Beliefs need to be pragmatic, grounded in reality, but there are other incentives influencing our beliefs and behavior, like being a good group member, the need to appear as beneficent & effective

On the Function of Beliefs in Strategic Social Interactions. Arnaud Wolff. Bureau d’Économie
Théorique et Appliquée, Document de Travail n° 2019 – 41, Oct 2019. http://www.beta-umr7522.fr/productions/publications/2019/2019-41.pdf

Abstract: We review the way beliefs have traditionally been formalized in game-theoretic settings, and argue that this formalization has its limits, especially in the realm of strategic social interactions. Normative game theory, with its emphasis on equilibrium concepts and its concern about how rational and intelligent players should play, has left little room for a formal characterization of the role of players’ beliefs. Given that beliefs determine play, we argue that a case can be made for a deeper understanding of their nature. We draw on the literature in evolutionary psychology and biology to decipher underlying, not readily apparent, incentives that might influence belief adoption. In fact, we take the view that beliefs are themselves subject to incentives, and that agents’ beliefs may therefore take on a predictable form if we are able to decipher the underlying incentives that they face. This predictable form might then be used to justify specific modelling assumptions, and accordingly improve the models’ predictive power.

Keywords: Beliefs, Game Theory, Social Incentives, Evolution, Coordination
JEL: B40, C70

Discussion
The key point we want to underline is that in strategic interactions, we might be able to predict the direction of people’s beliefs based on the underlying incentives that they face. Nonetheless, it is important to remember that all these incentives probably act in concert. For instance, one might want to be seen as acting consistently with respect to a particular (core) belief adopted by one’s own group. That is, the core belief, around which other related beliefs are tailored, is endogenously determined by one’s group belonging. Also, one might want to stay consistent with respect to a cherished belief, in order to appear as effective to others. A politician, for instance, might want to stay true to her principles in order to appear as confident, or in charge, thereby persuading others of her convictions.

The primary task of the theorist should be to decipher which incentives are the most relevant in the particular context studied (and why?). In fact, very little is known about the interplay of the different incentives individuals face, and about which ones are more binding (and when?). Pecuniary incentives might well be as important as social incentives (think about oil company managers that are convinced that their activities are not harmful for the environment). When, for instance, do pecuniary incentives take the ascendant over social incentives? Or, conversely, in which cases do social incentives (for instance, the incentive to appear as a good coalition member), trump financial incentives? It will likely be very important to determine how individuals deal with the numerous (hidden, underlying) trade-offs that they face, if we want to reap more interesting insights about human behavior. But to be successful, this endeavor requires that we take more seriously the evolutionary approach to human motivations.

Conclusion

Aumann (1976) has shown that if individuals start with the same priors beliefs, and their posteriors about the occurrence of some event are common knowledge, then these posteriors must be equal (i.e., their beliefs must be the same). One however often observes persistent disagreement. Is it because the respective posteriors only rarely fully become common knowledge, or is it because people don’t start off with the same priors? Geanakoplos and Polemarchakis (1982) have shown that in a finite period of time, honest, truth-seeking individuals will reach an agreement by communicating back and forth their posteriors, even if the event was not common knowledge to start with. It must therefore be the priors. Or is it because people are not honest, truth-seekers? We believe that the answer is a mix of both, and that the key to understanding why people are not honest, truth-seekers, and therefore do not converge towards a common posterior, is to decipher the underlying incentives they face to adopt their respective beliefs.

It has traditionally been assumed in economics and game theory that the agents in our models want to be right. They strive to get closer to truth, and they will sometimes undertake costly actions to reach their objective. This assumption is evidently uncontroversial when we consider agents taking decisions whose outcomes depend on the true state of nature. A trader investing in the stock market will want the best available information, while environmentally-friendly consumers will want to know everything about the products they buy. The beliefs need to be pragmatic, grounded in reality. But social life is complex, and there are other (maybe even more important) incentives influencing our beliefs and behavior. We have argued, based on the literature in evolutionary psychology and biology, that some additional, not readily apparent motivations presumably play a large role. These motivations comprise the need to appear as a good coalition (group) member, the need to appear as consistent, and the need to appear as beneficent and effective to others. These motivations are distinct (and without any doubt not exhaustive), but they probably act in concert. In all these cases, pragmatic beliefs are not very useful, because agents have no incentives to be right. Their decisions in these areas do not directly depend on the true state of nature. Instead, their incentives are social, and their beliefs will bear this sign.

Social beliefs have not been much studied, and they are not well understood. They do not respond to evidence as pragmatic beliefs do, and the reason is that they shouldn’t. We have conjectured that much of the apparent disagreement on largely factual matters is due to the above mentioned motivations (together with pecuniary incentives), and that without a deeper appreciation of the underlying (hidden) incentives that agents face, we will not be able to improve our understanding of how to tackle pressing issues such as climate denial, conspiracy theories, or anti-science movements. We believe that the tools of game theory can be successfully applied in those areas, helping us decipher which incentives are the more stringent and binding in different contexts. Nonetheless, this new endeavor requires a deeper comprehension of human motivations and of the particular (often hidden) incentives that we face, at the risk of being stuck in the study of proximate mechanisms, without grasping what the ultimate motives are.