Title: Equilibrium in Large-Scale Systems with Rational and Imitative Agents
Abstract: As engineering systems evolve toward massive decentralization, the traditional assumption of uniform “perfect rationality” among nodes has become a bottleneck for realistic performance analysis. In many practical scenarios, nodes exhibit correlated decision-making (herding), where they imitate majority actions rather than optimizing based on private signals. Such deviations render classical Nash equilibrium inadequate for predicting long-run system behavior.
We introduce the \(\alpha\)-Rational Nash Equilibrium (\(\alpha\)-RNE), a new solution concept for systems containing a mix of nodes/agents that either optimize individually or simply follow the majority. For binary action spaces under asynchronous (turn-by-turn) updates, we characterize the almost sure limits of the induced stochastic dynamics. The proof is constructive and proceeds via a sample-path analysis that progressively restricts the set of feasible limit points, ultimately establishing uniqueness of the limit for almost all trajectories. The derived limits correspond to the set of \(\alpha\)-RNEs.
We further discuss extensions to higher-dimensional action spaces via connections to differential inclusion-based stochastic approximation frameworks. The goal is to understand how node-level “irrationality” impacts global network efficiency, and we will conclude that “being irrational” can sometimes be the rational strategy for both the individual and the system at large.
Bio: Dr. Khushboo Agarwal is a Ramanujan Fellow in the Computer Systems Group at IIIT Hyderabad. She holds a Ph.D. and M.Sc. in Industrial Engineering and Operations Research from the Indian Institute of Technology Bombay, Mumbai. Before her current position, she worked as a post-doctoral researcher at Inria Sophia Antipolis, France. Her research interests include stochastic processes, game theory, and reinforcement learning.