Nash Equilibrium and Business Competitions
Have you ever wonder why business competitors are often located close to each other? Such as McDonald’s and Burger King, Starbucks and CTB, or CFCU and Tomkins Trust. Wouldn’t it be intuitive to avoid competitors so you can attract all customers close to you? In this video, Jac de Haan introduces two ice-cream vendor on a long beach, and explains why the vendors eventually will set up their cart at the center of the beach. To add in some mathematical proof, we will transform the animation into a numeric model.
For simplicity, assume there are only 3 possible locations, A (0.25 miles from the left end), B (0.5 miles form the left), and C (0.75 miles from the left). Thus, both vendors have 3 strategies, and let the payoff be the percentage of customers they can attract. Further assume customers have no preference for vendors, but will select the one that is closer. And if the vendor is further than 0.25 miles away, there is a slight chance that customers will give up.
From a customer’s point of view, what is you preferred setting? Probably vendors at A, and C? Because then no matter where you are, there is a vendor within 0.25 miles. That sounds good! Let’s ask vendor 1 (Blue) to be at A and vendor 2 (grey) to be at C. Everybody seems happy until one day, vendor 1 realizes moving to point B will result in a higher payoff (62.5% of the customers)! Of course vendor 2 isn’t happy with the 37.5% customers left, so he/she decides to move to B as well. Now they are close to each other, just as what we see in real life. In fact, whatever point we initially assign the vendors to be, they will switch the location to get higher payoff until both of them are stuck at B. This is a Nash Equilibrium – a pair of strategy that are best response to each other, which means a single player (or vendor) cannot get a higher payoff by switching to other strategies.
This phenomenon can also be understand as a tragedy of commons – everyone tends to the maximize personal payoff. However, the outcome might have a lower collective payoff (remember some customers might give up since now the vendors can be 0.5 miles away). In real life examples, the situation is often more complicated: the center spot might be less desired as more companies join the competition; brands might target slightly different customers; and one company might have lower price than the other. However, there are often still “hot spots” of shops, restaurants, or gas stations. And for companies, they are not only “stuck” because they can’t reach to more customers by moving, but also because cost for transportation, construction, and operation might be higher if the new location is farther away from the city center.
Source:
TED-Ed. Why do competitors open their stores next to one another? YouTube.com. Oct 1, 2012. https://www.youtube.com/watch?v=jILgxeNBK_8