Selfconfirming Equilibrium: Providing Information Can Be More Effective Than Providing Incentives

In game theory, a Nash equilibrium is a situation where, given the choices of all players, no one has an interest in changing their own choice. It can be demonstrated that in some economically relevant games (for example, games with "strategic complementarities"), if information is complete (the rules of the game and preferences are common knowledge) and if the Nash equilibrium is unique, then it represents the necessary behavior under the assumptions of rationality and common belief in rationality, i.e., the behavior of rational and "intelligent" players, conscious of the rationality and "intelligence" of others. This result applies to many models of network interaction.

Since his 1987 thesis, Pierpaolo Battigalli (Department of Decision Sciences) has argued that the conditions of complete information and common belief in rationality limit the applicability of the Nash equilibrium concept. He has developed the idea of selfconfirming equilibrium: a possible steady state that incompletely informed players reach only through the repeated observation of the effects of their moves. If the effect of a move is satisfactory, players will tend to repeat it even if it is not objectively the best given the moves of others, precisely because they cannot know what the objectively best action is.

In a recent article with Nobel laureate Thomas Sargent, Professor Battigalli applied the concept of selfconfirming equilibrium to single-player games (such as that of a central bank repeatedly choosing the interest rate). Now, in a collaboration with Fabrizio Panebianco (Catholic University of Milan) and Paolo Pin (University of Siena), he applies it to more complex network games. For example, a company's activity on social media may aim to maximize a benefit (observable ex-post) that depends on the actions of followers, and the company must therefore determine the optimal level of its activity, considering that the actions of some followers may have negative effects. The authors demonstrate that if players do not have complete information and fear that interaction with followers may have negative effects, then some players may fall into an "inactivity trap" that, on the one hand, "immunizes" them against negative effects but, on the other hand, prevents them from discovering the extent of these effects and the optimal level of activity given others' actions. This can create situations where participation in network activity is lower than in the Nash equilibrium. In fact, it is as if inactive players did not exist, and these low-participation selfconfirming equilibria correspond to Nash equilibria of smaller games where there are no inactive players.

Prof. Battigalli and his colleagues also delve into the more complex case where the total benefit for the agent depends on global externalities, i.e., the activity on the social network of everyone, including those who are not followers. In a social network, everyone derives even a minimal benefit from the activity of all, to the extent that platform managers often send messages to inactive users encouraging them to reactivate. In this case, the overall activity in a selfconfirming equilibrium can be both lower and higher than in the Nash equilibrium. The reason is that, in addition to the equilibria described above, there are also equilibria where players overestimate the contribution of followers to realized benefits, undervaluing the contribution of global externalities. This attribution error leads them to be more active than justified by the (unobserved) activity of followers. When there are positive global externalities, the overall activity in the Nash equilibrium is lower than efficient because players do not "internalize" their contribution to others' benefits. The just-described selfconfirming equilibria, those with activity higher than the Nash equilibrium, are therefore more efficient.

"This kind of research is important not only from a theoretical perspective but can also help understand and possibly counter stable patterns of inefficient behavior," explains Prof. Battigalli. "If, for example, persistent discriminatory and segregating behaviors constitute a Nash equilibrium, then individuals understand they are making the best choice given everyone's behavior but are not considering the costs (externalities) that their conduct imposes on others. With this, a planner should try to provide incentives that change the structure of their benefits and push them to change their behavior."

"If, instead, we are in a situation of non-Nash selfconfirming equilibrium," the Professor continues, "individuals have an incomplete understanding of the system and simply do not realize that they are making a suboptimal choice. In this case, intervening on information can be more effective than intervening directly on incentives."

Pierpaolo Battigalli, Fabrizio Panebianco, Paolo Pin. "Learning and Selfconfirming Equilibria in network Games." Journal of Economic Theory, Volume 212, September 2023, 105700. DOI: https://doi.org/10.1016/j.jet.2023.105700.