analyze equilibria

This study addresses the ambiguity in policy analysis arising from the lack of a unified equilibrium selection mechanism in dynamic stochastic general equilibrium (DSGE) models under multiple equilibria. Viewing DSGE models as fixed-point selection devices within self-referential economies, the paper proposes a unified framework comprising model specification, a self-reference operator, and a programmable equilibrium selector. It formalizes equilibrium selection as a computable operation for the first time, demonstrating that the Blanchard–Kahn conditions correspond to a specific selector and introducing alternative rules—such as minimum variance and fiscal anchoring—to better reflect policy intent. Leveraging linear rational expectations systems and standard solution techniques like QZ decomposition and OccBin, the framework enables efficient computation and validation of selectors. This approach reinterprets mainstream DSGE solution methods, facilitates systematic comparison of selection rules, and significantly enhances model transparency and policy relevance.

This study investigates the statistical and numerical convergence properties of stochastic equilibrium models, establishing their existence and enhancing solution accuracy. Building on SELCKE theory, the authors integrate eigenvalue analysis, higher-order perturbation expansions, and a recursive equilibrium framework to construct a simulation procedure that verifies the existence of stochastic equilibria and elucidates the geometric convergence mechanism toward long-run equilibrium. Key contributions include characterizing conditions under which faster convergence rates and super-consistent parameter estimation emerge under higher-order shocks, demonstrating equivalence between menu-cost and Calvo pricing models, proving that the stochastic steady state yields the optimal perturbation solution, deriving an upper bound for the peak timing of impulse responses, validating the empirical plausibility of Taylor contracts, and effectively resolving boundary-induced blow-up issues in objective functions.

This paper addresses the computational challenge of general equilibrium in exchange economies featuring real financial markets, household production, and asset retention. Method: It formulates equilibrium computation as a max-inf optimization problem subject to no-arbitrage constraints, introduces the Walrasian dual function—novelly capturing market disequilibrium—and establishes its rigorous equivalence to equilibrium; further develops a lopsided-convergence theory for approximating max-inf points, overcoming existence and computability barriers in incomplete markets. Contribution/Results: The authors design an augmented Walrasian algorithm enabling efficient numerical solution of diverse complex exchange economies. Numerical experiments validate its accuracy and robustness, and the framework is successfully extended to applications including financial stability analysis and macroeconomic policy simulation.

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.

In discontinuous games, Nash equilibria may fail to exist, best responses may be undefined, and the long-run behavior of oscillatory dynamics remains difficult to characterize. Method: This paper introduces “equilibrium cycles”—a novel set-valued equilibrium concept—unifying three axiomatic requirements: external stability, internal instability, and minimality. It generalizes minimal curb sets to discontinuous games and establishes a rigorous correspondence between equilibrium cycles and strongly connected sink components of the best-response graph. Contribution/Results: We prove that every finite game admits at least one equilibrium cycle. The solution is robust, computationally tractable, and precisely captures the long-run outcomes of oscillatory dynamics. To our knowledge, this is the first set-valued equilibrium framework for discontinuous games that simultaneously guarantees existence and provides a dynamic interpretation.

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 explains the emergence of persistent market disequilibrium and price bubbles without invoking irrationality or optimistic expectations. By constructing a dynamic equilibrium model with heterogeneous agents holding noisy valuations, the authors model supply and demand as coupled stochastic processes and uncover a novel mechanism whereby exponential price growth arises solely from zero-mean valuation errors and biases in order statistics. The framework extends Miller’s disagreement theory to a dynamic setting and unifies Walrasian equilibrium and static risk premia as special cases. Integrating agent-based modeling, order statistics, and stochastic simulation, the model reproduces six distinct market regimes—including stable bands and bubble bursts—under a single behavioral rule, offering a unified account of empirical disagreement phenomena and highlighting how machine learning–based valuation algorithms may inadvertently amplify such statistical biases.

This study addresses a fundamental challenge in the formal verification of multi-agent systems: determining whether equilibrium strategies exist in multi-player graph games that satisfy given payoff constraints. The work provides a systematic investigation of the constrained existence problem under five distinct equilibrium concepts, integrating computational complexity theory, formal methods, and game theory to deliver a complete characterization of the associated complexity classes. In contrast to classical two-player zero-sum games, this research substantially extends the analytical framework by precisely delineating the computational boundaries of constrained equilibrium existence across different solution concepts, thereby establishing a rigorous theoretical foundation for verifying robustness in multi-agent systems.

This study investigates the stability and uniqueness of general equilibrium in economies characterized by a large number of goods and highly patient consumers. By constructing a finite-horizon exchange economy through truncation of an infinite-horizon discounted additive utility model, the paper examines how the effective number of goods influences the relative growth rates of substitution and income effects. The analysis demonstrates that, under sufficiently patient consumers and preferences satisfying a proposed “preference diversification” condition, an increase in the number of goods amplifies aggregate substitution effects while attenuating income effects. This mechanism guarantees that all equilibria are locally tâtonnement stable, which in turn implies equilibrium uniqueness. The work thus provides a novel microeconomic foundation for well-behaved equilibria in high-dimensional commodity spaces.

This study addresses the lack of uniqueness, stability, and attainability of competitive equilibria in general equilibrium theory by modeling the economic system as an asymptotically mean-stationary information process composed of agents with finite information capacity. Within an information-theoretic framework, the authors integrate finite-capacity channel models, statistical dependence operators, and multi-parameter joint limit analysis to rigorously embed the classical Walrasian equilibrium—as a zero-entropy limit—within an adaptive setting for the first time. The analysis demonstrates that as the entropy rate approaches zero and channel capacity diverges, the system converges to a rational expectations competitive equilibrium. Moreover, it uncovers positive-entropy dynamic structures in non-equilibrium states that lie beyond the descriptive scope of classical theory, thereby enriching the dynamic foundations of equilibrium analysis.