## Friday, December 5, 2008

### Econ 101: Game Theory and Car Dealers

The Oregonian reports today on the Oregon Automobile Dealers Association request to lawmakers that they prohibit the sale of cars on Sundays. Huh? Why on earth would dealers want lawmakers to limit how they operate? Isn't this the antithesis of allowing free markets to produce efficient outcomes?

Actually, in economics, game theory provides some useful insight into situations in which, when strategic interactions exist, the free market might lead to inefficient outcomes.

Let's try and see how auto dealers might be in just such a situation using the canonical example of the prisoner's dilemma game. Even though the title of the game refers to a particular story told with it, the canonical nature of the game is actually in the payoffs and outcomes. Here goes:

Suppose, for simplicity, that there are only two auto dealers. I shall describe their interaction with a payoff matrix (shown below). The two dealers are Honest Moe's and Crazy Larry's. Their strategies are either to stay closed on Sunday or to be open on Sunday. Honest Moe's payoffs from each of the four possible outcomes is the first number written (let's call it weekly profits) and Crazy Larry's is the second. Thus if both Honest Moe and Crazy Larry close on Sunday they will both get 120 and so on.

So what will happen if they are both left to their own devices? Well if Honest Moe knows Larry will close on Sunday, Moe will stay open because he can get 140 instead of the 120 he would get if he stayed closed. If Moe knows Larry will be open on Sunday, then Moe will open on Sunday because 100 is better than 80. The exactly same calculations apply for Larry. So, no matter what the other does, it is always better for each individual dealer to stay open on Sunday. Thus the outcome of the game is that both will be open Sunday and they both will get 100.

But is this the best outcome for the two dealers? No, they would both be better off if they both stayed closed on Sunday. This would give both of them payoffs of 120. This is the essence of the prisoner's dilemma: individual incentives lead this market into a sub-optimal outcome and thus the efficiency of the free market breaks down.

Just agreeing to stay closed on Sunday won't work, because each has an individual incentive to cheat and open up and get 20 more at 140 than at 120. In other words, the very best individual outcome is the be the only one open on Sunday.  So they need the option of opening up in Sunday removed from their choices and then they can both be made better off.

Whether consumers are better off is another story...

Gregory said...

This assumes the dealers create no value by opening on Sunday--in other words, the total sales will be the same either way, while reducing the industry's collective cost structure. Can't Portland-area car buyers defect to Vancouver to buy their cars on Sunday--if so, the move by the Association may be value destroying.

I recall Germany has (or used to have) laws that prevent certain types of businesses from opening on Sunday. I suspect the merchants themselves support this law for similar reasons.

Dann Cutter said...

Yup this is a pretty obvious strategy of trying to reduce staffing/operating costs on Sunday. Sundays are slow sale days, and are complicated by lenders being closed.

In areas where buyers can cross state lines, it may cause issues, but fundamentally the idea is not bad for dealers...

Unfortunately, there are two huge problems with this idea: first, semi ethical dealers will remain open to secure 'deals' which close the following day. This will eliminate some of the benefit. The second, consumers will lose - since it would eliminate one of the two days consumers have generally free to shop for large ticket items. Now, clearly not everyone does shop on Sunday... but it will be a fairly successful argument I think made by consumer advocates.

But reading the article, I think it will end up having a legal challenge and fall apart. Normally. Normally. I say this because they economy has people scared, and when people are scared they tend to blow through arguments way too quickly.

Wow... this whole comment was basically to say nothing. Dang.

Ed said...

Or this could be a ploy to get rid of the small dealers who need the Sunday sales to make a profit.

Patrick Emerson said...

By the way, I should have mentioned, Colorado has such a strange prohibtion on Sunday car sales and when I lived there, there was a debate about repealing the prohibition. I remember letters to the editor in support of the ban from consumers who liked the opportunity to browse car lots without salespeople pressuring them.