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On Pareto equilibria in vector-valued extensive form games

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  • Thomas Krieger

Abstract

In this paper we investigate the existence of Pareto equilibria in vector-valued extensive form games. In particular we show that every vector-valued extensive form game with perfect information has at least one subgame perfect Pareto equilibrium in pure strategies. If one tries to prove this and develop a vector-valued backward induction procedure in analogy to the real-valued one, one sees that different effects may occur which thus have to be taken into account: First, suppose the deciding player at a nonterminal node makes a choice such that the equilibrium payoff vector of the subgame he would enter is undominated under the equilibrium payoff vectors of the other subgames he might enter. Then this choice need not to lead to a Pareto equilibrium. Second, suppose at a nonterminal node a chance move may arise. The combination of the Pareto equilibria of the subgames to give a strategy combination of the entire game need not be a Pareto equilibrium of the entire game. Copyright Springer-Verlag 2003

Suggested Citation

  • Thomas Krieger, 2003. "On Pareto equilibria in vector-valued extensive form games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 449-458, December.
    • Handle: RePEc:spr:mathme:v:58:y:2003:i:3:p:449-458
    DOI: 10.1007/s001860300305
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    Cited by:

    1. Chi Zhang & Jose Ramirez-Marquez, 2013. "Protecting critical infrastructures against intentional attacks: a two-stage game with incomplete information," IISE Transactions, Taylor & Francis Journals, vol. 45(3), pages 244-258.
    2. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.

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