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Introduction to Game Theory: Strategies, Methods, and Applications

This presentation by Mrityunjay Sanwal at SMU II Sem introduces game theory, defined as the study of decision-making in competitive scenarios involving multiple rational players. It explores key concepts such as pure strategy games with saddle points and mixed strategy games without saddle points. The graphical method is illustrated through a case study of Coca-Cola vs. Pepsi, showcasing how Pepsi analyzes market shares and advertising strategies against its competitors. The pay-off matrix is used to determine optimal advertising strategies for maximum effectiveness.

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Introduction to Game Theory: Strategies, Methods, and Applications

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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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