Game Theory and the Economies of Agglomeration
reference: 1.Talwalkar. Presh. Article: Why Are Mcdonalds And Burger King Usually Located Near Each Other? Fast Food Location Game Theory. Mind Your Decisions. October 23, 2012. <https://mindyourdecisions.com/blog/2012/10/23/why-are-mcdonalds-and-burger-king-usually-located-near-each-other-fast-food-location-game-theory/>
2. Glaeser,Edward. Talk: Productivity & Growth: Education, Agglomeration & Entrepreneurship. New Zealand Productivity Commission. Aug 19, 2013. <https://www.youtube.com/watch?v=G7gK1ZEsQc8>
Four years ago while my brother and I were on a long road trip, I started the conversation with a question made me curious for a long time— why the fast chain restaurants, McDonald’s Taco Bell Burger King etc, always gather in the same area along the highway? Doesn’t this business strategy increase competition? After I raised the question my brother answered me using an analogy of “the ice-cream vendors on the beach” from his Econ class: Two vendors began businesses by taking over each side of the beach. One day Jack expands its business toward the center, taking some customers away from Chris, therefore Chris employs the same strategy to keep its competitive advantage, and gradually two businesses sits near each other at the center of the beach and each take half share of the market.
“Vendors on the beach” illustrate the concept of Nash equilibrium. Assume in the model below A and B both try starting business on a 1km-road, A is placed on 250m from the left and B sits besides A (i). A would mostly like attract people from this 250m-long area while the people from the rest area would go to B, therefore A only has 25% market share while B has 75% and this is clearly not the best response of A. in this case A would keep pushing toward the center until both store locate at the center, each taking 50% market share , which reached the Nash equilibrium in this “business game.“ (ii). A small size business cluster is formed.
Game theory is also applied when similar firms try to open multiple stores. Presh Talwalkar does calculations in his article.1 Suppose McDonald’s and Burger Kings will choose among 10 possible locations, which were scored from 1 to 10 based on their business potential. Two players seek profit maximization. If McDonald’s choses 6,7,8,9,10, its payoff is total 25 (6+7+8+9+10, 56% market share). After M took the best place, BK choses 5,6,7,8,9 and will have only 20 points (5+6+7+8+9 44% market share). Although BK is making good profit but its losing M thus this is a weak strategy. Therefore the equilibrium is reached only when both companies take the locations with highest points, which is 6-10, and each has payoff of total 20 points (each has 50% market share)
Business clustering is a topic wildly studied by scholars in urban economics. In talk Productivity & Growth: Education, Agglomeration & Entrepreneurship, Edward Glaeser, Professor of Economics at Harvard, gives a more qualitative explanation to the phenomenon of business cluster with the concept of “effect of agglomeration”.2 The clustering of economic activities attracts suppliers and consumers to the area therefore leads to higher scale of production of firms with lower transportation costs, greater local supply and accumulation of labor and human capital. This theory emphasizes the economic advantages business clustering brings to the firm, which in other words is the result of “collaboration between similar firms,” but dismisses the aspect of competition. Game theory answers the question by putting competing firm in the game scenario, and along with effect of agglomeration provides a more complete explanation to business clustering. This example further demonstrate a wide application of game theory in various fields such as business.