Game theory failure in Come Dine With Me?

Last week in my ECONS101 class, we covered game theory. One of the starting points of understanding game theory is to recognise dominant strategies. A strategy is dominant for a player if it provides that player with a better payoff than any other strategy, regardless of what the other players do. A player should always choose to follow their dominant strategy - to do otherwise would simply make them worse off.

The real world is filled with examples of game theory. However, most games don't have strongly dominant strategies, and even when they do, people may choose not to follow them. Take the example of the cooking programme, Come Dine With Me. In the show, the five contestants take turns to cook a meal and prepare an evening's entertainment for the other players. At the end of the evening, each contestant (except for the host) rates the evening on a scale of 1-10. The winner is the contestant who receives the highest total score for their evening as host. Importantly, none of the scores is revealed until the show is aired on television (some weeks or months later). So, there is no effective way to reward or punish other players, or to ensure cooperation (like two players each making a deal to rate the other player's evening highly).

Can you see the dominant strategy in Come Dine With Me? If you guessed that the dominant strategy is to rate every one of the other players a zero, regardless of how good (or not) their hosted evening was, then give yourself a gold star. Of course, that isn't what happens. So, why not?

A 2014 article by David Schüller (University of Duisburg-Essen), Harald Tauchmann (Friedrich-Alexander-University Erlangen-Nürnberg), Thorsten Upmann, and Daniel Weimar (both University of Duisburg-Essen), published in the Journal of Economic Psychology (ungated earlier version here), provides a partial answer. Schüller et al. used data from the German version of the show over the period from 2006 to 2011. They wondered whether it was the potential loss of reputation (from their family, friends, and acquaintances) that prevented players from choosing the dominant strategy. Essentially, no one wants to look like a dick on national television, so while it was the best strategy for winning, it might not be the best strategy overall in the 'game of life'. Instead, they expected the contestants to follow the social norm established in early episodes of the show. However, the data didn't support this social norm explanation:

We measured the impact of reputation by the voting behavior observed in previous shows. This had no significant influence on voting behavior once we accounted for the impact of the objective sophistication of a dinner and personal traits. Therefore, reputational factors as measured by past voting behavior does not seem to play an important role in this setting.

Instead, dinners that used more ingredients (a measure of 'sophistication') scored higher, the contestants who hosted later in the week scored higher (probably because they could learn about the other contestants and what would appeal to them), and contestants scored the others lower after they themselves had hosted. The authors argue that:

...a contestant who has already cooked attaches a higher weight to his own performance once it has been carried out... termed the 'overestimations effect'.

However, I prefer their alternative explanation, which is that:

 ...a contestant that has performed is now free to be more critical of the performance of others since he no longer has to fear being evaluated. However, this effect should play no role because the evaluations remain concealed until the show is broadcast.

Even though it should play no role in their evaluations, the contestants might be concerned that their evaluations are known to the television production crew, who might accidentally (or purposely) reveal that information to the other contestants. If they were found to be scoring the others as zeroes, then they could be punished. However, there is no risk of punishment after they have hosted. Still, despite this, the contestants weren't fully choosing the dominant strategy after hosting.

Coming back to the original hypothesis about social factors affecting the contestants' choices though, I think the authors could have done a better job of measuring this. Deviation from the social norm is a pretty weak way of measuring how concerned the contestants were about what the television viewers would think of them after the show. However, using publicly available data, better measures could not be used and so we are left wondering to what extent this drives the results.

I guess the moral of this post is that I should probably never be invited to participate in Come Dine With Me (not least because of the quality of the meal that would be served!).