The dessert co-ordination game

I was recently out having dinner with my family and it reached the part of the night where we needed to order desserts.

I did my usual thing of ordering a beer for dessert, which is all well and good, and it gave me an opportunity to sit around and watch everyone else determine what they were going to have.

It seemed obvious everyone else wanted an actual dessert, people were tossing up between different cheese dishes, with a person occassionally staring longingly at the chocolate cake on the menu.  However, then something very interesting happened – no-one ordered dessert.  Instead, everyone ended up getting coffee, tea, or hot chocolate.

The catalyst for this seemed to be my mother.  After saying to me that she was going to get a blue vein cheese platter she looked up to the person taking orders and asked for a pot of tea.  Immediately I saw other family members respond in a flurry, shouting out for coffee or hot chocolate.  At that moment I realised that my family had just fallen victim to an awful co-ordination failure.

As the waitress went away I said to the table that their choice of dessert was dependent on the choice of dessert other people were ordering – as no-one wants to be the only person digging into a big dessert.  As a result, we have two equilibrium, one where everyone buys a big tasty dessert, and another one where everyone buys a drink and misses out on the cheese or cake.  This is a pure and simple co-ordination game.

My family members admitted that this was the case, no-one wants to be the only person eating dessert and they also do not know whether the other people want a proper dessert or a drink.  As a result, they are relying on the actions of others.  Although it seems that it would have been, ex-post, parteo optimal to have everyone eating dessert, the people at the table did not realise that – and the fear of the potential cost of being the only person eating dessert had seen my mother switch to only purchasing a drink.  With her decision made, the rest of the table quickly followed her to this sub-optimal equilibrium.

To me the moral of the story is simple, my family should learn to communicate with each other in order to avoid pareto inferior equilibrium in the future.  My families response to this suggestion was simply that I’m a nerd, fair enough.

  • http://www.tvhe.co.nz/ jamesz

    I wonder if the equilibrium is sensitive to being discussed. It may be that discussing the fact that “no-one wants to be the only person digging into a big dessert” would cause the game to resolve to the no-dessert eqm anyway.

    • http://tvhe.co.nz/ Matt Nolan

      How are you commenting on this 3 days before it’s posted?

      Also indeed, the high cost of getting dessert when no-one else is compared to the cost of getting coffee when everyone else gets dessert is a pretty relevant issue here – and explains why this happens more commonly! It is still a pareto inferior eqm though, which is a pity.

      • http://www.tvhe.co.nz/ jamesz

        Oooops :P

        But while I’m here, what I meant was that the payoffs in the co-ordination game are probably a function of the resolution mechanism. So, ex ante, no dessert may be inferior. But, once you start discussing it, the ‘fatness’ becomes more salient to people and changes the payoffs such that ‘no dessert’ is now the optimal outcome. Essentially, talking about co-ordinating on dessert may re-frame the game.

        • http://tvhe.co.nz/ Matt Nolan

          That is true – and I did consider that the “fatness/unhealthiness” concern, combined with a cost of explicitly mentioning it, could actually imply that the eqm that we ended in is optimal.

          And that is the kicker, no matter how hard we try we can’t observe other peoples preferences, so it’s all conjecture!

          • http://offsettingbehaviour.blogspot.com/ Eric Crampton

            Knowing that other people feel bad about being the only one to order a beer or to order a big dessert, I make a deliberate point of doing both. For the benefit of others. Because I’m a humanitarian. Perhaps one of the only ones left.

        • http://twitter.com/fibby17 fibby

          In my experience, discussing it helps people to realise how silly it is. It’s common to hear the phrase “screw it” at this point, closely followed by “I’ll have the cheesecake”.

          • http://tvhe.co.nz/ Matt Nolan

            My family is as hard headed as I am – so if any of us were to suggest that it was silly, the rest of us would refuse to order anything as a matter of principle :D

            • http://www.facebook.com/philip.box Phil Box

              Heh, I am one of 11 kids, no one waited for anyone else to make a decision as to whether to eat dessert or not. It was tuck in or miss out. It still haunts me to this day. When the prawns land on the table there’s no waiting around for other people to take first pick. Dessert comes and I’ll have all of them. I feel like a vacuum cleaner sometimes. I apologise later when I realise I have made a pig of myself though. ;))

  • http://twitter.com/LewStoddart Lew

    Nice.

    Perhaps not in your family, but in some cases there’s a second coordination game at play — the game of “If you’re getting that, I’ll get this, then we can share and both get the benefit of tasting two desserts”. This is sometimes declared and sometimes not.

    I’ve seen it go massively multilateral where, frankly, it’d be easier to just have a lazy susan — but in a constrained-communication environment it seems this would be a terrible minefield of potential regret for people who want to optimise their dessert consumption by variety rather than quantity.

    L

    • http://tvhe.co.nz/ Matt Nolan

      Very true. Family events always make me more sympathetic to the idea of a benevolent social planner.

  • http://www.facebook.com/daniel.j.taylor.35 Daniel J. Taylor

    This situation sounds a bit like the Abeline Paradox, a phenomenon where people in a ground end up making decisions against thier initial judgement because the first person in the group voices a decision which they think appeases the rest of the group (not always that persons own personal judegement either). The rest of the group then voice decisions alaigning with the first persons decisions and often against thier own judgement for fear that they would be ostacising themselves from the group be making thier true judgement known.

    I wrote a paper earlier in the year expressing the reality this paradox plays within the participatory consultation processes of international development organisations ;-)

    • http://tvhe.co.nz/ Matt Nolan

      Good shiz, I’d be keen to read it!

      Coordination games are cool. Makes me wish I was doing applied game theory for a living ;)