coordination problem, for the game-theorists among you

[gusl]

Here's the game:

you want to go out and play soccer on Sunday

* If you go, your utility will depend on: (1) the weather, and (2) how many (and which) other people show up.
* If you stay at home, your utility is constant.

This is already complex enough, if you take into account the utilities of a complex social network (each player has a social-utility function over the set of which individuals come). It's already a hard coordination problem.


the benefits of planning ahead

But we also need to take into account the fact that many players benefit from scheduling themselves ahead of time (they can plan their other activities better). They want to plan ahead, counting on other people to be there.
This complicates things because other players will want to leave their decision as late as possible: they only want to play if the weather is good, and will be unwilling to make a commitment until they're fairly convinced that the weather will be decent. On the other hand, players will not want to commit unless they see other committed players. Should we reward early committers?


signalling

How can people signal the right degree of commitment, and how can we hold them accountable without being too rigid?

What are the best known solutions to this kind of problem? Does assuming rationality (or common-knowledge thereof) make a big difference?

This is very common problem in social situations. I bet the HikeTheGeek'ers would like to hear about any proposed solutions.

---

By the way, I have lost substantial utility in my life by trying too hard to optimize my social life. Mostly by doing nothing (the P's default under uncertainty).

Comments

[arun3.livejournal.com]

Your use of the word "utility" seems a bit odd. Especially in your first set of statements. It doesn't make sense if I substitute "usefullness" or "ability to be used".

[gustavolacerda.livejournal.com]

I'm speaking economese.

[arun3.livejournal.com]

Blast. It seems I forgot to ask you what it means. So, what do you mean by "utility", in the economic sense?

[gustavolacerda.livejournal.com]

http://en.wikipedia.org/wiki/Utility

[fub.livejournal.com]

It's a bit like the Prisoner's Dillemma, right?
My strategy would hinge on two things:
- Developing a heuristic to weigh the statements of commitment; and
- Having a contingency plan.

I start out a 'trusting fool': I will gladly believe someone when they say they will do X. However, they might not make good on their promise, leaving me with lesser utility -- so I know that I should weigh their promises lighter the next time.
The statements of commitment from all prospective participants then carry a certain collective weight, which I can use to determine whether I will participate.
At first, when I start out trusting every statement of commitment, I might get dissapointed a lot. That is why having a contingency plan comes in handy: if the soccer game does not happen, I can return home -- I lose a bit of utility by having to travel to and from the place of the soccer match, but the rest of the day is salvagable.

In short, I risk a bit of utility for the chance of a bigger utility reward, until I have developed a weighing scheme to assess the risk of my utility-gamble not paying off.

[gustavolacerda.livejournal.com]

But why would people make any commitment at all? Don't you need to reward them in some way?

[fub.livejournal.com]

Presumably they will derive greater utility from playing soccer than staying at home. In other words, the playing of soccer should be it's own reward.

If that is not the case, then you're probably better off not playing soccer with them in the first place.

[gustavolacerda.livejournal.com]

Ok. But the way I set up the game, you don't need to commit to other people in order to play: you can always come. Of course, if you're sure you're coming, committing costs nothing.

[fub.livejournal.com]

I had assumed that you would need a minimum of comitted players (say, X) in order to play. That way, if an Y number of people say they will be there and Y > X, then it is worth your while to come as well.
But if only Z people show up, and Z < X, then you're screwed and you can't play -- leaving you with a huge utility gap.

That is what I meant by likening this to the Prisoner's Dilemma.