How does this work, then? Can you justify that the bonus is free without circularity?
For two agents, I can.
Imagine a setup with two agents, otherwise identical, except that one owns a 1/2+-1/4 bet and the other owns 1⁄2. A government agency wishes to promote trade, and so will offer 0.1 to any agents that do trade (a one-off gift).
If the two agents are Bayesian, they will trade; if they are ambiguity averse, they won’t. So the final setup is strictly identical to the start one (two identical agents, one owning 1/2+- 1⁄4, one owning 1⁄2) except that the Bayesian are each 0.1 richer.
Right, except this doesn’t seem to have anything to do with ambiguity aversion.
Imagine that one agent owns $100 and the other owns a rock. A government agency wishes to promote trade, and so will offer $10 to any agents that do trade (a one-off gift). If the two agents believe that a rock is worth more than $90, they will trade; if they don’t, they won’t, etc etc
But it has everything to do with ambiguity aversion: the trade only fails because of it. If we reach into the system, and remove ambiguity aversion for this one situation, then we end up unarguably better (because of the symmetry).
Yes, sometimes the subsidy will be so high that even the ambiguity averse will trade, or sometimes so low that even Bayesians won’t trade; but there will always be a middle ground where Bayesians win.
As I said elsewhere, ambiguity aversion seems like the combination of an agent who will always buy below the price a Bayesian would pay, and another who will always sell above the price a Bayesian would pay. Seen like that, your case that they cannot be arbitraged is plausible. But a rock cannot be arbitraged either, so that’s not sufficient.
This example hits the ambiguity averter exactly where it hurts, exploiting the fact that there are deals they will not undertake either as buyer or seller.
I say this has nothing to do with ambiguity aversion, because we can replace (1/2, 1/2+-1/4, 1⁄10) with all sorts of things which don’t involve uncertainty. We can make anyone “leave money on the table”. In my previous message, using ($100, a rock, $10), I “proved” that a rock ought to be worth at least $90.
If this is still unclear, then I offer your example back to you with one minor change: the trading incentive is still 1⁄10, and one agent still has 1/2+-1/4, but instead the other agent has 1⁄4. The Bayesian agent holding 1/2+-1/4 thinks it’s worth more than 1⁄4 plus 1⁄10, so it refuses to trade. Whereas the ambiguity averse agents are under no such illustion.
So, the boot’s on the other foot: we trade, and you don’t. If your example was correct, then mine would be too. But presumably you don’t agree that you are “leaving money on the table”.
For two agents, I can.
Imagine a setup with two agents, otherwise identical, except that one owns a 1/2+-1/4 bet and the other owns 1⁄2. A government agency wishes to promote trade, and so will offer 0.1 to any agents that do trade (a one-off gift).
If the two agents are Bayesian, they will trade; if they are ambiguity averse, they won’t. So the final setup is strictly identical to the start one (two identical agents, one owning 1/2+- 1⁄4, one owning 1⁄2) except that the Bayesian are each 0.1 richer.
Right, except this doesn’t seem to have anything to do with ambiguity aversion.
Imagine that one agent owns $100 and the other owns a rock. A government agency wishes to promote trade, and so will offer $10 to any agents that do trade (a one-off gift). If the two agents believe that a rock is worth more than $90, they will trade; if they don’t, they won’t, etc etc
But it has everything to do with ambiguity aversion: the trade only fails because of it. If we reach into the system, and remove ambiguity aversion for this one situation, then we end up unarguably better (because of the symmetry).
Yes, sometimes the subsidy will be so high that even the ambiguity averse will trade, or sometimes so low that even Bayesians won’t trade; but there will always be a middle ground where Bayesians win.
As I said elsewhere, ambiguity aversion seems like the combination of an agent who will always buy below the price a Bayesian would pay, and another who will always sell above the price a Bayesian would pay. Seen like that, your case that they cannot be arbitraged is plausible. But a rock cannot be arbitraged either, so that’s not sufficient.
This example hits the ambiguity averter exactly where it hurts, exploiting the fact that there are deals they will not undertake either as buyer or seller.
No, (un)fortunately it is not so.
I say this has nothing to do with ambiguity aversion, because we can replace (1/2, 1/2+-1/4, 1⁄10) with all sorts of things which don’t involve uncertainty. We can make anyone “leave money on the table”. In my previous message, using ($100, a rock, $10), I “proved” that a rock ought to be worth at least $90.
If this is still unclear, then I offer your example back to you with one minor change: the trading incentive is still 1⁄10, and one agent still has 1/2+-1/4, but instead the other agent has 1⁄4. The Bayesian agent holding 1/2+-1/4 thinks it’s worth more than 1⁄4 plus 1⁄10, so it refuses to trade. Whereas the ambiguity averse agents are under no such illustion.
So, the boot’s on the other foot: we trade, and you don’t. If your example was correct, then mine would be too. But presumably you don’t agree that you are “leaving money on the table”.