The extensive form

Game Theory // Fall 2025

Prof. Santetti

marcio.santetti@emerson.edu

Bugs

Bugs

Jeffrey Katzenberg




Bugs

Jeffrey Katzenberg



Bugs

Michael Eisner




Bugs



1998: A Bug’s Life and Antz come out.



Katzenberg vs. Eisner in a game of strategy.

The start: Katzenberg leaves or stays?


Eisner: Produce Bug’s or not?


What about Katzenberg?


What about Katzenberg?




How much information does Katzenberg have?


Is it realistic to assume he knows about Eisner’s decision?

What about Katzenberg? Imperfect information


Early or not?

Is this a game?


Recall the 5 elements of a game of strategy:


  1. A list of players;
  2. A complete description of what the players can do (i.e., their actions);
  3. A description of what the players know when they act;
  4. A specification of how the players’ actions lead to outcomes;
  5. A specification of the players’ preferences over outcomes (i.e., the payoffs).

Is this a game?


Recall the 5 elements of a game of strategy:


  1. A list of players;
  2. A complete description of what the players can do (i.e., their actions);
  3. A description of what the players know when they act;
  4. A specification of how the players’ actions lead to outcomes;
  5. A specification of the players’ preferences over outcomes (i.e., the payoffs).

Information sets

Information sets


An information set specifies the players’ information at decision nodes in the game.


The information sets in a game precisely describe the different decisions that players have to make.


  • Every decision node is contained in an information set.

  • Some information sets consist of only one node.

1—4

5: Payoffs

How did it end?

Further examples

1: Two stores, two prices



What is the difference?

2: Draw your tree


Firm A decides whether to enter firm B’s industry. Firm B observes this decision. If firm A enters, then the two firms simultaneously decide whether to advertise.

Otherwise, firm B alone decides whether to advertise. With two firms in the market, the firms earn profits of $3 million each if they both advertise and $5 million if they both do not advertise.

If only one firm advertises, then it earns $6 million and the other earns $1 million. When firm B is solely in the industry, it earns $4 million if it advertises and $3.5 million if it does not advertise. Firm A earns nothing if it does not enter.

Next time: Strategies & the normal form