Potential Games: Best Response Dynamics and Nash Equilibria

This lecture focuses on potential games, a class of games that generalizes two-player static games to multiple players. The instructor begins by reviewing previous concepts, including Nash equilibria and their properties. The discussion then shifts to potential games, where each player optimizes a cost function based on the actions of others. The instructor explains the iterative best response approach, which can converge to a Nash equilibrium in potential games. The lecture emphasizes the importance of potential functions, which map strategy profiles to real numbers, and how they facilitate the convergence of best response dynamics. The instructor illustrates these concepts with examples, including congestion games, where players choose resources based on their costs. The lecture concludes with a discussion on the implications of adding resources in congestion games, highlighting the paradox that can arise when adding a new resource may lead to increased overall travel times. The session provides a comprehensive overview of potential games and their significance in game theory.