Multiagent Systems

of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 204/731
3. Decision Making (1) 2. Non-coop Games
Thus Player A’s expected utility is as follows:
1 when playing against B-I: 0x + 1(1 − x) = 1 − x,
2 when playing against B-II: 5 6 x + 1 2 (1 − x) = 1 2 + 1 3 x,
3 when playing against B-III: 1 2 x + 3 4 (1 − x) = 3 4 − 1 4 x.
This can be illustrated with the following picture (see
blackboard). Thus B-III does not play any role.
Thus the maxmin point is determined by setting
1 − x = 1 2 + 1 3 x,
which gives x = 3 8 . The value of the game is 5 8 .
The strategy for Player B is to choose B-I with probability 1 4
and B-II with probability 3 4 .