Game Theory - Quantitative Analysis for Decision Making
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The document discusses game theory, its history, key concepts, and applications in various fields such as economics, psychology, and military strategy. It explains important elements like players, strategies, payoffs, and the concept of Nash equilibrium, illustrating these principles with examples including the prisoner's dilemma and penny matching game. The theory, established by pioneers like John von Neumann and John Nash, provides mathematical insights into competitive decision-making scenarios.
Game Theory - Quantitative Analysis for Decision Making
- 1. QUANTITATIVE ANALYSIS FOR DECISION MAKING (QUANTITATIVE MANAGEMENT PROJECT)
- 2. WHAT IS GAME THEORY? HISTORY OF GAME THEORY APPLICATIONS OF GAME THEORY KEY ELEMENTS OF A GAME TYPES OF GAME NASH EQUILIBRIUM (NE) PURE STRATEGIES AND MIXED STRATEGIES 2-PLAYERS ZERO-SUM GAMES PRISONER’S DILEMMA
- 3. THE BRANCH OF MATHEMATICS CONCERNED WITH THE ANALYSIS OF STRATEGIES FOR DEALING WITH COMPETITIVE SITUATIONS, WHERE THE OUTCOME OF A PARTICIPANT’S CHOICE OF ACTION DEPENDS CRITICALLY ON THE ACTIONS OF OTHER PARTICIPANTS. GAME THEORY HAS BEEN APPLIED TO CONTEXTS IN WAR, BUSINESS AND BIOLOGY. THE MATHEMATICS OF HUMAN INTERACTIONS.
- 4. THE MATHEMATICAL THEORY OF GAMES WAS INVENTED BY JOHN von NEUMANN AND OSKAR MORGENSTERN (1944) JOHN FORBES NASH Jr. INVENTS CONCEPT OF NASH EQUILIBRIUM (1950) JOHN HARSANYI, JOHN FORBES NASH AND REINHARD SELTEN WON NOBEL PRIZE IN ECONOMICS FOR GAME THEORY (1994)
- 5. PSYCHOLOGY LAW MILITARY STRATEGY MANAGEMENT SPORTS GAME PLAYING MATHEMATICS COMPUTER SCIENCE BIOLOGY ECONOMICS POLITICAL SCIENCE INTERNATIONAL RELATIONS PHILOSOPHY
- 6. PLAYERS : WHO IS INTERACTING? STRATEGIES : WHAT ARE THEIR OPTIONS? PAYOFFS : WHAT ARE THEIR INCENTIVES? INFORMATION : WHAT DO THEY KNOW? RATIONALITY : HOW DO THEY THINK?
- 7. COOPERATIVE OR NON COOPERATIVE ZERO-SUM AND NON-ZERO SUM SIMULTANEOUS AND SIQUENTIAL PERFECT INFORMATION AND IMPERFECT INFORMATION FINITE AND INFINITE STRATEGIES
- 8. THE UPPER VALUE OF THE GAME IS EQUAL TO THE MINIMUM OF THE MAXIMUM VALUES IN THE COLUMNS. THE LOWER VALUE OF THE GAME IS EQUAL TO THE MAXIMUM VALUES OF THE MINIMUM VALUES IN THE ROW.
- 9. B A Y1 Y2 MINIMUM X1 X2 MAXIMUM 6 7 10 7 6 -12 10 -12 6 7
- 10. A MIXED STRATEGY GAME EXISTS WHEN THERE IS NO SADDLE POINT. EACH PLAYER WILL THEN OPTIMIZE THEIR EXPECTED GAIN BY DETERMINING THE PERCENT OF TIME TO USE EACH STRATEGY.
- 12. A STABLE STATE OF A SYSTEM INVOLVING THE INTERACTION OF DIFFERENT PARTICIPANTS, IN WHICH NO PARTICIPANT CAN GAIN BY A UNILATERAL CHANGE OF STRATEGY IF THE STRATEGIES OF THE OTHERS REMAIN UNCHANGED.
- 13. For example, imagine a game between Tom and Sam. In this simple game, both players can choose strategy A, to receive $1, or strategy B, to lose $1. Logically, both players choose strategy A and receive a payoff of $1. If you revealed Sam's strategy to Tom and vice versa, you see that no player deviates from the original choice. Knowing the other player's move means little and doesn't change either player's behaviour. The outcome A, A represents a Nash Equilibrium.
- 14. PENNY MATCHING : • EACH OF THE TWO PLAYERS HAS A PENNY. • TWO PLAYERS MUST SIMULTANEOUSLY CHOOSE WHETHER TO SHOW THE HEAD OR THE TAIL. • BOTH PLAYERS KNOW THE FOLLOWING RULES: 1. IF TWO PENNIES MATCH (BOTH HEADS OR BOTH TAILS) THEN PLAYER 2 WINS PLAYER 1’S PENNY. 2. OTHERWISE, PLAYER 1 WINS PLAYER 2’S PENNY. -1 , 1 1 , -1 -1 , 1 1 , -1 HEAD TAIL PLAYER 2 HEAD TAIL PLAYER1
- 15. • NO COMMUNICATION - STRATEGIES MUST BE UNDERTAKEN WITHOUT THE FULL KNOWLEDGE OF WHAT THE OTHER PLAYERS (PRISONERS) WILL DO. • PLAYERS (PRISONERS) DEVELOP DOMINANT STRATEGIES BUT ARE NOT NECESSARILY THE BEST ONE. - ALBERT W. TUCKER
- 16. 10 YEARS FOR BILL 1 YEAR FOR TED BOTH GET 5 YEARS 1 YEAR FOR BILL 1O YEARS FOR TED BOTH GET 3 YEARS CONFESS NOT CONFESS BILL CONFESS NOT CONFESS TED
- 17. DEBOTTAM PAUL CHOUDHURY ISHITA BOSE SAUMYAJIT BANDAPADHYAY DEBOSMITA MAJUMDER JHILIK CHATTERJEE