| PhD Seminar

Name of the Speaker: Mr. Aaditya Kumar (EE21D411)
Guide: Dr. Puduru Viswanadha Reddy
Venue: ESB-234 (Malaviya Hall)
Date/Time: 6th September 2024 (Friday), 2:00 PM
Title: Implementation of Credible Incentive Equilibrium Strategies in Static Network Games

Abstract :

Network games are increasingly used to model and analyze multi-agent decision problems, where each individual's objectives depend not only on their own actions but also on the actions of their neighbors within an interaction network. Applications of network games include distributed control of smart grids, congestion control in transport networks, cyber-physical security, and opinion formation in social networks. The Nash equilibrium is the most widely studied solution concept for non-cooperative games. However, when a Nash equilibrium is realized, agents with conflicting interests may not act in a way that maximizes the overall welfare of the network. Moreover, reaching a Nash equilibrium relies on the challenging assumption of common knowledge of rationality. In scenarios characterized by bounded rationality, agents form models of their opponents based on limited beliefs and react accordingly. This motivates the use of a different solution concept to achieve desirable social outcomes in network games. Consistent Conjectural Variations Equilibrium (CCVE) offers a non-cooperative solution framework by identifying equilibrium strategies within the space of reaction functions, which are strategies that incentivize desired outcomes.

This work investigates achieving desired outcomes in static network games through credible incentive equilibrium strategies as a CCVE. We focus on two main questions: first, which desired outcomes can be implemented using incentive strategies as an equilibrium? Second, what are the characterizations of the incentive functions that can implement a desired outcome? In the existing literature, these notions are explored for 2-player games. We extend the notions of incentive equilibrium and credibility to network games, where players interact over a connected graph. Credibility conditions ensure agents use incentive strategies when neighbors deviate from the agreed outcome. Assuming payoff functions that are concave in the agent’s actions, we restrict incentive strategies to be continuous and piecewise affine functions satisfying a consistency condition. We show that the conditions for the existence of credible incentive equilibrium strategies involve solving two convex optimization problems. In particular, we reformulate these existence conditions in terms of the feasibility of a system of lower-dimensional linear inequalities and a point in a polyhedral cone. Finally, we illustrate our results with numerical examples.

Speaker Bio: