general equilibrium theory

This paper investigates the existence of Walrasian equilibria and the lattice structure of equilibrium price vectors in two-sided matching markets with indivisible goods. Focusing on the unit-demand/unit-supply setting, it employs Tarski’s fixed-point theorem—novelly applied in this context—to deliver a concise, unified proof of equilibrium existence and of the complete lattice structure of the equilibrium price set, thereby replacing conventional approaches based on convex analysis or iterative constructions. The authors rigorously establish that the set of equilibrium prices is a nonempty complete lattice, and that there exists a unique minimum and a unique maximum equilibrium price vector. This order-theoretic approach highlights the fundamental role of ordinal structure in indivisible markets, strengthens the theoretical foundations for price mechanism design, and provides new analytical tools for algorithmic implementation and comparative statics.

The non-uniqueness of Nash equilibria in extensive-form games poses a fundamental refinement challenge. Method: We propose the first equilibrium selection framework satisfying three axioms simultaneously: backward induction, strategy-invariance, and stability—integrating axiomatic game theory, topological equilibrium theory, quasi-perfect equilibrium analysis, and index theory. Contribution/Results: We prove that any solution satisfying these three axioms must select only stable (i.e., index-nonzero) equilibria in generic extensive-form games. Further, strengthening the invariance axiom uniquely characterizes the connected components of all index-nonzero equilibria. This work provides the first complete axiomatic characterization of index-nonzero equilibrium components, establishing a rigorous, general, and operational theoretical foundation for equilibrium refinement.

This paper addresses the lack of a pure choice-theoretic foundation for Nash equilibrium. We propose the first axiomatic characterization framework for Nash equilibrium based solely on abstract choice functions. Our approach introduces two novel axioms—*contraction consistency* and *expansion consistency*—inspired by classical choice-theoretic principles, supplemented by two additional intuitive axioms. Together, these fully characterize the Nash equilibrium correspondence across arbitrary strategy sets (finite or infinite) and encompass both pure-strategy and mixed-strategy equilibria. Crucially, the framework dispenses with standard assumptions such as utility representation, rationalizability of preferences, or continuity, thereby delivering a genuinely choice-theoretic definition of Nash equilibrium. The resulting characterization unifies diverse game structures—including finite, infinite, and continuous games—enhancing the generality, interpretability, and formal rigor of the equilibrium concept. This work establishes a new paradigm for interdisciplinary research at the interface of game theory and decision theory.

This paper establishes a novel microeconomic foundation for competitive market equilibrium under information asymmetry. It addresses canonical asymmetric-information markets—commodity, credit, and insurance—and introduces the first analytically tractable one-dimensional normal-equilibrium framework that unifies price formation and resource allocation mechanisms. Methodologically, it integrates general equilibrium theory, Bayesian game modeling, and a normal-distribution assumption to derive closed-form equilibrium solutions. Theoretically, it rigorously proves the existence, uniqueness, and dynamic stability of equilibrium within this framework, and enables cross-market comparative statics. By overcoming the analytical intractability inherent in conventional models of asymmetric information, the framework provides a scalable, empirically testable microfoundation applicable to diverse real-world markets.

Walrasian equilibrium lacks theoretical existence guarantees in non-convex markets, yet its observed frequency in European day-ahead electricity auctions varies markedly across countries (10%–80%). Method: We shift analytical focus from preference functions to the geometric structure of demand sets—recognizing that real-world bids are predominantly divisible (convex) with only limited indivisibilities—and develop an approximate equilibrium theory grounded in demand-set non-convexity. Our approach integrates micro-level commercial bid data analysis, Walrasian equilibrium theory, stochastic market modeling, and rigorous error-bound analysis. Contribution/Results: We prove that markets dominated by convex demand admit significantly tighter bounds on approximate equilibrium deviation. Empirically, we verify that approximately 80% of trading days in multiple European markets achieved equilibrium in 2023, aligning closely with theoretical predictions. This work provides the first structural explanation and quantifiable theoretical framework for high-frequency equilibrium emergence in non-convex markets.

This work addresses the long-standing challenge of Nash equilibrium existence in infinite games, which traditionally relies on strong assumptions and lacks a unified framework. By abandoning countable additivity and introducing finitely additive mixed strategies, the paper establishes—under the most general setting—that a Nash equilibrium exists for any nonempty set of players and any bounded utility functions. This result unifies existing equilibrium existence theorems and demonstrates that the equilibrium correspondence is nonempty, compact-valued, and upper hemicontinuous. The proof synthesizes tools from finitely additive measure theory, analysis of upper hemicontinuous correspondences, and finite approximation techniques, thereby enabling direct equilibrium analysis of infinite games previously considered intractable.

This study addresses the existence of random allocations that are both weakly Pareto efficient and envy-free under a general setting encompassing indivisible goods, divisible resources, and complex scenarios involving temporal or heterogeneous commodities. By constructing a unified framework, allocations are modeled as probability measures on a compact metric space, with agents’ preferences represented by continuous, concave utility functions defined over the space of probability measures. Leveraging tools from functional analysis, measure theory, and convex analysis, the paper establishes—for the first time—the existence of such allocations in settings that include non-atomless preferences, and shows they can be represented as probability measures supported on finite partitions. This framework not only unifies classical problems such as school choice and fair cake-cutting but also extends to novel applications beyond the scope of existing theory.

This study addresses the continuity of the equilibrium correspondence in infinite-dimensional commodity spaces, circumventing the traditional reliance on differentiability assumptions. Within a Banach lattice framework, economies are modeled as Borel probability measures over a space of characteristics, with aggregate endowments defined via Bochner or Gel'fand integration. The analysis of equilibrium behavior is carried out in an appropriately chosen Polish topology. By providing a unified treatment of locally convex space models, the approach encompasses complex economic settings such as infinite-horizon planning, monopolistic competition, and asymmetric information. The paper establishes that the equilibrium correspondence is continuous on a dense subset of the set of economies that admit equilibria, thereby substantially extending the scope of both classical and recent continuity theorems.

This study addresses the computational complexity of von Neumann–Morgenstern (vNM) stable sets in one-to-one matching markets, which arises from the definition of domination. By generalizing the classical Decomposition Lemma to arbitrary internally stable matching pairs, the work uncovers an intrinsic connection between internal stability and the cyclic structure of the market, and constructs a reduced environment in which all undominated outcomes are concentrated. Building on this reduction, it establishes an equivalence between vNM stable sets and the core of the simplified market, thereby proving their unique existence and providing an efficient constructive algorithm for their computation. This paper presents the first structural characterization and practical algorithmic solution for vNM stable sets in such settings.

This study addresses the existence of pure-strategy Nash equilibria in finite non-cooperative games, overcoming the limitation of Nash’s theorem, which guarantees only mixed-strategy equilibria. By analyzing structural properties of best-response correspondences and integrating order-theoretic structures with constructive existence proofs, the authors develop a unified analytical framework. They introduce several generalized classes of games—including extensions of one-sided competition games and games defined via aggregate payoff maximizers over ordered sets—thereby unifying and extending existing sufficient conditions for equilibrium existence. The work highlights the pivotal roles of acyclicity and aggregativity in ensuring pure-strategy equilibria, establishing their existence across a broad range of finite games and providing a theoretical foundation for equilibrium computation and mechanism design.