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Games with Type Indeterminate Players

A Hilbert Space Approach to Uncertainty and Strategic Manipulation of Preferences
  • Ariane Lambert-Mogiliansky
  • Ismael Martínez-MartínezEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8951)

Abstract

We develop a basic framework encoding preference relations on the set of possible strategies in a quantum-like fashion. The Type Indeterminacy model introduces quantum-like uncertainty affecting preferences. The players are viewed as systems subject to measurements. The decision nodes are, possibly non-commuting, operators that measure preferences modulo strategic reasoning. We define a Hilbert space of types and focus on pure strategy TI games of maximal information. Preferences evolve in a non-deterministic manner with actions along the play: they are endogenous to the interaction. We propose the Type Indeterminate Nash Equilibrium as a solution concept relying on best-replies at the level of eigentypes.

Keywords

Type Indeterminacy Superposition of preferences Hilbert space of types Type Indeterminate Nash Equilibrium 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ariane Lambert-Mogiliansky
    • 1
  • Ismael Martínez-Martínez
    • 2
    Email author
  1. 1.Paris School of EconomicsParisFrance
  2. 2.Düsseldorf Institute for Competition Economics (DICE)Heinrich Heine Universität DüsseldorfDüsseldorfGermany

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