Benji’s Reviews > Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations > Status Update

Despite the fact that strong argument can be made in its favor, the concept of backward induction is not without controversy. To see why this is, consider the well-known Centipede game. There exist different accounts of this situation, and they depend on the probabilistic assumptions made, on what is common knowledge, and on exactly how one revises one's belief in the face of measure-zero events.

One general lesson is that while this transformation can always be performed, it can result in an exponential blowup of the game representation. This is an important lesson, since the didactic example of normal-from games are very small, wrongly suggesting that this form is more compact.

The correlated equilibrium is a solution concept that generalizes the Nash equilibrium. Some people feel that this is the most fundamental solution concept of all. A Nobel-prize winning game theorist, R. Myerson, has gone so far as to say that 'if there is intelligent life on other planets, in a majority of them, they would have discovered correlated equilibrium before Nash equilibrium.'

Since iterated removal of strictly dominated strategies preserves Nash equilibria, we can use this technique to computational advantage.

Agents might play maxmin strategies in order to achieve good payoffs in the worst case, even in a game that is not zero sum. However, consider a setting in which the other agent is not believed to be malicious, but is instead entirely unpredictable. In such a setting, it can make sense for agents to care about minimizing their worst-case losses, rather than maximizing their worst-case pay-offs.

(Mini(Max(Regret))) An agent's minimax regret is an action that yields the smallest maximum regret.