From Asymmetric Information to Social Knowledge: A Game Theoretic Example of Strategic vs. Bayesian Beliefs’ Updating

this paper provides a counterexample to a famous theorem of Aumann (1976) which states that common priors and common knowledge of the posteriors imply that the latter must be identical. This theorem, also known as an ‘agreement theorem’ after the title of the original paper, is based on the so-called ‘Harsanyi doctrine’, that is, on the idea that different probability assessments can only be the result of differential information. In its turn, the theorem is crucial to the epistemic conditions for Nash equilibrium, since common priors and common knowledge of the conjectures essentially mean that players already agree on how the game will be played. Consequently, the argument is simply that when knowledge is about a conflictual phenomenon, disagreement is not only possible but also rational, though not in a Bayesian sense. More specifically, since the point is made with a game-theoretic example of the evolution of the institutional structure of production, the rationality of such disagreements is relative to the proposed solution concept, which in addition to the absence of incentives to unilateral changes of strategies requires the absence of tendencies to change the rules of the game. In particular, then, the paper shows that, when the assumptions that allow the commitment to methodological individualism are dropped, assessing the conditional probability of events taking account of the likely outcomes, that is, updating beliefs strategically rather than by a fatalistic application of the Bayes’ law, is not wishful thinking but a quite logical consequence of a cognitive conflict which arises from an underlying real conflict and may lead to efficient and egalitarian institutional changes. The basic shift in the focus of the analysis, in other words, consists of passing from the problem of asymmetric information about an observer-independent phenomenon to the problem of a different interpretation of the same observer-dependent phenomenon, a shift that in the domain of cognition mirrors the shift from Pareto-efficient exchanges among given individuals to structurally inefficient conflicts between groups in the reality domain. The contribution of the paper, in this sense, is the attempt to model the process through which agreement, rather than being dogmatically assumed from the outset, turns out to be socially constructed by interested parties. .