Infinite Horizon Markov Economies

ICLR 2026 Conference SubmissionAnonymous Authors
Algorithmic game theoryEquilibrium computationMarkov pseudo-gamesMarkov exchange economies
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.

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Overview

Overall Novelty Assessment

The paper introduces Markov pseudo-games, a framework generalizing both Markov games and pseudo-games to capture time, uncertainty, and action-dependent feasibility sets. It proves equilibrium existence and provides a polynomial-time solution method. Within the taxonomy, the work resides in 'Markov Exchange Economy Computation,' a leaf containing only three papers. This is a relatively sparse research direction within the broader field of fifty papers, suggesting the specific combination of Markovian structure, pseudo-game formulation, and computational tractability remains underexplored.

The taxonomy reveals that neighboring leaves address related but distinct challenges. 'OLG and Finite Horizon Computation' focuses on overlapping generations and finite-dimensional settings, while 'Stationary Markov Equilibrium Computation' emphasizes game-theoretic methods without the exchange economy context. The 'Existence and Characterization of Equilibria' branch provides theoretical foundations for incomplete markets and debt constraints, but excludes computational methods. The paper bridges these areas by combining game-theoretic equilibrium computation with infinite-horizon exchange economy models, positioning itself at the intersection of strategic interaction and economic equilibrium.

Among twenty-one candidates examined, none clearly refute the three main contributions. The Markov pseudo-games framework examined ten candidates with zero refutations, the reformulation of recursive Radner equilibria examined six with zero refutations, and the generative adversarial policy network examined five with zero refutations. This limited search scope—top-K semantic matches plus citation expansion—suggests that within the examined literature, the specific combination of pseudo-game formulation, polynomial-time convergence guarantees, and application to infinite-horizon Markov exchange economies appears novel. However, the small candidate pool means broader prior work may exist outside this search.

Given the sparse taxonomy leaf and absence of refutations among examined candidates, the work appears to occupy a relatively unexplored niche. The analysis covers a focused subset of the literature rather than an exhaustive survey, so definitive claims about absolute novelty remain premature. The contribution's distinctiveness likely stems from integrating game-theoretic pseudo-games with economic equilibrium computation, a combination not prominently represented in the examined papers.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
21
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: equilibrium computation in infinite horizon stochastic exchange economies. The field structure reflects a blend of theoretical foundations and computational challenges arising when agents trade endowments over an unbounded future under uncertainty. The taxonomy organizes work into several main branches: Stochastic Game Equilibrium Computation focuses on strategic interactions and solution concepts such as stationary or Markov perfect equilibria, often drawing on game-theoretic methods like those in Stationary Stochastic Games[2] and Perfect Stationary Equilibria[4]. Infinite Horizon Exchange Economy Models and Computational Methods for Exchange Economies address the core problem directly, developing algorithms and existence results for economies with incomplete markets or debt constraints, as seen in Incomplete Markets Horizon[11] and Debt Constraints Equilibrium[21]. Optimal Portfolio and Consumption Problems examine individual decision-making under risk, while Financial Market Equilibria with Frictions and Energy Market Equilibria and Trading extend equilibrium analysis to settings with transaction costs, information asymmetries, or sector-specific constraints like carbon trading in Energy Carbon Trading[8]. Stochastic Equilibrium Methods and Applications provides broader methodological tools, including mean-field approaches and recursive techniques. A particularly active line of work centers on Markov exchange economy computation, where researchers seek tractable recursive formulations that exploit the economy's state structure. Infinite Horizon Markov[0] sits squarely in this cluster, emphasizing computational strategies for Markovian equilibria in stochastic exchange settings. Nearby, One Asset Equilibrium[22] explores simplified asset structures to gain analytical and numerical tractability, while Stochastic Finance Equilibria[1] broadens the scope to financial market settings with various frictions. These works share a common challenge: balancing the richness of infinite-horizon stochastic dynamics with the need for feasible computation, often trading off between model generality and algorithmic efficiency. Open questions persist around the existence and uniqueness of recursive equilibria, the role of market incompleteness, and the scalability of numerical methods to higher-dimensional state spaces. Infinite Horizon Markov[0] contributes to this dialogue by proposing computational techniques tailored to Markov structures, complementing the theoretical insights of Markov Equilibrium Strategies[3] and the complexity analyses in Markov Equilibrium Complexity[6].

Claimed Contributions

Markov pseudo-games framework with equilibrium existence and polynomial-time solution method

The authors introduce Markov pseudo-games (MPGs), a game-theoretic framework that combines dynamic uncertainty from Markov games with action-dependent feasibility from pseudo-games. They establish existence of generalized Markov perfect equilibria in concave MPGs and provide a polynomial-time algorithm for computing approximate stationary points of exploitability under mild assumptions.

10 retrieved papers
Reformulation of recursive Radner equilibria as Markov pseudo-game equilibria

The authors prove that the set of recursive Radner equilibria in infinite-horizon Markov exchange economies equals the set of generalized Markov perfect equilibria in an associated Markov pseudo-game. This reformulation establishes existence of recursive Radner equilibria and enables their computational approximation through the MPG framework.

6 retrieved papers
Generative adversarial policy network for computing equilibria in infinite-horizon economies

The authors implement their solution method as a generative adversarial policy network (GAPNet) using neural network parameterizations. They demonstrate its practical effectiveness by computing equilibria in various infinite-horizon economies with different utility functions and transition structures.

5 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Markov pseudo-games framework with equilibrium existence and polynomial-time solution method

The authors introduce Markov pseudo-games (MPGs), a game-theoretic framework that combines dynamic uncertainty from Markov games with action-dependent feasibility from pseudo-games. They establish existence of generalized Markov perfect equilibria in concave MPGs and provide a polynomial-time algorithm for computing approximate stationary points of exploitability under mild assumptions.

Contribution

Reformulation of recursive Radner equilibria as Markov pseudo-game equilibria

The authors prove that the set of recursive Radner equilibria in infinite-horizon Markov exchange economies equals the set of generalized Markov perfect equilibria in an associated Markov pseudo-game. This reformulation establishes existence of recursive Radner equilibria and enables their computational approximation through the MPG framework.

Contribution

Generative adversarial policy network for computing equilibria in infinite-horizon economies

The authors implement their solution method as a generative adversarial policy network (GAPNet) using neural network parameterizations. They demonstrate its practical effectiveness by computing equilibria in various infinite-horizon economies with different utility functions and transition structures.