SS3 Second Term Further Mathematics Lesson Note – Games Theory

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WEEK 5

TOPIC: Games Theory

CONTENT:  

1. Introduction to games theory
2. Description of types of games
3. Solution two person zero sum games using pure and mixed strategies
4. Matrix games

SUB-TOPIC 1:

Game theory is a study of strategic decision making. It is also the study of mathematical models of conflict and cooperation between intelligent rational decision makers.

Another term suggested game theory as a more descriptive name for the discipline that it is an interactive decision theory. Game theory is mainly used in economics, political science and psychology, as well as logic and biology.

The theory first addressed zero sum games, such that one person’s gains exactly equal net losses of the other participant(s). Today, however, game theory applies to a wide of behavioural relations, and has developed into an umbrella term for the logical side of decision science, to include both human and non-humans, like computers. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by a theorist named John Von Neumann. He used Brownness’s fixed-point theorem on continuous mapping into compact convex sets in his original proof, which became a standard method in a game theory and mathematical economics. The second edition of his book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

This theory was developed extensively in the 1950s by many scholars. Games theory was later applied to biology in the 1970s.

EVALUATION 

1. Define games theory
2. Explain zero sum’s game
3. Mention the subjects where games theory is useful

SUB-TOPIC 2: Description of types of games

1. Cooperative or non-cooperative – a game is cooperative if the players are able to form binding commitments. For example the legal system requires them to adhere to their promises. In non cooperative games this is not possible. Communication among players is allowed in cooperative games, but not in non-cooperative

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