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

Shuige Liu

Papers from arXiv.org

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.

Date: 2018-02, Revised 2025-11
New Economics Papers: this item is included in nep-gth and nep-knm
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