Problem
Research questions and friction points this paper is trying to address.
Partially Observable Markov Games
Infinite-horizon
Belief State
Nash Equilibrium
Approximation
Nash Approximation Gap in Truncated Infinite-horizon Partially Observable Markov Games
🤖 AI Summary
This work addresses the challenge of solving infinite-horizon partially observable Markov games (POMGs), whose intractability stems from the unbounded growth of belief states and action spaces over time. The authors propose a finite-memory truncation framework that approximates the original problem as a Markov game with finite state and action spaces, wherein agents make decisions based solely on a bounded-length window of public and private information. Under filtering stability conditions, they establish—for the first time—that Nash equilibria of the truncated game constitute ε-Nash equilibria for the original POMG, with the approximation error ε vanishing asymptotically as the memory window length increases. This approach not only yields a scalable method for approximate equilibrium computation but also provides rigorous theoretical guarantees on error convergence.
📝 Abstract
Partially Observable Markov Games (POMGs) provide a general framework for modeling multi-agent sequential decision-making under asymmetric information. A common approach is to reformulate a POMG as a fully observable Markov game over belief states, where the state is the conditional distribution of the system state and agents' private information given common information, and actions correspond to mappings (prescriptions) from private information to actions. However, this reformulation is intractable in infinite-horizon settings, as both the belief state and action spaces grow with the accumulation of information over time. We propose a finite-memory truncation framework that approximates infinite-horizon POMGs by a finite-state, finite-action Markov game, where agents condition decisions only on finite windows of common and private information. Under suitable filter stability (forgetting) conditions, we show that any Nash equilibrium of the truncated game is an $\varepsilon$-Nash equilibrium of the original POMG, where $\varepsilon \to 0$ as the truncation length increases.
Innovation
Methods, ideas, or system contributions that make the work stand out.
finite-memory truncation
Partially Observable Markov Games
belief-state approximation
ε-Nash equilibrium
filter stability
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