Variations on 2-Player Games

Multiplayer games

Use vector of values for each node

Example, three players

     to move
     1                                (1 2 3)
                        +---------------+ +------------------+
     2               (1 2 3)                             (-1 5 2)
              +--------+ +-----+                   +--------+ +-------+
     3     (1 2 3)          (6 1 2)            (-1 5 2)            (5 4 5)
            /  \              / \                 / \                / \
     1 (1 2 3) (4 2 1)  (6 1 2) (7 4 -1)  (5 -1 -1) (-1 5 2)  (7 7 -1) (5 4 5)

      1) each player maximizes utility
      2) each node stores a vector of utilities
      3) entire vector is backed up

Player 3, if in leftmost state, should choose first move because higher utility values. Result will be terminal state with utility values (v1 = 1, v2 = 2, v3 = 3).

This vector is backed up to the parent node.

Need to consider cooperation among players