4 ms·
But isn't this true of all games? In games of imperfect information, there is still a perfect, computable solution. It just happens to be a mixed strategy. And
by tedsanders 10y ago
But isn't this true of all games? In games of imperfect information, there is still a perfect, computable solution. It just happens to be a mixed strategy. And if the argument is that games of imperfect information allow exploitative strategies to succeed against non-equilibrium strategies, well the same is true of chess: the very idea of a trap is usually making a suboptimal move to hopefully exploit an imperfect opponent's likely mistake.
- DanWaterworth 10y agoWhen you have imperfect information, understanding the other player's strategy becomes part of the game. A perfect solution may be computable against any deterministic strategy, but its stops being a possibility when you don't know the other player's strategy.
- cousin_it 10y agoNo, tedsanders is right. If the game has imperfect information but is zero-sum (i.e. the goals of players are perfectly opposed), you can always compute the subgame-perfect Nash equilibrium in mixed strategies, and it will be the best way to play against all possible opponents, both deterministic and random. Mind games (bargaining, precommitment, etc.) only become important in non-zero-sum games, where the goals of players align in some ways and oppose in others. For example, if chess had an additional possible outcome where both players lose, that could make it impossible to find a single best strategy.
- DanWaterworth 10y agoThanks, that's an interesting nuance.