From the title, I thought you were going to talk about thermodynamic game theory, where an agent’s policy is a softmax of their reward. At absolute zero, agents can get stuck in hellish Nash equilibria, but a milder temperature can help them escape to better equilibrium. Actually, Ellison showed that with lower temperatures you spend exponentially more time in better equilibria, it just also takes exponentially longer to first reach them.
What do the thermodynamics of hell look like? Let me layout the problem in my own notation. Suppose:
There are a large number of souls in hell. of them to be precise.
The temperature is set to the average of their knobs, between 0 and 1. Initially it is agreed to set it to .
The ‘defectors’ always set their knob to zero. The ‘cooperators’ set their knob so that, if a fraction had defected, the new temperature is . This is only possible as long as
If a previously cooperative soul defects, and not enough others defect, then the temperature increases by in the next iteration. If a previously defective soul cooperates, it decreases by . In both scenarios, the payoff is for cooperation, at least until the system collapses to zero. Thus, each soul is
more likely to cooperate than defect. The lower the inverse-temperature, the more likely each one is to defect. The probability enough souls defect so that the system collapses is
The social/political ramifications are:
If you are in a good equilibrium, the group is less likely to endorse leaving it to find a better one.
If you cannot lower the temperature of hell, you can maintain the equilibrium by lowering the temperature of actions.
This also seems to be the primary philosophy of conservatism. “The equilibrium is/was already good, and even if it was not, we want to conserve the current system because high-temperature actions are radical and scary.” I should also add that the second clause gains more credence when you realize that the free energy
gets smaller as the action-temperature increases, so you lose many of the best equilibria. Who is to know if that doesn’t also include the current one?
From the title, I thought you were going to talk about thermodynamic game theory, where an agent’s policy is a softmax of their reward. At absolute zero, agents can get stuck in hellish Nash equilibria, but a milder temperature can help them escape to better equilibrium. Actually, Ellison showed that with lower temperatures you spend exponentially more time in better equilibria, it just also takes exponentially longer to first reach them.
What do the thermodynamics of hell look like? Let me layout the problem in my own notation. Suppose:
There are a large number of souls in hell.
The temperature is set to the average of their knobs, between 0 and 1. Initially it is agreed to set it to
The ‘defectors’ always set their knob to zero. The ‘cooperators’ set their knob so that, if a fraction
If a previously cooperative soul defects, and not enough others defect, then the temperature increases by
more likely to cooperate than defect. The lower the inverse-temperature, the more likely each one is to defect. The probability enough souls defect so that the system collapses is
The social/political ramifications are:
If you are in a good equilibrium, the group is less likely to endorse leaving it to find a better one.
If you cannot lower the temperature of hell, you can maintain the equilibrium by lowering the temperature of actions.
This also seems to be the primary philosophy of conservatism. “The equilibrium is/was already good, and even if it was not, we want to conserve the current system because high-temperature actions are radical and scary.” I should also add that the second clause gains more credence when you realize that the free energy
gets smaller as the action-temperature increases, so you lose many of the best equilibria. Who is to know if that doesn’t also include the current one?