Formalizing strategies

Game Theory // Fall 2025

Prof. Santetti

marcio.santetti@emerson.edu

Strategy

Recall the Katzenberg-Eisner (Bug’s-Antz) game:

Strategy



  • What are each player’s actions?

Strategy



  • What are each player’s strategies?

Strategy


The most important concept in Game Theory is the notion of strategy.


A strategy is a complete contingent plan for a player in a game.


A complete contingent plan is a full specification of a player’s behavior, which describes the actions that the player would take at each of his possible decision points. In other words, a player’s strategy describes what they will do at each of their information sets.

Strategy



Things that strategies cover:


  • Avoid mistakes;

  • Now what am I supposed to do?



Notation

Notation




Si : The strategy space (also called strategy set) of player i.

Notation


Notation


Notation

Next time: The normal form