5 ms·
The nash equilibrium is defined by a strategy that cannot be improved by changing your own strategy, assuming the other players' strategies stay the same. Agen
by yifanl 4y ago
The nash equilibrium is defined by a strategy that cannot be improved by changing your own strategy, assuming the other players' strategies stay the same.
Agent 1 doesn't care if Agent 2 and 3 win less than him, he only feels a strategy is better than the Nash strategy if his expected score becomes higher than .296, which your simulation seems to show has not been achieved.
- seanw265 4y agoPlease see my follow-up comment with another simulation that shows how the expected score can rise well above .296. https://news.ycombinator.com/item?id=33025759 https://news.ycombinator.com/item?id=33025759
- yifanl 4y agoI don't believe cases where changing your strategy in a non-equilibrium state are considered, as the assumption that no other player will shift their own strategy will not hold. Otherwise, you might as well consider the case P1 always chooses 1, P2 always chooses 1 and P3 always chooses 2.