Game Theory Behind Gas Station Clustering
In the above article, “Why Gas Stations Are So Close To Each Other”, Jonathan Becher uses game theory to explain the reasoning behind why gas stations are usually found relatively close to one another (a common, but often overlooked occurrence), and why this placement is actually the most socially optimal option. Becher cites Presh Talwalkar’s article “Hotelling’s Game, or Why Gas Stations Have Competitors Nearby” (link: https://mindyourdecisions.com/blog/2008/03/25/game-theory-tuesdays-hotelling%e2%80%99s-game-or-why-gas stations-have-competitors-nearby/) which includes a more in-depth explanation of this phenomenon. Interestingly, Talwalker connects the principles underlying the placement of gas stations in a city to those underlying presidential elections: more often than not, the nominees tend to be the most moderate in their party, and it is usually the most moderate candidate who wins the presidential election.
To understand why this is the case with presidential elections, let’s dissect the more concrete example of gas stations; once we fully understand why gas stations cluster, we can apply that to presidential elections. The reasoning behind gas station clusters is explained by the Facility Location Game, found in section 6.10 of the textbook, and when you think about it, it is somewhat intuitive. In a nutshell, it goes like this:
Suppose you have gas station companies 1 and 2. Each is choosing where to construct a gas station along a 120 mile stretch of highway running north to south, and each wants to place its gas station somewhere where the gas station will attract the highest number of cars. Cars will use the closest gas station, and the concentration of cars on the highway is uniform. For the sake of this example, anything outside the 120-mile stretch is irrelevant and should be discounted. Here are three situations in which the gas stations will attract an equal number of cars: 1) if both of the gas stations are in the middle of the highway, then one will attract all of the cars south of that location, while the other will attract all cars north of that location 2) if gas station 1 locates at the start of the 120 mile stretch and then station 2 locates at the end of the 120 mile stretch then gas station 1 will attract all cars south of the midpoint of the highway, while the station 2 will attract all cars north of that point. 3) if gas station 1 locates at the 30-mile mark while gas station 2 is at the 90-mile mark, then the first will attract cars from the beginning of the highway until the midpoint and the other will attract drivers from the midpoint to the end of the stretch of highway.
However, only the first example is stable; the other two examples, though they yield an equal number of cars to each gas station are unstable because the locations of each gas station in examples 2 and 3 incentivize each station to relocate to maximize the number of cars they attract. In example 2, if gas stations companies 1 and 2 chose to construct stations at different ends of the stretch, all gas station 1 would have to do would be to see that 2 has committed to construction at one of the ends (the 120-mile mark, for example), and then station 1 could simply construct its station at the 119-mile mark, thus attracting cars from mile 0 to mile 119.5. Each company realizes that they should construct a gas station at the midpoint of the highway, as they know otherwise they will be taken advantage of by the competing gas station company. Thus there exists a Nash equilibrium at the midpoint; it is the only Nash equilibrium in this game, as all other strategies are strictly dominated.
Although Talwalker’s claim that the workings behind gas station construction are similar to those in presidential elections may at first be rather counterintuitive, when we think about presidential elections in terms of the Facility Location Game it makes sense: the two candidates are trying to obtain as many votes as each is able to; considering the fact that the majority of people do not subscribe to extreme political ideologies, taking an extreme stance isn’t generally rewarded, because all the other candidate has to do would be to take a less extreme stance in order to appeal to a majority. A key difference between gas station placement and presidential elections is that due to the nature of presidential elections if candidate A was very right-wing, the candidate B couldn’t adjust by becoming only slightly less right-qing than A; each candidate is limited to movement within the side of the political spectrum of the party in which they were voted presidential candidate, whereas, with gas station placement, movement isn’t as limited. However, this limitation doesn’t change the dominant strategy of each candidate – to be the most moderate.
For more on the advantage of being politically moderate during presidential elections, please see: https://www.nytimes.com/2018/05/08/upshot/unable-to-excite-the-base-moderate-candidates-still-tend-to-outdo-extreme-ones.html