Why is this strategy profile a Nash equilibrium? Because no player is better off deviating from this strategy profile, assuming all other players stick to the strategy profile.
Only if we limit thinking to 1 round at a time. But thinking longer term: anyone changing to 30 (end being punished for it), immediately changed the landscape for everyone else: punishment reached it’s maximum, from now on everyones’ incentive is to lower theirs for immediate reward. And knowing that and thinking ahead at least two rounds, players are better off deviating, thus they would. Or at least they should.
The definition of Nash equilibrium is that you assume all other players will stay with thier strategy.
If, as in this case, that assumption does not hold then you have (I guess) an “unstable” equilibrium.
Only if we limit thinking to 1 round at a time. But thinking longer term: anyone changing to 30 (end being punished for it), immediately changed the landscape for everyone else: punishment reached it’s maximum, from now on everyones’ incentive is to lower theirs for immediate reward. And knowing that and thinking ahead at least two rounds, players are better off deviating, thus they would. Or at least they should.
The definition of Nash equilibrium is that you assume all other players will stay with thier strategy. If, as in this case, that assumption does not hold then you have (I guess) an “unstable” equilibrium.