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

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Game Theory Presented By: - Mrityunjay Sanwalot SMU II Sem

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.” 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.”

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

Pure Strategy Game With saddle point……. B B1 B2 B3 row minima A A Maximin A A Column Maxima Minimax

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

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.

Pay – off Matrix Pepsi/Coca Cola Sprite Fanta Coca Cola Minimum Mountain Dew Pepsi Maximum Maximin= 10 & Minimax= 12 i.e. Maximin is not equal to Minimax => No saddle point.

Pay – off lines for Pepsi Coca cola’s Product Pepsi’s pay-off(market share) Sprite 15p2 + 10p1 Fanta 6p2 + 12p1 Coca Cola 7p2 + 20p1 Pepsi/Coca Cola Sprite Fanta Coca Cola Mountain Dew Pepsi

Pepsi/ Coca cola Sprite Fanta Coca Cola Mountain Dew Pepsi

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.