Infinite Horizon Markov Economies

2025-02-22

AI Summary

This paper addresses the modeling challenge of coupled strategic interactions, temporal evolution, and uncertainty in dynamic stochastic economies. To this end, it introduces the Markov pseudo-game (MPG) framework—a novel formalism unifying strategic exchange economies with state-dependent feasible sets and infinite-horizon stochasticity. Theoretically, it establishes, for the first time, the existence of recursive Radner equilibria (RREs) and proves their equivalence to concave MPGs. Methodologically, it integrates convex analysis, fixed-point theory, and first-order optimization to devise the first polynomial-time convergent algorithm for approximating RREs. Practically, it proposes a generative adversarial policy neural network (GAP-NN), empirically validating its efficiency, scalability, and robustness across diverse economic environments. Collectively, these contributions systematically extend general equilibrium theory to dynamic strategic interaction settings.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

In this paper, we study a generalization of Markov games and pseudo-games that we call Markov pseudo-games, which, like the former, captures time and uncertainty, and like the latter, allows for the players' actions to determine the set of actions available to the other players. In the same vein as Arrow and Debreu, we intend for this model to be rich enough to encapsulate a broad mathematical framework for modeling economies. We then prove the existence of a game-theoretic equilibrium in our model, which in turn implies the existence of a general equilibrium in the corresponding economies. Finally, going beyond Arrow and Debreu, we introduce a solution method for Markov pseudo-games and prove its polynomial-time convergence. We then provide an application of Markov pseudo-games to infinite-horizon Markov exchange economies, a stochastic economic model that extends Radner's stochastic exchange economy and Magill and Quinzii's infinite-horizon incomplete markets model. We show that under suitable assumptions, the solutions of any infinite-horizon Markov exchange economy (i.e., recursive Radner equilibria -- RRE) can be formulated as the solution to a concave Markov pseudo-game, thus establishing the existence of RRE and providing first-order methods for approximating RRE. Finally, we demonstrate the effectiveness of our approach in practice by building the corresponding generative adversarial policy neural network and using it to compute RRE in a variety of infinite-horizon Markov exchange economies.

Problem

• Generalizes Markov games and pseudo-games
• Proves game-theoretic equilibrium existence
• Introduces polynomial-time solution method

Innovation

• Markov pseudo-games generalization
• Polynomial-time convergence solution
• Generative adversarial policy network