The problems come up in game theory and involve situations in which the equilibrium strategies of the players are mixed Nash.
This is a large class of problems involving games as simple as rock-paper-scissors, but also more common and practical problems like whether or not to stop at an intersection, and whether a football team should run or pass on first down.
In managerial economics, mixed Nash is the best we can do for the hold-up games that show up all over the real world: when should we choose to make others wait for us to act.
I’ve always felt that mixed Nash was kludgy. It’s obvious that it’s possible, but it’s so glaringly obvious and largely pointless that I’ve always wondered why we bother. Aumann made this point, and I’m pretty sure that I picked that up in Murray Brown’s game theory class in 1982 or so.
The new result shows that the calculation of the mix involved in these mixed strategies is effectively impossible to compute.
If we can’t compute them theoretically, how can we envision individuals ever choosing them?
What’s the way out? I’m not sure there is one, but for my part, it makes me happier about reducing my coverage of these. It also tends to confirm Aumann’s assertion that a lot of what we think is rational is actually just a consequence of people holding to irrational beliefs.