Game_Theory

Study of Interdependence. Studies interaction among a group of players who make rational choices based on a strategic analysis of what others in the group might do.

History

Early predecessors

economic analysis of imperfectly competitive market.
Augustin Cournot 1833
Francis Edgeworth 1881

Modern

  1. Ernst_Zermelo - Zermelo's theorem

Statement

In Chess, either White can force a win, or Black can force a win, or both sides can force a draw.

  1. John von Neumann
    Theory_of_Games_and_Economic_Behavior by John von Neumann and Oskar Morgenstern
  2. John Nash
    Nash Equilibrium
    Zero_Sum_Games to Nonzero_Sum_Games
  3. John Harsanyi and Reinhard Selten

Rules of Game

Rules have to specify 4 things

  1. Who is playing
  2. What are they playing with - the alternative actions, or choices, the strategies, that each player has available
  3. When each player gets to play - in what order
  4. How much they stand to gain (or lose) from the choices made in the game

Assume Common_Knowledge about the rule

Representation

Normal Form

or Strategic Form

Extensive Form