Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 201/731
3. Decision Making (1) 2. Non-coop Games
Definition 3.14 (Maxmin strategy)
Given a game 〈{1, 2}, {A 1 , A 2 }, {µ 1 , µ 2 }〉, the maxmin
strategy of player i is a mixed strategy that maximises the
guaranteed payoff of player i, no matter what the other
player −i does:
argmax si
min
s −i
µ expected
i (s 1 , s 2 )
The maxmin value for player i is
max si min s−i µ expected
i (s 1 , s 2 ).
The minmax strategy for player i is
argmin si
max
s −i
µ expected
−i (s 1 , s 2 )
and its minmax value is min s−i max si µ expected
−i (s 1 , s 2 ).