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Game Theory

Game Theory. Presented By: - Mrityunjay Sanwalot SMU II Sem. Introduction.

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Game Theory

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  1. Game Theory Presented By: - MrityunjaySanwalot SMU II Sem

  2. Introduction • Game theory may be defined as – “ a body of knowledge that deals with making decisions when two or more intelligent and rational opponents are involved under conditions of conflict and competition.”

  3. (Saddle Point Exists) Linear Programming Method Arithmetical Method Graphical Method

  4. Pure Strategy Game • With saddle point……. B B1 B2 B3 row minima A A1 1 2 2 1 Maximin A2 0 -4 -1 -4 A3 -2 3 -2 -2 Column 1 3 2 Maxima Minimax

  5. Mixed Strategy Game • Without saddle point……. • Graphical Method Eg: - Coca-Cola v/s Pepsi

  6. Pepsi calculated the market share of two products, Pepsi and Mountain Dew, against its major competitor Coca Cola’s three products, Coca Cola, Fanta and Sprite and tried to find out the effect of additional advertisement in any of its products against the other.

  7. Pay – off Matrix Maximin= 10 & Minimax= 12 i.e. Maximin is not equal to Minimax => No saddle point.

  8. Pay – off lines for Pepsi

  9. Pay-off corresponding to Sprite = Pay-off corresponding to Fanta => 15p2 + 10p1 = 6p2 + 12p1 Since, p1 + p2 = 1 Putting p2 = 1 – p1 and solving… Gives p1 = 9/11 or 81.81% p2 = 2/11 or 18.18% Which means, Pepsi should advertise Mountain Dew 18.18% times and Pepsi 81.81% times of total advertisement in order to obtain optimum result irrespective of rival product’s strategy. Substituting p1 and p2: We get, Value of the game = 120/11.

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