It was in Thomas Sargent’s class at NYU that I first came upon the “want” operator. When complexity started to overwhelm, he would write “want” on the white board, followed by a colon.
This way he would force himself to pause, think, and write down what it was that he aimed for. At such moment he would turn around and intently stare at us, his students, wanting us to do the same. I learned that the want operator was always there for you, like Google Maps in an unknown city.
Want: Competitive bidding with costly participation.
This is what Boyan and I were on a mission for. It came up when we were thinking about bidding by high-frequency traders (HFTs). HFTs “pay to play.” Putting a price quote out is costly for due to quote-to-trade ratios, limited bandwidth, and finite computing power. Those who decide to play bid simultaneously and the highest bidder gets the trade.
If agents pay to play, what equilibria arise? In a paper posted today, we find the following:
There is a unique equilibrium.
The optimal strategy for agents is to toss a biased coin when deciding to participate or not. And if participating, they draw a bid from a distribution. Both the probability of playing and the bid distribution are calculated explicitly.
If the number of agents is increased, each agent plays with lower probability. The net effect nevertheless is that more bidders participate. This might not be so surprising. What is remarkable is that the highest bid is lower in expectation.
“You can’t always get what you want. But if you try sometimes you just might find. You just might find. You get what you need.” Did the Stones take a macro class at NYU?
You find the paper here.