Post on 05-Apr-2018
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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