Hidden Order in Daily Life

CCST9017 Hidden Order in Daily Life:

A Mathematical Perspective Lecture 2 Introduction to Game Theory

Dr. Tuen Wai Ng Department of Mathematics

Content

Prisoner’s Dilemma Dominant Strategy Equilibrium Mixed Nash Equilibrium An important concept introduced by the mathematician John Nash who was then awarded the Nobel Prize in Economics

Nash at HKU,2003

Content

An explanation of the mathematics in the movie “A Beautiful Mind” and John Nash's Nobelwinning theory

Statement of John Nash's Nobel-winning theorem

What is Game Theory ?

Game theory is the study of mathematical models on conflicts and co-operations between rational individuals. It studies the behavior of decision makers whose decisions affect each other. Game theory provides the language and framework for the discussion of problems in economics, social sciences, evolutionary biology,etc.

John von Neumann

Game theory was first developed by the mathematician John von Neumann in 1928. Born in 1903, Hungary. Involved in the development of atomic bombs. Designed and built the first computer.

John von Neumann

Game theory was first developed by John von Neumann in 1928. At that time, it was only considered as a branch of pure mathematics. In 1944, he and Oskar Morgenstern published the book“Theory of Games and Economic Behavior”.

Prisoner’s Dilemma

This most famous example in game theory was invented by John Nash’s thesis advisor Albert W. Tucker. John and Peter have been arrested for possession of guns. The police suspects that they are going to commit a major crime. John and Peter are interrogated in separate rooms. A clever attorney offers each of them the following deal.

Prisoner’s Dilemma

If no one confesses, they will both be jailed for 2 years. If only one confesses, he’ll go free and his partner will be jailed for 10 years. If they both confess, they both get a 5 year sentence .

Matrix Representation of Prisoner’s Dilemma

Peter Don’t Confess confess Confess...