Equilibria under Dynamic Benchmark Consistency in Non-Stationary Multi-Agent Systems

2025-01-21

AI Summary

This paper investigates equilibrium evolution under dynamic competition in non-stationary multi-agent systems, focusing on strategic adaptation under partial information in time-varying domains such as online advertising and retail. Methodologically, it introduces the novel concept of “dynamic benchmark consensus” and a tracking error analysis framework—overcoming limitations of static equilibrium benchmarks—and integrates online learning, non-stationary game theory, and dynamic regret analysis to design provably convergent internally and externally dynamically consistent strategies. Theoretically, under slowly varying (sublinear) environments, the joint strategy distribution converges to a sequence of coarse correlated equilibria. Moreover, the proposed approach substantially strengthens theoretical guarantees on both individual utilities and social welfare in smooth games.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

We formulate and study a general time-varying multi-agent system where players repeatedly compete under incomplete information. Our work is motivated by scenarios commonly observed in online advertising and retail marketplaces, where agents and platform designers optimize algorithmic decision-making in dynamic competitive settings. In these systems, no-regret algorithms that provide guarantees relative to emph{static} benchmarks can perform poorly and the distributions of play that emerge from their interaction do not correspond anymore to static solution concepts such as coarse correlated equilibria. Instead, we analyze the interaction of extit{dynamic benchmark} consistent policies that have performance guarantees relative to emph{dynamic} sequences of actions, and through a novel extit{tracking error} notion we delineate when their empirical joint distribution of play can approximate an evolving sequence of static equilibria. In systems that change sufficiently slowly (sub-linearly in the horizon length), we show that the resulting distributions of play approximate the sequence of coarse correlated equilibria, and apply this result to establish improved welfare bounds for smooth games. On a similar vein, we formulate internal dynamic benchmark consistent policies and establish that they approximate sequences of correlated equilibria. Our findings therefore suggest that, in a broad range of multi-agent systems where non-stationarity is prevalent, algorithms designed to compete with dynamic benchmarks can improve both individual and welfare guarantees, and their emerging dynamics approximate a sequence of static equilibrium outcomes.

Problem

• Dynamic Equilibrium
• Adaptability in Algorithms
• Information Incompleteness

Innovation

• Dynamic Environment Algorithm
• Adaptive Mechanism
• Equilibrium State Optimization