual knowledge. Hence, without mutual knowledge, there is no common knowledge either.

Why did you study this aspect and what did you find?

As mentioned earlier, if subjects have other-regarding preferences, the game that they actually play differs from the one, which is purely based on monetary payments. In these cases, it seems plausible that mutual knowledge of preferences is violated. The goal of our paper is to study the impact of this aspect on Nash equilibrium behavior. We find that subjects not only fail to accurately predict other players’ preferences, the lack of such information also significantly affects their behavior. More specifically, in a treatment with mutual knowledge of preferences, people significantly more often played their Nash equilibrium strategies. That means, it might be advisable to use a more general equilibrium concept whenever we analyze situations in which it is unlikely that players know each other’s preferences.

Further reading

Brunner, C., Kauffeldt, T.F., and Rau, H. (2020): "Does mutual knowledge of preferences lead to more Nash equilibrium play? Experimental evidence," revise and resubmit European Economic Review.

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