The Nash Equilibrium with Inertia in Population Games

by   Basilio Gentile, et al.

In the traditional game-theoretic set up, where agents select actions and experience corresponding utilities, an equilibrium is a configuration where no agent can improve their utility by unilaterally switching to a different action. In this work, we introduce the novel notion of inertial Nash equilibrium to account for the fact that, in many practical situations, action changes do not come for free. Specifically, we consider a population game and introduce the coefficients c_ij describing the cost an agent incurs by switching from action i to action j. We define an inertial Nash equilibrium as a distribution over the action space where no agent benefits in moving to a different action, while taking into account the cost of this change. First, we show that the set of inertial Nash equilibria contains all the Nash equilibria, but is in general not convex. Second, we argue that classical algorithms for computing Nash equilibria cannot be used in the presence of switching costs. We then propose a natural better-response dynamics and prove its convergence to an inertial Nash equilibrium. We apply our results to predict the drivers' distribution of an on-demand ride-hailing platform.


Regular Potential Games

A fundamental problem with the Nash equilibrium concept is the existence...

Learning and Selfconfirming Equilibria in Network Games

Consider a set of agents who play a network game repeatedly. Agents may ...

Learning Nash Equilibria in Monotone Games

We consider multi-agent decision making where each agent's cost function...

Approximate Nash Equilibrium Learning for n-Player Markov Games in Dynamic Pricing

We investigate Nash equilibrium learning in a competitive Markov Game (M...

Rational Consensus

We provide a game-theoretic analysis of consensus, assuming that process...

Competitive Safety Analysis: Robust Decision-Making in Multi-Agent Systems

Much work in AI deals with the selection of proper actions in a given (k...

Blockchain Governance: An Overview and Prediction of Optimal Strategies using Nash Equilibrium

Blockchain governance is a subject of ongoing research and an interdisci...