How I bought our car using game theory and had some fun along the way

January 15, 2021
posted in
written by Dieter van de Scheur

While I had been utilising TWS Partners’ game theory methodology professionally for a few years, as well as training many Procurement professionals on the topic, I had never found myself in a position to utilise the methodology in my private life. Until the moment came around in late 2016 when we were looking to buy a second car, as we had family expansion under way…

As (Procurement) professionals, we already have quite some degree of risk aversion towards trying new initiatives, but I can say with quite some certainty that the hurdle for trying new approaches for significant purchases in one’s private life feels significantly higher.

Still, after some deliberations and discussions with my wife, we decided to give game theory a go to create a fair and transparent sourcing process, based on Total Value of Ownership (TVO). What happened next was exciting, insightful and rewarding…

Structuring the sourcing process

We structured our sourcing process taking the following steps:

  1. We looked for a car brand and model that met our high-level requirements (amongst others, these were roughly a mid-sized hatchback with automatic transmission, built earliest 2011 with ~80.000km for a budget of €10k). After test driving multiple brands and models, we settled on a preference for a Toyota Auris.
  2. Finding as many Toyota Auris cars for sale that met our requirements.
  3. Making all the Toyota cars comparable from a TVO perspective. This was the most challenging task in the process and involved the following steps:
    a) Listing all relevant Auris specifications that could vary and added value to us
    b) Determine a baseline for each specification, e.g. white as a base colour, 80k km as a base mileage, April 2011 as manufacture date etc.
    c) Determine what a deviation from the baseline would ‘cost’ us or be ‘worth’ to us. Something worse than the baseline would result in a penalty, while an improvement to the baseline would result in a bonus
    d) Insert all Auris cars from step 2 into the bonus/penalty matrix and assign them bonus or penalty values for each specification
  4. After step 3 we were able to combine the listed sales price with the bonus/penalty values in order to come to the TVO ‘comparison price’, which would ultimately decide which car we would buy.
  5. The most experimental aspect of the whole process was the communication strategy towards the car dealers of the ‘auction’ we were about to run for the purchase of just one car. We had no clue whether or not they would be open to the process and if they were, whether we would see considerable concessions compared to the classic bargaining game for a car, even though game theory was on our side. We wrote an email to each of the car sellers explaining our TVO approach and that we would buy the car from the seller with the best TVO value and that they were given one shot at submitting their best offer in order to win the sale. In Auction Theory we call this a First Price Sealed Bid. Additionally, we said that if they had the best TVO we would still need to be satisfied with the test drive of the car, which we deliberately did not want to do upfront.
  6. The final step was compiling the revised bids from the sellers, determining the winner and notifying the winning seller.

Below gives an overview of the TVO setup and the outcomes of steps 3, 4 and 6. Note that a bonus is listed as a negative value, as it reduced the TVO of the car.

So, we ended up buying our car from Seller D, paying €9,900 for the car which represented the lowest TVO for us at €7,806.

Our experiences and observations

There are some observations and perspectives I would like to share on the process.

  1. While our approach was to first narrow down our preference for a car brand and model, this process can certainly also be used when considering and comparing different brands. Of course, that increases the complexity and will require more effort, but do not let that stop you…
  2. From a pure game-theoretical perspective, we were attempting to apply the concept of commitment to a so-called “one shot game” in which the purists among us will know that commitment is not worth much, as I was at no point obliged to follow through on my purchase to the seller with the best TVO and could even have attempted to further negotiate a better offer.
  3. The seller himself addressed the process when we concluded the deal and indicated that he thought it was very cool and had never seen it used before, followed by the question what I did for a living. He also indicated he gave his best price as he felt like there was not much to lose in doing so (Note: in bargaining theory this can be classified as ‘cheap talk’, meaning that we should not put too much weight on such a comment as it is unverifiable).
  4. While some sellers decided not to ‘play ball’ and simply ignored the request to participate, the ones who did participate delivered 11%-18%, with the winning seller dropping 17%. These are certainly not results many achieve when haggling for a car with a seasoned car seller.
  5. If you find yourself in the process of buying a new car of a certain brand and model, I would strongly recommend using auctions mechanisms, as it will not require extensive efforts to make cars comparable via Bonus/Penalty, as car dealers can all quote a new car to your exact specifications.

Finally, go through life with an open mind to new and different approaches and see how they work out for you. Even if it is not always a success, you will gain valuable new insights compared to always sticking to the same way of doing things. You may even have some fun along the way, just like we had buying our car using a different approach.

Next personal challenge: selling a house using game theory…stay tuned…


Title image by Omer Rana on Unsplash