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Aequationes mathematicae

, Volume 76, Issue 3, pp 281–304 | Cite as

On the utility of gambling: extending the approach of Meginniss (1976)

  • Che Tat Ng
  • R. Duncan Luce
  • Anthony A. J. Marley
Research paper

Summary.

J. R. Meginniss modified expected utility to accommodate a concept of the utility of gambling that led to a representation composed of a utility expectation term plus an entropy of degree κ term. He imposed several apparently strong assumptions. One of these is that a number of unknown generating functions are identical. A second is that he assumed he was working with given probabilities. Here we follow his general framework but weaken considerably those assumptions. Our problem is reduced to solving some functional equations induced by gamble decomposition. From the solutions, we obtain the representation of the utility function. Further axiomatic restrictions are imposed that lead ultimately to Meginniss’ earlier result.

Mathematics Subject Classification (2000).

94A17 91B16 39B22 

Keywords.

Entropy expected utility functional equations gamble decomposition utility of gambling 

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Copyright information

© Birkhäuser Verlag AG 2008

Authors and Affiliations

  • Che Tat Ng
    • 1
  • R. Duncan Luce
    • 2
  • Anthony A. J. Marley
    • 3
  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Institute for Mathematical Behavioral SciencesUniversity of CaliforniaIrvineUSA
  3. 3.Department of PsychologyUniversity of VictoriaVictoriaCanada

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