Question answer - Game Theory & Tax

Suppose that two internet companies are racing to set up online bookstores (imagine that this is before Amazon.com). One of the internet companies is from India, and one is from North America. The sunk costs to set up operations are $200,000; once those are spent, each firm has the capacity to meet any market demand. If both firms set up bookstores, they will be seen as perfect substitutes in the eyes of customers. Nonetheless, if one or both firms develop bookstores, total value created in the market is estimated to be $10 million. (They both are targeting the US market.) 1. The firms have to choose whether to set up or not. Write down the simultaneous move game that describes this strategic situation. What is (are) the Nash equilibrium outcome(s)? Why is it reasonable (or not reasonable) to think of this as a simultaneous move game? There are two firms, wondering whether to enter a market or not. The fixed costs in order to get the business started are $0.2Mio. The market they are targeting has a total value of $10Mio. If they would both enter the market, their offers would be seen as perfect substitutes which would yield in a value of $5Mio for each firm. Why is it reasonable (or not reasonable) to think of this as a simultaneous move game? In order to evaluate which company should choose which strategy, the game theory is a powerful tool as it provides a framework that helps to reason about situations of strategic interdependence. In this game, there are two players, and the payoff of the actions each player does depends on the actions of the other player. By assumption, all players are informed about the available actions. However, each player selects an action without knowing what the other player is going to choose. In the given situation, there are two companies which are considering to enter a particular market. Each company is aware of the other and what choices it has. Furthermore, the decision of the competitor will be reflected in the payoffs of the company as it either is able to get a market share of 100 % and thus revenues of $10Mio or has to equally share the market value and gets just $5Mio. Finally, even though the companies have to decide simultaneously to pursue the market entry and create the sunk costs of $0.2Mio, they have to make the decision without knowing what the competitor does, as the investment of the sunk costs is not immediate apparent. This is what makes this a simultaneous-move game. Write down the simultaneous move game that describes this strategic situation. Situation 1: Firm India decides to enter and Firm North America decides to enter. Both companies would be facing costs of $0.2 Mio and can expect to gain revenues of $5Mio. Hence, the payoff for each firm would be $5Mio - $0.2Mio = $4.8Mio. Situation 2: Both firms, firm India and firm North America, decide not to enter the market, what would for both companies lead to a payoff of $0, as no costs incur neither do any profits. Situation 3: Firm India decides to enter the market whereas firm North America decides not to enter the market. Given this situation, firm India is facing $0.2Mio sunk costs and a revenue of $10Mio which leads to a payoff of $9.8Mio. Firm North America has no costs and no profits, thus a payoff of $0. Situation 4: Firm India decides not to enter the market whereas firm North America decides to enter the market. Given this situation, firm North America is facing $0.2Mio sunk costs and a revenue of $10Mio which leads to a payoff of $9.8Mio. Firm India has no costs and no profits, thus a payoff of $0. The quantitative perspective is presented in the table below. The convention is that the row player’s payoff is listed first and the column player’s payoff is listed second. Firm North America Enter Not enter Firm India Enter 4.8 ; 4.8 9.8 ; 0 Not enter 0 ; 9.8 0 ; 0 What is (are) the Nash equilibrium outcome(s)? In order to evaluate how both companies will react, a Nash equilibrium is helpful. In a Nash equilibrium, no player wants to change his strategy given the expected strategy of the competitor. Let us start from the perspective of firm India. Given that firm North America enters the market, firm India’s best choice is to enter the market, too. Given that firm North America does not enter the market, firm India’s best choice is still to enter the market, as this would result in a higher payoff than not entering the market. It is obvious, that entering the market is a dominant strategy for firm India, this means that no matter what firm North America does, firm India should always enter the market. Let us look at the situation from firm North America’s perspective. Given that firm India enters the market, it is firm North America’s best choice to also enter the market. Given that firm India does not enter the market, firm North America’s best choice is still to enter the market. As the table reveals, firm North America has a dominant strategy as well. It is always better to enter the market than not enter the market. In this case, there is only one Nash equilibrium and it leads to the suggestion that both firms should enter the market. Firm India has to expect that Firm North America will enter the market as this is its dominant strategy. Given this expected strategy, it is better for firm India to also enter the market and vice versa. As every player has a dominant strategy, there is a second way to find the Nash equilibrium. For firm India it is always beneficial to enter the market, thus the second option can be crossed out. The same is true for firm North America. This leaves us with the same result, both firms should enter the market. Firm North America Enter Not enter Firm India Enter 4.8 ; 4.8 9.8 ; 0 Not enter 0 ; 9.8 0 ; 0 2. Suppose that selling books in India incurs a higher tax than in North America. This is a unit tax on the sale of the book, determined by the location of the seller, not the customer. How might that change the outcome?