6.034 Artificial Intelligence - Recitations, fall 2004 online slides on games

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# 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