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Business

Introduction to Game theory-Operation research,

Biju BodheswarFolgen

- 2. Introduction We studied models with internal interest LPP, Transportation, Assignment etc In practical life, it is required to take decisions • in a competing situation • there are two or more opposite parties with conflicting interest and • the outcome is controlled by the directions of all parties concerned 3
- 3. Let’s play the “grade game” If you put A and your pair puts B, then you will get grade 10, and your pair grade 3; If both you and your pair put A, then you both will get the grade 7 If you put B and your pair puts A, then you will get the grade 3 and your pair grade 10; If both you and your pair put B, then you will both get grade 9 4 Write down on a paper either the letter A or the letter B. Think of this as a "grade bid". I will randomly pair your paper with one other's paper. Neither you nor your pair will ever know with whom you were paired. Here is how grades may be assigned for this class:Rules
- 4. Outcome matrix • Just reading the text is hard to absorb, let’s representing the game:use a concise way my pair of A B A me B grades 6 7,7 10,3 3,10 9,9
- 5. The grade game: discussion What did you choose? Why? Two possible way of thinking: – Regardless of my partner choice, there would be better outcomes for me by choosing A rather than B; – We could all be collusive and work together, hence by choosing B we would get higher grades. • • 8
- 7. There may be win win situations or Win Lose situations or even Lose Lose
- 8. What is a Game....? 1. How many persons are involved...? 2. Is any rule is needed ...? 3. What is the outcome...?
- 9. What is a Game....? Game is an activity between two or more persons according to a set of rules at the end of which each person receives some benefits or satisfaction or suffers loss
- 10. What is a Game theory....? Is a theory of conflict. It is a mathematical theory which deals with competitive situations
- 11. A Competitive situation is called game 8 •The number of competitors called players •The players act rationally and intelligently •Each player has available to him a finite number of choices or possible course of action called strategies. •The players select their respective course of action (strategies) simultaneously •The players make individual decisions without direct communication •The payoff is fixed and determined in advance
- 12. Terms 8 Strategy :- is a course of action taken by one of the participants in a game Pay off matrix – is the result or outcome of the strategy is the pay off Two person zero sum game: a game of two persons, in which the gain of one player are the losses of the other player
- 13. Decision Making Situations 8 Decision Making Under certainty Under risk Under Uncertainty Pure strategy Mixed strategy 2x2 (Arithmetical method) 2xm or nx2 (Graphical Method) Mxn (LPP)
- 14. Pure strategy: is a decision where the players always choose a particular course of action Mixed Strategy : play different strategies each at a certain time. The player decides in advance to use all or some of his available course of action in some fixed proportion
- 15. Value of the game: Maximum generated gain to player. (fair game = value of the game is zero) 1. What is the expectation of a successful player? 2. What is the expectation of an unsuccessful player? Maximin: Maximum of minimum pay off or outcome MiniMax: Minimum of the Maximum pay off
- 16. Company StrategiesUnionStrategies I II III IV V I 2 0 0 50 30 II 40 20 10 20 50 III -40 -30 0 -30 60 IV 50 10 -50 -20 -60 Row minimu m 2 10 -40 -60 Column Maximum 50 20 10 50 60 10 10 Saddle Point Minimum in the row and maximum in the column A Company Management and Labour Union are negotiating a new 3 year settlement. Strategy I. Hard and Aggressive Bargaining II. Reasoning & Logical Approach III. Legalistic strategy IV. Conciliatory approach
- 17. Value of Game = 10 Union’s strategy = II – Reasoning and logical approach Company’s strategy = 3 – Legalistic strategy Will continue.......