Game theory revolutionized strategic thinking in economics and beyond. It all started with von Neumann and Morgenstern's groundbreaking book in 1944, which laid the foundation for analyzing decision-making in competitive situations.

John Nash's concept of Nash equilibrium was a game-changer. It helped predict outcomes in non-cooperative games, showing how players' strategies interact. These ideas spread far beyond economics, shaping fields like politics, biology, and computer science.

Key Figures in Game Theory

Pioneers of Game Theory

• John von Neumann, a Hungarian-American mathematician, physicist, and computer scientist
  • Considered one of the foremost mathematicians of the 20th century
  • Made significant contributions to various fields, including game theory, quantum mechanics, and computer science
  • Co-authored the seminal book "Theory of Games and Economic Behavior" with Oskar Morgenstern in 1944
• Oskar Morgenstern, an Austrian-American economist and mathematician
  • Collaborated with John von Neumann to develop the foundations of game theory
  • Their joint work, "Theory of Games and Economic Behavior," introduced the concept of game theory to the field of economics
  • Emphasized the importance of strategic decision-making in economic interactions

John Nash's Contributions

• John Nash, an American mathematician and economist
  • Made groundbreaking contributions to game theory, particularly in the area of non-cooperative games
  • Introduced the concept of Nash equilibrium, a fundamental concept in game theory
  • Nash equilibrium describes a state in which each player in a game has chosen a strategy, and no player can benefit by changing their strategy while the other players keep theirs unchanged
  • Received the Nobel Memorial Prize in Economic Sciences in 1994 for his work on game theory (along with John Harsanyi and Reinhard Selten)
  • Nash's life and work were portrayed in the Academy Award-winning film "A Beautiful Mind" (2001)

Foundational Concepts

Game Theory Basics

• Game theory is a mathematical framework for analyzing strategic interactions between rational decision-makers
  • Focuses on situations where the outcome for each participant depends on the actions of all participants
  • Assumes that players are rational and aim to maximize their own payoffs or utilities
  • Applies to various fields, including economics, political science, psychology, and computer science
• Theory of Games and Economic Behavior, the seminal book by von Neumann and Morgenstern
  • Introduced the formal study of game theory and its applications to economic decision-making
  • Laid the groundwork for the development of game theory as a distinct field of study
  • Presented the concept of a zero-sum game, where one player's gains are exactly balanced by the losses of the other player(s)

Strategic Interaction

• Strategic interaction refers to situations where the actions of one player affect the outcomes and decisions of other players
  • Players must consider the potential strategies and responses of other players when making their own decisions
  • Occurs in various contexts, such as market competition, political campaigns, and international relations
  • Game theory provides a framework for analyzing and predicting the outcomes of strategic interactions
  • Examples of strategic interaction include price competition between firms, arms races between nations, and negotiation strategies in business deals

Influential Models and Equilibria

Nash Equilibrium

• Nash equilibrium is a key concept in game theory, introduced by John Nash
  • Describes a state in which each player has chosen a strategy, and no player can benefit by unilaterally changing their strategy
  • In a Nash equilibrium, each player's strategy is a best response to the strategies of the other players
  • Can be pure (deterministic) or mixed (probabilistic)
  • Provides a way to predict the outcome of strategic interactions and identify stable states
  • Examples of Nash equilibrium include the outcome of the Prisoner's Dilemma game and the equilibrium prices in a duopoly market

Prisoner's Dilemma

• The Prisoner's Dilemma is a classic example in game theory that illustrates the conflict between individual and collective rationality
  • Two suspects are interrogated separately and given the choice to confess or remain silent
  • If both confess, they each receive a moderate sentence; if both remain silent, they receive a light sentence; if one confesses and the other remains silent, the confessor goes free while the silent suspect receives a heavy sentence
  • The Nash equilibrium of the Prisoner's Dilemma is for both players to confess, even though remaining silent would lead to a better collective outcome
  • Highlights the tension between self-interest and cooperation in strategic interactions
  • The Prisoner's Dilemma has been applied to various real-world situations, such as arms races, environmental conservation, and public goods provision