Multiagent Systems

of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 192/731
3. Decision Making (1) 2. Non-coop Games
Games can be represented graphically using an
n-dimensional payoff matrix. Here is a generic picture
for 2-player, 2-strategy games:
Player 1 a1 1
a 2 1
Player 2
a 1 2 a 2 2
(µ 1 (a 1 1, a 1 2), µ 2 (a 1 1, a 1 2)
(µ 1 (a 2 1, a 2 2), µ 2 (a 2 1, a 2 2)
(µ 1 (a 1 1, a 1 2), µ 2 (a 1 1, a 2 2)
(µ 1 (a 2 1, a 1 2), µ 2 (a 2 1, a 2 2)
We often forget about ϱ (thus we are making no
distinction between actions and outcomes). Thus we
simply write µ 1 (a 1 1, a 1 2) instead of the more precise
µ 1 (ϱ(〈a 1 1, a 1 2〉).