It’s good to note that Nash equilibrium is only one game-theoretic solution concept. It’s popular in part because under most circumstances at least one is guaranteed to exist, but folk theorems can cause there to be a lot of them. In contexts with lots of Nash equilibria, game theorists like to study refinements of Nash equilibrium, i.e., concepts that rule out some of the Nash equilibria. One relevant refinement for this example is that of strong Nash equilibrium, where no subset of players can beneficially deviate together. Many games don’t have any strong Nash equilibrium, but this one does have strong Nash equilibria where everyone plays 30 (but not where everyone plays 99). So if one adopts the stronger concept, the issue goes away.
But is that reasonable reassurance or just wishful thinking (wishful concept selection)? Really answering that requires some theory of equilibrium selection. One could consider learning algorithms, evolutionary dynamics, some amount of equilibrium design / steering, etc., to get insight into what equilibrium will be reached. My own intuition is still to be cautiously optimistic about folk theorems, since I generally think the better equilibria are more likely to be selected (more robust to group deviations, satisfy individual rationality by a larger margin, etc.). But I would also like to have a better theory of this.
Nice provocative post :-)
It’s good to note that Nash equilibrium is only one game-theoretic solution concept. It’s popular in part because under most circumstances at least one is guaranteed to exist, but folk theorems can cause there to be a lot of them. In contexts with lots of Nash equilibria, game theorists like to study refinements of Nash equilibrium, i.e., concepts that rule out some of the Nash equilibria. One relevant refinement for this example is that of strong Nash equilibrium, where no subset of players can beneficially deviate together. Many games don’t have any strong Nash equilibrium, but this one does have strong Nash equilibria where everyone plays 30 (but not where everyone plays 99). So if one adopts the stronger concept, the issue goes away.
But is that reasonable reassurance or just wishful thinking (wishful concept selection)? Really answering that requires some theory of equilibrium selection. One could consider learning algorithms, evolutionary dynamics, some amount of equilibrium design / steering, etc., to get insight into what equilibrium will be reached. My own intuition is still to be cautiously optimistic about folk theorems, since I generally think the better equilibria are more likely to be selected (more robust to group deviations, satisfy individual rationality by a larger margin, etc.). But I would also like to have a better theory of this.