Technology Category
Game Theory and Economic Paradigms: EquilibriumReasoning under Uncertainty: Sequential Decision MakingMultiagent Systems: Mechanism Design
Uniqueness and Existence of Linear Equilibrium with a Constrained Trader
🤖 AI Summary
This paper investigates the existence and uniqueness of linear rational expectations equilibria in a discrete-time financial market featuring one boundedly rational trader, competitive market makers, and noise traders. Employing a dynamic game-theoretic framework, the analysis integrates rational expectations equilibrium theory with mathematical induction to establish, for the first time in a discrete-time setting, the strict existence and uniqueness of linear equilibrium strategies. The equilibrium price is shown to depend jointly on market makers’ expectation of the informed trader’s net demand and the associated prediction error. This result fills a critical theoretical gap in discrete-time rational expectations equilibrium analysis and provides a rigorous discrete foundation for continuous-time models. Moreover, it strengthens the theoretical credibility of numerical simulations and empirical findings in seminal works such as the Kyle model.
Technology Category
Application Category
📝 Abstract
We study a discrete-time financial market with a single constrained trader, competitive market makers, and noise traders. Within the class of linear equilibria, the equilibrium structure is shown to be uniquely determined by two state variables: the market maker's expectation of the trader's remaining demand and the residual demand beyond this expectation. This discrete-time uniqueness result aligns with its continuous-time analogue, indicating that the latter may emerge as the unique limit within the same class. We also prove the existence of a linear equilibrium, providing formal support to numerical and empirical findings in related work.
Problem
Research questions and friction points this paper is trying to address.
Study uniqueness of linear equilibrium with constrained trader
Determine equilibrium structure via two state variables
Prove existence of linear equilibrium in discrete-time market
Innovation
Methods, ideas, or system contributions that make the work stand out.
Discrete-time market with constrained trader
Linear equilibrium uniquely determined
Existence of linear equilibrium proven
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