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Game Theory

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Game Theory Rationality

Assumptions:

humans are rational beings

humans always seek the best alternativein a set of possible choices

Why assume rationality?

narrow down the range of possibilities

predictability

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What is Game Theory?

Game theory is a study of how tomathematically determine the beststrategy for given conditions in order tooptimize the outcome

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Game Theory

Finding acceptable, if not optimal,strategies in conflict situations.

Abstraction of real complex situation

Game theory is highly mathematical Game theory assumes all human

interactions can be understood andnavigated by presumptions.

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Why is game theory important?

All intelligent beings make decisions all the time.

AI needs to perform these tasks as a result.

Helps us to analyze situations more rationally andformulate an acceptable alternative with respect tocircumstance.

Useful in modeling strategic decision-making

Games against opponents

Provides structured insight into the value ofinformation

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Zero-Sum Games

The sum of the payoffs remains constantduring the course of the game.

Two sides in conflict

Being well informed always helps a player

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Non-zero Sum Game

The sum of payoffs is not constant duringthe course of game play.

Players may co-operate or compete

Being well informed may harm a player.

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Games of Perfect Information

The information concerning an

opponents move is well known in

advance.

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Imperfect Information

Partial or no information concerning theopponent is given in advance to the

players decision.

Imperfect information may be diminishedover time if the same game with the sameopponent is to be repeated.

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Matrix Notation (Column) Player II

Strategy A Strategy B

(Row) Player IStrategy A (P1, P2) (P1, P2)

Strategy B (P1, P2) (P1, P2)

Notes: Player I's strategy A may be different from Player II's.

P2 can be omitted if zero-sum game

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Games of Conflict

Two sides competing against each other Usually caused by complete lack of

information about the opponent or thegame

Characteristic of zero-sum games

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Maximin & Minimax Equilibrium

Minimax - to minimize the maximum loss(defensive)

Maximin - to maximize the minimum gain(offensive)

Minimax = Maximin

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Mixed Strategy

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Limitations & Problems

Assumes players always maximize theiroutcomes

Some outcomes are difficult to provide autility for

Not all of the payoffs can be quantified

Not applicable to all problems