# Lecture 4 - Lecture 4 Introduction to Game Theory Source/1...

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Lecture 4 Introduction to Game Theory Source: /1 / D.R.Anderson, D.J.Sweeney, T.A.Williams. Quantitative Methods for Business, South- Western College Publishing, 11-th edition. Chapter 5. Contents: 4.1 Introduction to Game Theory 4.2 Mixed Strategy games 4.1 Introduction to Game Theory In decision analysis, a single decision maker seeks to select an optimal decision alternative after considering the possible outcomes of one or more chance events. In game theory, two or more decision makers are called players, and they compete as adversaries against each other. Each player selects a strategy independently without knowing in advance the strategy of the other player or players. The combination of the competing strategies provides the value of the game to the players. Game theory applications have been developed for situations in which the competing players are teams, companies, political candidates, armies, and contract bidders. In this section, we describe two-person, zero-sum games . Two-person means that two competing players take part in the game. Zero-sum means that the gain (or loss) for one player is equal to the corresponding loss (gain) for the other player. As a result, the gain and loss balance out so that the game results in the sum of zero. What one player wins, the other player loses. Let us demonstrate a two-person, zero-sum game and its solution by considering two companies competing for market share. Example 4.1. Competing for Market Share Suppose that two companies are the only manufacturers of a particular product; they compete against each other for market share. In planning a marketing strategy for the coming year, each company is considering three strategies designed to take market share from the other company. The three strategies, assumed to be the same for both companies, are as follows: Strategy 1 Increase advertising Strategy 2 Provide quantity discounts Strategy 3 Extend product warranty A payoff table showing the percentage gain in the market share for Company A expected for each combination of strategies follows. The notations a 1 , a 2 , and a 3 identify the three strategies for Company A; the notations b 1 ,b 2 , and b 3 identify the three strategies for Company B. It is a zero-sum game because any gain in market share for Company A is a loss in market share for Company B. Company B Increase Advertising b 1 Quantity Discounts b 2 Extend Warranty b 3 Company A Increase Advertising, a 1 4 3 2 Quantity Discounts, a 2 -1 4 1 Extend Warranty, a 3 5 -2 0 1

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In interpreting the entries in the table we see that if Company A increases advertising ( a 1 ) and Company В increases advertising ( b 1 ), Company A will come out ahead with an increase in market share of 4%. On the other hand, if Company A provides quantity discounts ( a 2 ) and Company В increases advertising ( b 1 ), Company A is projected to lose 1% of market share to Company B. Company A is seeking payoff values that show relatively large increases in its market share. Company В is seeking payoff values that show decreases or small increases in Company A's market share, and thus better results for Company B.
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