In this talk, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best responses, an equilibrium cycle is a set-valued solution concept that can be demonstrated even in games where best responses do not exist (for example, in discontinuous games). The equilibrium cycle identifies a Cartesian product set of action profiles that satisfies three important properties: stability against external deviations, instability against internal deviations, and minimality. This set-valued equilibrium concept generalizes the classical notion of the minimal curb set to discontinuous games. In finite games, the equilibrium cycle is related to strongly connected sink components of the best response graph. We give several examples of equilibrium cycles from the economics literature, and also demonstrate them in an analysis of competing ride hailing platforms. This is joint work with Tushar Walunj, Shiksha Singhal and Veeraruna Kavitha.
Jayakrishnan Nair is a Professor of Electrical Engineering at IIT Bombay. His research draws on tools from queueing theory, applied probability, game theory, and control theory to address design, resource allocation and learning problems in networks, service systems, and smart power grids.