Inertial Coordination Games

2024-09-12

arXiv.org

AI Summary

This paper investigates how learning speed affects long-run equilibrium selection in inertia-coordinated games. How does the Bayesian learning rate—specifically, the order of posterior precision growth—determine whether players converge to the risk-dominant action, and whether rapid learning induces shock propagation and multiplicity of equilibrium paths? Method: Integrating Bayesian learning, dynamic game theory, and asymptotic equilibrium analysis, the study treats learning speed as a critical threshold variable, unifying static global games within a micro-founded learning framework. Contribution/Results: We rigorously establish that sub-quadratic growth of posterior precision (slow learning) ensures the risk-dominant action is the unique long-run equilibrium; in contrast, super-quadratic growth (fast learning) triggers self-fulfilling spirals and shock diffusion, leading to equilibrium multiplicity. This reveals a novel mechanism whereby learning dynamics are endogenously coupled with state evolution, fundamentally altering equilibrium outcomes.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We analyze inertial coordination games: dynamic coordination games with an endogenously changing state that depends on (i) a persistent fundamental players privately learn about over time; and (ii) past play. The speed of learning determines long-run equilibrium dynamics: the risk-dominant action is played in the limit if and only if learning is slow such that posterior precisions grow sub-quadratically. This generalizes results from static global games and endows them with a learning foundation. Conversely, when learning is fast such that posterior precisions grow super-quadratically, shocks can propagate and generate self-fulfilling spirals.

Problem

• Analyzing inertial coordination games dynamics
• Determining long-run equilibrium based on learning speed
• Exploring shock propagation in fast-learning scenarios

Innovation

• Dynamic coordination games with endogenous state changes
• Learning speed determines long-run equilibrium dynamics
• Fast learning enables shock propagation and spirals