|
|
|
|
|
|
by credulousperson
1366 days ago
|
|
|
Indeed the Nash equilibrium is not always what we would like to call "optimal", especially in games with more than two players. As you notice, it is possible the Nash equilibrium strategy will be crushed if more than one agent chooses a different strategy (i.e. a situation where players are deviating from a strategy in a non-unilateral fashion). If Agent 1 and Agent 2 work collude beforehand they can completely crush Agent 3. The Nash equilibrium only says the agent will lose more if they change while the others use the follow the same strategy (i.e. a unilateral deviation). In defense of the Nash equilibrium, there are some reasons we can sort of assume that the two players will pick a strategy which happen work together to beat us by a lot. For example, one of the two other players could just play the Nash strategy along with us, in which case we know the other player will not be able to exceed the equilibrium value. There is no way the player can pick a strategy all by themselves which is guaranteed to win more than the equilibrium value. For the other players to actually have a guaranteed higher probability of winning, they must coordinate playing their strategy with the other player and trust that the other player will keep their word. This is known as forming a coalition. There are some other notions of equilibrium which take this into account and do not permit coalitions to change the value (see: strong Nash equilibrium), but it won't exist for many games (like this one). |
|
|