lecture8 notes

G is called an ordinal potential game if it admits an

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: physical systems. It will be useful both for locating pure strategy Nash equilibria and also for the analysis of “myopic” dynamics. 12 Game Theory: Lecture 8 Potential Games Potential Functions and Games Let G = �I , (Si ), (ui )� be a strategic form game. Definition A function Φ : S → R is called an ordinal potential function for the game G if for each i ∈ I and all s−i ∈ S−i , ui (x , s−i ) − ui (z , s−i ) > 0 iff Φ(x , s−i ) − Φ(z , s−i ) > 0, for all x , z ∈ Si . G is called an ordinal potential game if it admits an ordinal potential. Definition A function Φ : S → R is called an (exact) potential function for the game G if for each i ∈ I and all s−i ∈ S−i , ui (x , s−i ) − ui (z , s−i ) = Φ(x , s−i ) − Φ(z , s−i ), for all x , z ∈ Si . G is called an (exact) potential game if it admits a potential. 13 Game Theory: Lecture 8 Potential Games Example A potential function assigns a real value for every s ∈ S . Thus, when we represent the game payoffs with a matrix (in finite...
View Full Document

This document was uploaded on 03/19/2014 for the course EECS 6.254 at MIT.

Ask a homework question - tutors are online