Jim Ratliff’s graduate-level course in game theory
Lecture notes, in 14 chapters, from a one-semester game-theory course I taught to second-year PhD economics students at the University of Arizona during 1992-1997. Useful to first-year PhD and advanced undergrad students. The exposition is detailed, rigorous, and self-contained.
§ 1 Strategic-form games
Chapter 1 of Jim Ratliff's graduate-level game-theory course. The strategic form (or "normal form") of a game is the familiar "game matrix," which is defined by a set of players, the actions available to each player, and each player's payoffs to combinations of actions. We discuss best-responses to a pure-strategy profile, mixed strategies, expected payoffs to a mixed-strategy profile, the best-response correspondence, and best-response mixed strategies.
§ 4.1 Introduction to extensive-form games
Chapter 4.1 of Jim Ratliff's graduate-level game-theory course. The extensive form of a game can capture complex temporal and informational structure that the strategic form cannot. The extensive form elaborates upon a tree of nodes, each of which belongs to a specific player and at which that player has a defined set of actions. An information set is a set of nodes all belonging to a given player between which the player cannot distinguish when having reached one of those nodes. Collectively, the information sets define what each player knows at each point in the game. We discuss the assumption of perfect recall. We define the crucial concept of a subgame.
