The Dollar Bill on the Pavement
From Prof. Cowen:
I was walking in New York near Wall Street and I saw a green folded up note that looked to be money. I too paused and thought of the old joke that if it was money someone would have picked it up already, but I picked it up anyway and took a closer look…..alas, it was a cleverly folded piece of paper designed to look like money when dropped on the sidewalk, although it was actually an advertisement.
These stories make for a good game theory problem. The applicable model also explains imperfect efficiency coexisting with lack of profit opportunity in the real stock market.
I am the first player. My choice is to pick up the piece of paper or not. Picking it up is costly.
The advertiser is the second player. His choice is how many ads disguised as dollars to distribute. Putting out more ads is costlier.
Exogenously, there are a fixed number of real dollars bills floating around sidewalks.
The unique equilibrium is in mixed strategies. My strategy is to pick up the paper with probability X. The advertiser’s strategy is to distribute Y ads. Y is big enough that I am indifferent between picking up the paepr or not. X is big enough that the advertiser is indifferent between advertising and not.
It’s a bit trickier to make it work than I thougth in this setting, but I think it’ll fly.