Zero-Sum Games: Concepts and Applications

This lecture introduces the concept of zero-sum games, where one player's gain is another's loss. It begins with a review of static games and Nash equilibria, emphasizing the unique properties of zero-sum games. The instructor discusses the security levels and strategies for both players, illustrating how these concepts apply to real-world scenarios such as advertising and decision-making under uncertainty. The lecture includes examples like Rock-Paper-Scissors and matching pennies to demonstrate the principles of Nash equilibria in zero-sum contexts. The instructor explains the min-max property, which states that the maximum of the minimum outcomes is equal to the minimum of the maximum outcomes in these games. The discussion extends to mixed strategies, highlighting how they can be computed using linear programming techniques. The lecture concludes with historical insights into the development of game theory, particularly the contributions of John von Neumann and John Nash, and emphasizes the computational ease of finding equilibria in zero-sum games compared to non-zero-sum games.