Economic Economics – A Game of Theories Part II

Hanbo Li


July 8th, 2012

Applying game theory to purchasing a new car.

As university students, the problem of buying a new car may present itself in the near future. The misalignment of incentives between you the buyer and the commission-driven car salesman is always there, hiding insidiously behind the salesman’s phony smile. In fighting this imbalance, economics, more specifically, game theory might be of use. Bruce Bueno de Mesquita, author of The Predictioneer’s Game and The Dictator’s Handbook, explains how.

Firstly, you need to have exactly what you want in mind – for example a silver Volkswagen Polo. Ignorance of your own preference will be exploited. Then look up all the dealerships which stock this car, and are close enough to you such that you are willing to go there. Contact all of these dealers via phone or email, telling them that you are interested in buying this car. Ask them for their lowest complete price – including taxes etc, and inform them that you are contacting other dealers with the same offer; you will go to the dealership which has offered the lowest price, and will purchase the car for the agreed price, immediately (sorting out your financing beforehand is essential).

There may be some resistance from the dealer, who has not sold a car this way. He may ask you to come in, to which just respond that it is inconvenient for you to, and you would rather sort out the transaction before you go in.

To analyse how this could work, we must make some simplifying assumptions (otherwise it would not be economics). The dealers make their offers simultaneously, or without knowledge of the other’s offer. Assume that there are only two dealers in this situation, and that they can independently offer the car for $18,000 or $20,000. The lower offer will have a 100% chance of acquiring the sale, while tied offers have a 50/50 chance. The payoffs can be arranged as follows:

Dealer 1\Dealer 2 Low High
Low $9,000; $9000 $18,000; $0
High $0; $18,000 $10,000; $10,000

e.g. If they both offer $18,000, they each have a 50% chance of receiving $18,000, so their expected payoff is .

The ‘low strategy dominates the ‘high’ one: no matter what the other dealer offers, bidding low always has a better outcome than bidding high – $9,000 > $0 and $18,000 > $10,000. Each dealer’s best strategy is therefore to offer the lower price, giving you the better deal. The logic holds true even when there are more dealers, and the prices which they can afford are not as discrete.

Of course, one could recreate this and go to the dealerships physically, but this would take a lot of time, and contacting dealers indirectly guards against the main criticism of game theory: irrationality; in negotiating the price indirectly, you are not exposed to the professional slipperiness of the dealers, have more time in responding, and are hence more likely to act rationally. One limitation to this strategy, though, is that it only works for new cars. New cars are commodities, whose only difference are their prices, while used cars are unique and should be physically examined.

On a side note, notice that the construction of this example is identical to that of the Prisoner’s Dilemma.

The views expressed within this article are those of the author and do not represent the views of the ESSA Committee or the Society's sponsors. Use of any content from this article should clearly attribute the work to the author and not to ESSA or its sponsors.

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