Maastricht University School of Business and Economics Maastricht, 4th December 2011 Bastian Hauk, BH ID number: i6034999 Study: International Business Course Code: EBC1009 Economics & Business Group Number: 31 Economics Tutor: Khan Writing Tutor: Hetty Bennink Writing Assignment: Main Paper
Table of Contents
Page 1. Introduction 2. Economic Principle: Game Theory 3. Applied Economic Principles 3.1. Theory of Game for simultaneously Decision Making 3.2. The extended Version for consecutive Decision Making 4. Conclusion References 4 6 7 8 2 2
1 Introduction In the United States of America there are only two very well-known discount retailers: Target and Walmart. Both are currently operating all over the country which places each of them among the biggest corporations in the United States. Nearly every American has been to at least one of them because they sell almost everything and E. Basker described this service “one-stop shopping” (2007).
In 2007, Walmart operated more than 3,400 stores across the USA and a survey showed that by the end of 2005 46 percent of Americans lived within 5 miles of the nearest store; within 15 miles even 88 percent (Basker, 2007). Target operated 1,750 stores in January 2011 (Target Corp., 2011). Since their wide range of products is quite similar they are large competitors.
Thus, they are constantly waging price war against each other. In addition, they make use of strategic interaction and especially of game theory which is a mathematical model describing a decisionmaking process and showing how the players make different decisions that potentially affect each other’s interests (von Stenge, & Turocy, 2001). This paper analyses strategic interaction between Walmart and Target with respect to the game theory and the extended version. In order to do so it introduces first the theoretic background of strategic interaction.
Afterwards it applies game theory and the extended version to this case in order to show the impact of strategic interaction on both discount retailers. It concludes by stating the importance of strategic interaction to optimal decision making and its relevance for Walmart and Target.
2 Economic principles: game theory and extended version The theory of games describes certain concepts in which several players influence each other’s decisions in situations of conflict and competition (Moffatt, 2011). In order to apply game theory there must be at least two players. The three basic elements of a game are the player, the strategies he can choose from and the payoffs the players receive from each combination of strategy. The payoff matrix describes the outcomes in a certain game for each possible combination of strategies as shown in Figure 2.1. 2
Player One Strategy 1 Strategy 1 Outcome Player 1 Strategy 2 Outcome Player 1
Outcome Player Two Strategy 2 Player 2 Outcome Player 1
Outcome Player 2 Outcome Player 1
Outcome Player 2 Figure 2.1: Payoff matrix for a two player game
Outcome Player 2
If one player used a dominant strategy, his choice yields a higher payoff, regardless what the other player does and as a result he has no incentive to change his strategy. For this example, player one’s dominant strategy would be strategy one if he received a higher outcome no matter which strategy player two chooses, but only if he then receives the highest payout. There are also some particular outcomes; for example the Nash equilibrium which occurs when any combination of strategies is the best strategy with the best possible outcome for all players (McDowell, Thom, Frank, & Bernanke, 2009).
An outcome created by two dominant strategies which is worse than the outcome created by two dominated strategies is called prisoner’s dilemma. The prisoner’s dilemma only occurs when each player’s dominant strategy results in a smaller payoff than it would have if they had chosen the dominated strategy. Game theory also assumes that the decisions are made simultaneously. To illustrate a game in which the players decide interdependent, the economist uses the extended version of game theory which is displayed with a game tree (McDowell, Thom, Frank, & Bernanke, 2009).
Company 1 Decision: Action A or Action B
Company 2 Decision: Action C or Action D
Outcome 1 Outcome 2
Company 2 Decision: Action C or Action D
Outcome 3 Outcome 4
Action D Figure 2.2: Decision tree Figure 2.2 is an example of a game tree. Company 1 first decides which action they will take, which can be either A or B. Company 2 then has the choice how they want to react and whether they take action C or D. The best outcome can only be achieved with a backward induction as a result of evaluating the results first and afterwards predicting the other player’s strategy. For example, outcome 3 would be the best outcome for company 2 if company 1 chose action B and therefore company 2 chooses action C. Outcome 2 would gain the highest profit for company 2 if company 1 took action A.
3 Applied Economic Principles 3.1 Theory of game for simultaneously decision making As stated in the introduction this two very large American retailers are competitors and have a very similar customer base. The income of Targets customer base is slightly higher but it is not relevant for strategic interaction (Neuman, 2011).
Theory of game helps to understand the different prices and how the different price strategies affect consumer behavior. This example is not based on any specific data. However, it is logic for somebody willing to buy a certain good to substitute the same good with an identical one if the price is lower and there are not any additional efforts to make. By applying game theory, the three basic elements have to be clear. 4
Walmart and Target are the players. Different pricing of a certain product -a television- are the strategies while the different profits are the results of each combination of the strategies. Both companies have two pricing strategies: either to charge a low price of €300 or a high price of €500. They have to make the decision simultaneously, for instance before they release the television to the market. It is important to know that the customers are also willing to purchase the television for the high price.
Target High Price (€500) High Price (€500) Walmart Walmart earns €10,000 profit Low Price (€300) Walmart earns €15,000 profit Figure 3.1: Payoff matrix for Walmart and Target Figure 3.1 shows a potential payoff matrix for this strategic interaction. It shows all possible outcomes for the two pricing strategies. Walmart and Target would both make €10,000 profit if they charged the high price and €7,500 profit if they charged the low price. If Walmart chose the low pricing strategy and Target used the high pricing strategy Walmart would gain €15,000 compared to the €5,000 profit Target would make. Target also makes €15,000 profit using the low price if Walmart decides to charge the high price. What does that mean for both companies?
Since both of them would earn a higher profit by setting the price low in this scenario, both companies would choose “Low Price” as a dominant strategy. On the contrary, “High Price” would be the dominated strategy. Nash equilibrium can be found when both companies pick the “low price” strategy because they don’t have an incentive to change their strategy. This payoff 5
Low (€300) Target earns €15,000 profit Walmart earns €5,000 profit Target earns €7,500 profit Walmart earns €7,500 profit
Target earns €10,000 profit
Target earns €5,000 profit
matrix also shows that the strategy combination of “high price” and “high price” would be the best possible outcome for both firms. But rather than applying the dominated strategy Walmart and Target use the dominant strategy. This dilemma is called prisoner’s dilemma. Those dilemmas exist quite often and there are many reasons why they exist, for instance, both companies do not want the other one to make a higher profit or even to have the chance to receive a higher profit.
3.2. The extended version for consecutive decision making Therefore Target and Walmart react and might change the strategy they had choosen. Both competitors often change their strategies. Although Singh (2006) stated that prices at Walmart are about 15 percent lower than in traditional supermarkets, Neuman (2011) proved by comparing almost 60 items that Target’s prices were a bit lower than Walmart’s. It is hard to rely on data which are released with a 5 year time difference but it shows that both firms constantly adjust the prices to be competitive.
High Price Target High Price Walmart Low Price
€10,000 for Target €10,000 for Walmart €15,000 for Target €5,000 for Walmart €5,000 for Target €15,000 for Walmart €7,500 for Target €7,500 for Walmart
High Price Low Price Target Low Price
Figure 3.2: Decision Tree for Walmart and Target
Since the decisions of both companies are not made simultaneously the reacting firm -in this case Target- has to find out what action to take in order to receive the highest profit for either move Walmart makes. Walmart moves first and selects either strategy. Target is in the position to decide and how it wants to react. Thus, Target uses backward induction. First it evaluates the best results for each action Walmart uses; €15,000 profit if Walmart sets a high price and €7,500 profit if Walmart sets a low price.
Afterwards it chooses the strategy how to get to that profit. Finally Walmart moves and selects the low or the high price strategy and Target is able to react sufficiently. Assume that Walmart chooses the high price strategy then Target sets low prices and due to that Target earns the highest possible profit.
Walmart and Target are large competitors on the American retailer market and therefore strategic interaction is very important for them. Both companies know the ways to decide how to act concerning different strategies. Both companies know that it is necessary for them to react and choose the best strategy. In the first example both companies simultaneously introduce a television to the market. Their dominant strategy is to set a low price because both of them hope that the other company chooses the high price strategy.
This is one example of a free market wherein the customers always choose the low price if available. Walmart and Target would earn a larger profit if both set the high price. In the other case Walmart moves first and afterwards Target chooses the strategy which leads to the highest outcome. The reacting company’s best strategy in the extended version of game theory is always the low price strategy. On the contrary, when two companies have to decide simultaneously it is not always the best choice to choose the low price strategy although it is their dominant strategy.
References Basker, E. (2007). The Causes and Consequences of Wal-Mart’s Growth. The Journal of Economic Perspectives, 21 (3), 177-198. McDowell, M., Thom, R., Frank, R., & Bernanke, B. (2009). Principles of Economics, 2nd European Edition. Maidenhead, UK: McGraw-Hill Education. Moffatt, M. (2008). What are Game Theory and Bargaining Theory? Retrieved December 4, 2011, from http://economics.about.com/cs/studentresources/f/game_theory.htm Neuman, S. (2011).
Target Takes Aim At Walmart, With Some Success, NPR. Retrieved December 4, 2011, from http://www.npr.org/2011/08/19/139793948/target-takes-aim-at-walmartwith-some-success Singh, V., Hansen, K., & Blattberg, R. (2006). A Market Entry and Consumer Behavior: An investigation of a Wal-Mart Supercenter. Marketing Science, 25 (5), 457-476 Target Corp. (2011). Target Annual Report 2010. Minnesota, US: Target. Retrieved December 7, 2011 from http://www.sec.gov/Archives/edgar/data/27419/000104746911002032/a2201861z10k.htm#bg11101a_main_toc Turocy, T.L, von Stenge, B (2001). Game Theory. Academic Press Limited, 2 (2), 69-73. 10.1080/07430170152379371 doi: