Trust Falls

I started reading Cowbirds in Love at the behest of one of my friends/nemeses.  When I arrived at this comic, I was largely nonplussed -- until I read the alt text, that is.  I hope I get extra credit for what follows.

			P2					P2
			Fall	Don't			Fall	Don't
	P1	Catch	1,1	0,0		Catch	-1,1	0,0
		Don't	-1,-1	0,0		Don't	1,-1	0,0
			1 is trustworthy					1 is untrustworthy

I would like to note that the utility values in this game are derived from the expression on the stick figures' faces.  

This time, Player 1 (the one catching) might be one of two sorts of people:  Trustworthy or untrustworthy.  Player 2 (the one falling) would like to fall and be caught, because this is the objective of the game.  She does not know which type Player 1 is, but she thinks there's a p chance that Player 1 is trustworthy.  She also knows that trustworthy people always catch, and untrustworthy people never catch (perhaps untrustworthy people aren't entirely untrustworthy after all).  Nobody gets anything if Player 2 doesn't fall.  It is called "trust falls" after all.

Through the power of algebra, I present the following utility comparisons.
Player 2 should fall if: p + (1-p)(-1) > 0, or if p > 1/2
Abracadabra, or something like that.

So if Player 2 thinks Player 1 is very likely to not be a jerk, she should fall.  Otherwise, she should glare at him sternly.

There are actually a few different ways to approach this problem as a game representation.  If anybody's interested, I'll spend the next post discussing those.

Walking is Difficult

Hello everybody!

For this very first post, I thought I'd provide an example of a situation that might warrant some game theoretic analysis. I often walk places, which is a thing that quite a few people seem to do.  This means that sometimes other people end up walking straight toward me.  I don't want to bump into them, they don't want to bump into me.  The following game is an example of that situation

		P2
		Turn	Straight
P1	Turn	1,1	1,2
	Straight	2,1	0,0

Here it doesn't really matter whether I'm Player 1 or Player 2, as their preferences are symmetrical.  Neither person knows what the other will choose, but they do know what outcome they want.

When we look at the pure strategy equilibrium of this game, it's best for the players to play different strategies.    Put another way, if you pick Turn, I should pick Straight.  If you pick Straight, I should pick Turn.  To anybody who's faced this situation, this result is fairly obvious.

However, determining who ought to turn is a rather more difficult endeavor.  Without knowing what you're inclined to do, I might decide to go straight, since I know that you know that turning is better than a collision.  If we both think this, we'll shortly perform a rather awkward sort of dance.

You might be inclined to ask:  Michael, even if I know this, what should I do when I find myself in this situation?

Clearly the best thing to do is for you to always turn.  That way, I'll never have to worry about running into anyone.