That model works, but it requires irrational agents to make it work. The bubble isn’t really “stable” in a game-theoretic equilibrium sense; it’s made stable by assuming that some of the actors aren’t rational game-theoretic agents. So it isn’t a true Nash equilibrium unless you omit all those irrational agents.
The fundamental difference with a signalling arms race is that the model holds up even without any agent behaving irrationally.
That distinction cashes out in expectations about whether we should be able to find ways to profit. In a market bubble, even if it’s propped up by irrational investors, we expect to be able to find ways around that liquidity problem—like shorting options or taking opposite positions on near-substitute assets. If there’s irrational agents in the mix, it shouldn’t be surprising to find clever ways to relieve them of their money. But if everyone is behaving rationally, if the equilibrium is a true Nash equilibrium, then we should not expect to find some clever way to do better. That’s the point of equilibria, after all.
That model works, but it requires irrational agents to make it work. The bubble isn’t really “stable” in a game-theoretic equilibrium sense; it’s made stable by assuming that some of the actors aren’t rational game-theoretic agents. So it isn’t a true Nash equilibrium unless you omit all those irrational agents.
The fundamental difference with a signalling arms race is that the model holds up even without any agent behaving irrationally.
That distinction cashes out in expectations about whether we should be able to find ways to profit. In a market bubble, even if it’s propped up by irrational investors, we expect to be able to find ways around that liquidity problem—like shorting options or taking opposite positions on near-substitute assets. If there’s irrational agents in the mix, it shouldn’t be surprising to find clever ways to relieve them of their money. But if everyone is behaving rationally, if the equilibrium is a true Nash equilibrium, then we should not expect to find some clever way to do better. That’s the point of equilibria, after all.