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Explanation of Game Theory Game Theory can be regarded as a multi-agent decision problem Game Theory can be regarded as a multi-agent decision problem There are many people contending for limited rewards/payoffs There are many people contending for limited rewards/payoffs
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Introduction toIntroduction to Game TheoryGame Theory
Presented by Presented by 蘇柏穎蘇柏穎 2004/12/92004/12/9
OutlineOutline What is Game Theory?What is Game Theory? ApplicationsApplications The formulations of a gameThe formulations of a game The strategies of a gameThe strategies of a game One example: The Prisoner’s One example: The Prisoner’s
DilemmaDilemma
Explanation of Game TheoryExplanation of Game Theory Game Theory can be regarded as a Game Theory can be regarded as a
multi-agentmulti-agent decisiondecision problem problem There are many people contending There are many people contending
for limited for limited rewards/payoffsrewards/payoffs
大老二大老二
Rules that Players FollowRules that Players Follow
1. They have to make certain moves 1. They have to make certain moves on which their payoff dependson which their payoff depends
2. These people have to follow certain 2. These people have to follow certain strategiesstrategies while making these while making these movesmoves3. Each player is supposed to behave 3. Each player is supposed to behave rationallyrationally
SummarySummary Game Theory is the analysis of Game Theory is the analysis of
situations which involve conflict situations which involve conflict and/or cooperationand/or cooperation
OutlineOutline What is Game Theory?What is Game Theory? ApplicationsApplications The formulations of a gameThe formulations of a game The strategies of a gameThe strategies of a game One example: The Prisoner’s One example: The Prisoner’s
DilemmaDilemma
Business and EconomicsBusiness and Economics
Artificial IntelligenceArtificial Intelligence
Everything About CompetitionEverything About Competition
OutlineOutline What is Game Theory?What is Game Theory? ApplicationsApplications The formulations of a gameThe formulations of a game The strategies of a gameThe strategies of a game One example: The Prisoner’s One example: The Prisoner’s
DilemmaDilemma
Two Formulations of a GameTwo Formulations of a Game
Extensive formExtensive form game treegame tree
Strategic formStrategic form matrix gamematrix game
Extensive form: Extensive form: The Game Tree FormulationThe Game Tree Formulation
The Game Tree for The Game Tree for Paper-Scissors-StonePaper-Scissors-Stone
U1
U2
(0,0) (1,-1) (-1,1) (-1,1) (0,0) (1,-1) (0,0)(-1,1)(1,-1)
StoneScissorsPaper
Game in Extensive FormGame in Extensive Form The internal nodes of T are the The internal nodes of T are the decision decision nodesnodes of the players of the players The edges of T are the The edges of T are the actionsactions that the pl that the player can chooseayer can choose Each leaf of T is labeled by an n-tuple (hEach leaf of T is labeled by an n-tuple (h11,,hh22,…,h,…,hnn) of ) of payoffspayoffs
Strategic form: Strategic form: The Matrix FormulationThe Matrix Formulation
The Strategic Form for The Strategic Form for Paper-Scissors-StonePaper-Scissors-Stone
StoneStone ScissorScissorss
PaperPaper
StoneStone 0, 00, 0 1, -11, -1 -1, 1-1, 1
ScissorScissorss
-1, 1-1, 1 0, 00, 0 1, -11, -1
PaperPaper 1, -11, -1 -1, 1-1, 1 0, 00, 0
Row player
Column player
Comparison Between Two FormsComparison Between Two Forms
Tree formulationTree formulation can represent all can represent all possible states that a game can havepossible states that a game can have
Matrix formulationMatrix formulation can only can only represent one interaction represent one interaction
Matrix is easier to store and do Matrix is easier to store and do arithmetic computationsarithmetic computations
OutlineOutline What is Game Theory?What is Game Theory? ApplicationsApplications The formulations of a gameThe formulations of a game The strategies of a gameThe strategies of a game One example: The Prisoner’s One example: The Prisoner’s
DilemmaDilemma
Strategies of a GameStrategies of a Game Deterministic strategiesDeterministic strategies Randomized strategiesRandomized strategies
• Mixed strategiesMixed strategies• Behavioral strategiesBehavioral strategies• General strategiesGeneral strategies
Deterministic StrategiesDeterministic Strategies The The pure strategiespure strategies are the are the
deterministic strategiesdeterministic strategies
Random Strategies:Random Strategies:
Mixed StrategiesMixed Strategies
Mixed StrategiesMixed Strategies The player has a set of The player has a set of pure pure
strategies Sstrategies S He defines a He defines a probability distributionprobability distribution
over the pure strategiesover the pure strategies He can only throw a dice at the He can only throw a dice at the
beginningbeginning of the game of the game After that, he must stick to the After that, he must stick to the
strategy he choosesstrategy he chooses
Random Strategies:Random Strategies:
Behavioral StrategiesBehavioral Strategies
Behavioral StrategiesBehavioral Strategies The player defines a The player defines a probability probability
distributiondistribution among action edges of among action edges of each decision node.each decision node.
When he reaches a When he reaches a decision nodedecision node, he , he throws a dice to decide which throws a dice to decide which strategy should be usedstrategy should be used
Random Strategies:Random Strategies:
General StrategiesGeneral Strategies
General StrategiesGeneral Strategies A general strategy of a player is A general strategy of a player is
probability distributionprobability distribution of all of all behavioral strategiesbehavioral strategies of the player of the player
OutlineOutline What is Game Theory?What is Game Theory? ApplicationsApplications The formulations of a gameThe formulations of a game The strategies of a gameThe strategies of a game One example: The Prisoner’s One example: The Prisoner’s
DilemmaDilemma
The Prisoner’s DilemmaThe Prisoner’s Dilemma Two robbers are arrested by the Two robbers are arrested by the
policepolice They are interrogated respectivelyThey are interrogated respectively Each of them have two choices: Each of them have two choices:
confess or deceiveconfess or deceive
Payoff of the GamePayoff of the Game
ConfessConfess DeceiveDeceive
ConfessConfess 20, 2020, 20 0, 300, 30
DeceiveDeceive 30, 030, 0 10, 1010, 10
Competition over 5 Competition over 5 different strategiesdifferent strategies
http://http://www.gametheory.net/Web/PDilwww.gametheory.net/Web/PDilemma/Pdilemma.htmlemma/Pdilemma.html
If people do not believe that Game If people do not believe that Game Theory is simple, it is only because Theory is simple, it is only because they do not realize how complicated they do not realize how complicated life is.life is.
~Modified ~Modified from from von Neumann, von Neumann, John John
Thanks EveryoneThanks Everyone