Game Theory

This introductory lecture establishes the core elements of game theory, defining players, strategies, and payoffs. It rigorously analyzes strictly dominant and dominated strategies, leading to a foundational discussion of the Prisoner's Dilemma and coordination problems.

This lecture introduces the formal ingredients of a game, including players, strategies, and payoffs. It details the iterative deletion of dominated strategies and distinguishes between mutual and common knowledge within game-theoretic contexts.

This lecture from Yale's Game Theory course applies the principle of iterative deletion of dominated strategies to analyze the Median Voter Theorem in electoral competition. It critically examines the model's predictive power and introduces the concept of best response strategies.

This lecture introduces the formal definition of a best response strategy within game theory, using the example of penalty kicks in soccer. It then applies this concept to analyze profit-sharing partnership games and previews the foundational concept of Nash Equilibrium.

This lecture formally defines Nash equilibrium, explores its derivation in various strategic games, and distinguishes it from concepts of dominance. It further analyzes Pareto efficient equilibria within coordination problems, illustrating scenarios such as bank runs and fashion cycles.

This lecture formally defines and applies the Nash Equilibrium concept to classic coordination games, including the Battle of the Sexes. It then presents a rigorous mathematical analysis of the Cournot duopoly model, examining firm competition and welfare implications.

This lecture analyzes Nash equilibrium concepts through market competition models, including the Bertrand duopoly with both homogeneous and differentiated products, and extends the framework to political economy with the candidate-voter model.

This lecture analyzes the Nash equilibrium in the candidate-voter model and explores Schelling's location game to demonstrate how segregation can emerge without individual preference. It further differentiates between centralized and individualized randomization (mixed strategies), exemplified by Rock, Paper, Scissors.

This lecture elaborates on mixed strategies, defining their payoffs as weighted averages of pure strategies and identifying Nash equilibria in a tennis game scenario.

Explores three distinct interpretations of mixed strategies, applying them to varied contexts from sports to tax compliance, and analyzes the implications of mixed equilibria.

Introduces the concept of evolutionary stability, examining how it relates to economic principles like domination and Nash equilibrium within biological contexts.

Applies evolutionary stability to social conventions and aggressive strategies, particularly the Hawk vs. Dove game, to predict behavioral variations and cyclic dynamics.

Analyzes sequential games using backward induction, focusing on moral hazard problems and remedies such as incentive design and commitment strategies like collateral.

Applies backward induction to the Stackelberg model of quantity competition, demonstrating first-mover advantages derived from commitment and information, not just timing.

Discusses Zermelo's theorem for finite games, defines strategies in perfect information games, and identifies Nash equilibria in sequential games that are inconsistent with backward induction.

Examines the chain-store paradox and the role of reputation in making threats credible, then analyzes dueling games of pre-emption using dominance and backward induction.

Develops bargaining models from ultimatum games to alternating offers, introducing discounting and exploring conditions under which the first offer leads to an equal split.

Introduces information sets to define games of imperfect information and subgames, extending strategies to these games and revealing Nash equilibria inconsistent with backward induction.

We analyze three games using our new solution concept, subgame perfect equilibrium (SPE). The first game involves players' trusting that others will not make mistakes.

Analyzes wars of attrition, demonstrating how long and costly fights can arise even with rational players, and exploring equilibria in both finite and infinite versions of the game.

Discusses repeated games and the intuition of future rewards/punishments for present cooperation, analyzing the failure of cooperation in finite Prisoners' Dilemma scenarios.

Examines the credibility of promises and threats in repeated games for sustaining cooperation, focusing on the grim strategy as a subgame perfect equilibrium under patience and continuation probability.