1. Games with Incomplete Preferences
Juho Kokkala
supervisors
Prof. Raimo P. Hämäläinen
Dr. Tech. Kai Virtanen
Systems Analysis Laboratory
Aalto University School of Science and Technology

2. Games with Incomplete Preferences
Normal-form non-cooperative game with 2-N players
Strategy set for each player i
Preference relation over outcomes for player i
Incomplete: players may be indecisive between some outcomes
Common knowledge of strategy sets and preferences
Bade (2005): Each Nash equilibrium of this game is a Nash equilibrium of a completion of the game

3. Rationalizable Strategies
Rationality: players select only nondominated strategies
Strategy s dominates strategy s’ if it yields
a preferred outcome no matter what the opponents play
Common knowledge of rationality, no additional assumptions
→ Rationalizable strategies (Pearce 1984, Bernheim 1984)
Kokkala J., Virtanen K., and Poropudas J.: Rationalizable strategies in games with incomplete preferences Manuscript in preparation
No new rationalizable strategies appear when preference information is added

4. Special case of games with incomplete preferences Vector-valued payoff
Multicriteria Games
Special case of games with incomplete preferences
Vector-valued payoff
Player i desires to maximize
Preferences represented by weights related to (e.g., Shapley 1959)
Our manuscript
Incomplete preference information represented by a set of feasible weights
Preference programming (Hämäläinen and Salo 1995)
Player i prefers outcome over outcome if
Restricting the set of feasible weights corresponds to additional preference information
Nondominated strategies
Rationalizable strategies

5. References
S. Bade: Nash equilibrium in games with incomplete preferences, Economic Theory, 26(2): , 2005
B.D. Bernheim: Rationalizable strategic behavior, Econometrica, 52(4): , 1984
D.G. Pearce: Rationalizable strategic behavior and the problem of perfection, Econometrica, 52(4): , 1984
A. Salo and R.P. Hämäläinen: Preference programming through approximate ratio comparisons, European Journal of Operational Research, 82(3): , 1995
L.S. Shapley: Equilibrium points in games with vector payoffs, Naval Research Logistics Quarterly, 6(1):57-61, 1959