Games Theory – SS3 Further Mathematics Lesson Note (Second Term)

Game Theory is a set of concepts aimed at decision-making in situations of competition or conflict (as well as of cooperation and interdependence) under specified rules. It is a decision theory which is applicable to competitive situations.

Behavioural objectives

By the end of the lesson, students should be able to:

• define game theory and a competitive game;
• state the properties of a competitive game;
• list the types of games and give an example of each;
• explain what a payoff (outcome) matrix is and how to read a positive or negative outcome for players A and B.

What is a competitive game?

A competitive game is a competitive situation which occurs between two or more persons.

What are the properties of a competitive game?

• The number of participants is stated or finite.
• Each action or operation of an individual is certain.
• The choices of the players are made simultaneously, so that each participant’s choice stays private from the others until he makes his decision.
• The players must know all the courses of action available, but must not know which of these courses will be chosen.

What are the types of games?

• One-person games
• Two-person games
• Two-person zero-sum games
• N-person games

One-person games

This is a game that consists of one player. There is no competition or conflict in it, because the interest of the only player is at stake. An example is the solitaire game.

Two-person games

This involves two players who have conflicting interests. Each player has several possible choices open to them at each play of the game. Examples are checkers and chess.

N-person games

This involves an unspecified number of players. Examples are poker (a card game) and Monopoly (a board game).

What is a payoff (outcome) matrix?

A payoff matrix is an expression of the first law of decision science. Each row represents one action that the decision maker might or might not freely choose to perform, while each column represents a possible state of nature.

Given two players A and B, if the outcome is positive, it represents a gain to player A and a loss to player B. If the outcome is negative, it represents a loss to A and a gain to B.

Evaluation

1. Define game theory.
2. State two properties of a competitive game.
3. List the four types of games.
4. Why is there no competition or conflict in a one-person game? Give an example.
5. In a payoff matrix for players A and B, what does a positive outcome mean for each player?

Assignment

Write short notes on two-person games and N-person games, giving two examples of each type where the note allows.