Infinite Horizon Markov Exchange Economy (Sadie Zhao)

We introduce the infinite horizon Markov exchange economy, a dynamic stochastic general equilibrium (DSGE) model that explicitly incorporates time and uncertainty, generalizing both the Radner stochastic exchange economy and the infinite horizon incomplete markets model by Magill and Quinzii. To analyze this model, we propose generalized Markov games, an extension of standard Markov games where each player’s actions not only influence their rewards but also alter the available actions for others. We demonstrate that every infinite horizon Markov exchange economy can be associated with a generalized Markov game, wherein the set of Markov perfect generalized Nash equilibria (MPGNE) corresponds to the economy's recursive Radner equilibria (RRE). We establish the existence of MPGNE in concave generalized Markov games, thereby proving the existence of RRE in infinite horizon Markov exchange economies under standard assumptions about consumer preferences and endowments. Additionally, we introduce two neural network-based methods to approximate MPGNE in these games, with convergence guarantees. The first, Generative Adversarial Policy Networks (GAPNets), employs a generator (resp. an adversary) which seeks a policy profile that minimizes (resp. maximizes) the players’ cumulative regret for unilaterally deviating from the generator’s policy profile to that of the adversary. The second method extends traditional projection techniques in economics by using neural networks as function approximators, aiming to minimize the first-order Bellman error for each player.

Based on joint work with Denizalp Goktas, Amy Greenwald, and Yiling Chen.