Last Mover Advantage

Have you ever played the game of, “guess a number between 1 and 100, the person closest to the correct number wins”?

The optimal guess is always one away from the other person’s guess. If the first person guesses 50, the optimal guess is 51. Then 49, then 52, and so on. The guesses cluster around the midpoint.

The first person to play usually has a disadvantage. Suppose the first person guesses 10, and the second person guesses 11. The second person controls every outcome 11-100.

This is a last mover advantage (although the second-to-last guesser technically has the advantage, assuming optimal play).

Let’s give a more significant example of this phenomenon. Suppose there is a town with 16 blocks arranged on a road:

__   __   __   __   __   __   __   __   __   __   __   __   __   __   __   __

Two food joints (joint A and joint B) are deciding where to set up shop. They could set up on opposite sides of the town:

 A    __   __   __   __   __   __   __   __   __   __   __   __   __   __   B 

Let us assume, for the sake of simplicity, that customers will always visit the fast food joint that is closest to them. You will split the town with the current layout:

 A    <     <     <     <     <     <     <     >    >     >     >    >    >     >    B 

That’s not very efficient. Suppose the joints decide to set up shop closer to the center of town, so that customers do not have to travel so far:

__   __   __   __   A   __   __   __   __   __   __    B   __   __   __   __

Each joint continues to dominate one side of the town:

 >    >     >     >    A    <     <     <      >    >     >      B    <     <     <     < 

This is the distribution that requires people to travel the shortest to get fast food.

But you know they won’t do that. Why? Because of game theory. If A moves closer to the midpoint, what happens?

 >     >     >     >     >      >     >     A    <    __    >     B     <     <     <     < 

And A would have moved even closer to B, like this:

 >     >     >     >     >     >     >     >      >      >     A     B     <     <     <     < 

If not for the fact that B would never be so foolish as to let the above happen. This is how things will actually play out:

 >     >     >     >     >     >     >     A     B    <     <     <     <     <     <     < 

Clustering around the midpoint. This is the less efficient organization, but the outcome of game theory.

This is why fast food joints tend to be built near each other. A Wendy’s will actually do better next to a McDonalds than it will by its own. This phenomenon part of how cities form.

You would think a joint would do better by its own, because there’s less competition. But you are actually reducing your competitive advantage by going farther away from your opponent.

Keep in mind, we are assuming the joints are of uniform quality, and the only difference is where they are built.

With that said, this has implications for virtually all marketing; just switch out “location” with “marketing strategy.”

This has interesting ramifications for traditional politics, as per this continuum:

This, of course, is a simplification of the political landscape. But the important thing is to recognize a continuum.

Have you ever thought the parties are two boring and non distinctive sides of the same coin? That’s because they have nothing to gain from losing the mid-ground.

In elections with a simple majority winner-take-all voting system, only two parties are viable, because a third party will leech votes from its most ideologically similar contender. It is also important to remember that parties can change their platforms as many times as they want to appeal to more voters.

Under these constraints, when the optimal political alignment is right next to and slightly more center than your opponent, candidates will theoretically become as centrist (and therefore as similar to each other) as possible.

The fact that they are so close together is the reason power-changes between parties are common. Permanent majorities do not exist in US politics. It’s not because the parties fail or succeed to persuade anyone. It’s because the parties are always changing to accommodate voter opinion.

We are holding a few variables constant. For example, we are assuming that everyone votes. In real elections, voter apathy is very significant. 

That is one reason I don’t support mandatory voting. The desire to overcome apathy is an incentive for the parties to differentiate themselves.

What about primaries? The political continuum is split in two:

In the primaries, the candidates of each party rush to the center of their respective political spectrums. In the general, the spectrum is once again united, and the candidates subsequently change their stances. They again migrate towards moderation.