Games with Incomplete Preferences

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
• juho.kokkala_at_tkk.fi

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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

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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
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

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References

• S. Bade Nash equilibrium in games with
  incomplete preferences, Economic Theory,
  26(2)309-332, 2005
• B.D. Bernheim Rationalizable strategic behavior,
  Econometrica, 52(4)1007-1028, 1984
• D.G. Pearce Rationalizable strategic behavior
  and the problem of perfection, Econometrica,
  52(4)1029-1050, 1984
• A. Salo and R.P. Hämäläinen Preference
  programming through approximate ratio
  comparisons, European Journal of Operational
  Research, 82(3)458-475, 1995
• L.S. Shapley Equilibrium points in games with
  vector payoffs, Naval Research Logistics
  Quarterly, 6(1)57-61, 1959