Multistage Games

Introduction

Normal-form games models a game where players choose their moves simultaneously without observing other players moves. Extensive-form games adds a possibility playing sequentially - allowing players to learn about the choices of previous players, so the player can condition his moves based on previous players decisions. Extensive-form games have their payoff expressed after the end of the game (one "grand game"). In reality, dynamic play over time may be more complex than one game that unfolds over time. Instead, players can play one game that is followed by another, or maybe even several other games.

- Should we consider each game independently, or should we expect players to consider the sequence of different games as one "grand game"? 
- How to evaluate total payoffs from a sequence of payoffs in each of the sequentially played stage-games? What is the value of payoff in period N and in period N+20? 
- Will the players moves vary if the stage-game were not played sequentially but as independent games?
- Will a player vary from the stage-game Nash Equilibrium to a different action, which will result him a higher payoff in following stage-games? 

Definition

A definition of multi-stage game by S. Tadelis is following: A multi-stage game is a finite sequence of stage-games, each one being a game of complete but imperfect information (a simultaneous move game). These games are played sequentially by the same players, and the total payoffs from the sequence of games will be evaluated using the sequence of outcomes in the games that were played. We adopt the convention that each game is played in a distinct period, so that game 1 is played in period 1, game 2 in period 2, and so on. We will also assume that after each stage is completed, all the players observe the outcome of that stage, and that this information structure is common knowledge.

Information Sets

Information sets model the information players have when they are choosing their actions. They can be viewed as a generalization of the idea of a history.

Solved Example

(more examples are better; one simple, others more advanced)

Relevant facts

(how the phenomenon is used, etc.)

Exercises

that students could use to practice the problem and that could be an inspiration for test questions