Information Sufficiency, Stability, and Efficiency in Decentralized Decision-Making

TL;DR

This paper introduces a formal framework to analyze the sufficiency of information in decentralized decision-making, linking informational requirements to solution concepts like the core and revealing asymmetries in market equilibrium convergence.

Contribution

It develops a syntactic model using sequent calculus to explicitly characterize the reasoning process and minimal informational conditions for justifying cooperative decisions.

Findings

The core corresponds to the set of payoffs justifiable under minimal information.

Competitive equilibrium requires only local information, unlike the core which demands increasing informational capacity.

The framework reinterprets the core as a boundary of justifiable outcomes based on information sufficiency.

Abstract

This paper develops a formal framework for analyzing information sufficiency in cooperative decision-making. Departing from models of incomplete information that emphasize accuracy of beliefs, we ask what kind and amount of information are required for justifying a choice. Using Gentzen-style sequent calculus, we construct a syntactic model that makes explicit an agent's reasoning process: from which information, through what inference procedure, and to what conclusion. We define a syntactic criterion, called C$_i$-acceptability, to determine when a proposed distribution is justifiable given limited structural information. We show that if every coalition is known to at least one of its members, then the set of unanimously accepted payoffs coincides with the core; moreover, this informational requirement is minimal when we consider all games sharing the same set of players. This reinterprets the core not as a predictive solution, but as the boundary of what can be justified under minimal information. Moreover, our results offer a new perspective on Debreu-Scarf theorem: while the core converges to the competitive equilibrium in replicated markets, this convergence obscures a key asymmetry. Competitive equilibrium requires only local information -- preferences and prices -- regardless of market size, whereas reaching the core entails increasing informational demands that may ultimately exceed any agent's cognitive capacity.