衡量信息负担：从基于联盟的推理到价格体系
Measuring Information Burden: From Coalition-Based Reasoning to the Price System
AI总结：
本文通过形式化框架衡量价格体系节省的信息量，证明在可转移效用博弈中，核心与一致同意等价所需的最小信息结构是每个联盟至少被其一个成员所知，且平均每代理信息负担随经济规模指数增长。
摘要：
价格体系常被认为能节约信息。本文探讨其节省了多少信息。我开发了一个形式化框架，用于衡量如果代理人必须单独对可行的联盟替代方案进行推理，他们将不得不承担的信息负担。以Debreu和Scarf（1963）的收敛定理为基准，我询问为了个体接受决策能够恢复核心，必须持有多少联盟可行性信息，以及这些信息如何分布。代理人的信息被表示为形式语言中带有意义的有限句子集，推理被建模为Gentzen的序列演算中的证明。主要结果刻画了在固定玩家集上所有可转移效用博弈中，一致接受性与核心一致的最小信息结构：每个联盟必须至少被其一个成员所知。即使从所有成员中移除关于单个联盟的信息，也足以破坏某些博弈中的等价性。将此结果应用于$k$倍复制经济，我识别并计数了那些其可行性信息必须在人群中分布的承重联盟。相关的平均每代理信息负担增长为$Θ(4^k/k^{3/2})$——随经济规模指数增长。这正是价格体系所节省的，精确且形式化。
英文摘要：
The price system is often said to economize on what individuals need to know. This paper measures a particular informational burden associated with decentralized reasoning in its absence: the coalition-feasibility information required for individual rejection decisions to recover the core. We develop a proof-theoretic framework in which information is represented by economically meaningful sentences and reasoning by derivations in Gentzen's sequent calculus. An agent rejects a proposed payoff vector only when she can establish the existence of a profitable coalitional deviation; failure to reject may instead reflect ignorance. For each transferable-utility game, the main theorem characterizes the informational distributions under which the set of unopposed payoff vectors coincides with the core: every noncore payoff vector must have a blocking coalition known to at least one of its members. This yields a game-specific measure of minimum informational burden. We extend the characterization to pure-exchange economies through a first-order framework that preserves finite informational premises. Applying the result to Shapley's (1975) replica economy, within the core-convergence tradition of Debreu and Scarf (1963), we show that the minimum average coalition-level informational burden grows as $Θ(4^k/k^{3/2})$, exponentially with replication. The result quantifies an informational requirement of direct decentralized coalitional reasoning that price-mediated coordination can spare agents, without claiming to measure the total informational savings of prices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
