Question

Describe how the minimax and alpha–beta algorithms change for two-player, nonzero-sum games in which each player has a distinct utility function and both utility functions are known to both players.

Answer 1

Answer:

The explanation of this question is given below in explanation section

Explanation:

Minimax

Minimax will work as usual if it’s set up right. We’ll be backing up a vector of  evaluations and at each level the player will choose what is best for him, even if it is also good for  the other player. Thus if we assign increasingly positive values for states increasingly better for  Max and increasingly negative values for states increasingly better for Min, then minimax will work  unmodified. If both players have increasingly positive values, each player just picks the maximum  value, so it’s a “maximax” algorithm.

Alpha-beta algorithm

However, alpha-beta pruning will not work because built into it is the idea that what’s  good for max is bad for min – for example min won’t let max go down a path since min can force  something worse, so max knowing this doesn’t have to explore that path. But without zero-sum  assumption, the same state could be good for both min and max; you can’t assume that just because  max likes it that min won’t, and vice versa.