Computability of Simple Games: A Complete Investigation of the Sixty-Four Possibilities

@article{Kumabe2011ComputabilityOS,
  title={Computability of Simple Games: A Complete Investigation of the Sixty-Four Possibilities},
  author={M. Kumabe and H. Mihara},
  journal={Public Choice: Analysis of Collective Decision-Making eJournal},
  year={2011}
}
  • M. Kumabe, H. Mihara
  • Published 2011
  • Mathematics, Computer Science, Economics
  • Public Choice: Analysis of Collective Decision-Making eJournal
  • Classify simple games into sixteen “types” in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and algorithmic computability. For each such class, we either show that it is empty or give an example of a game belonging to it. We observe that if a type contains an infinite game, then it contains both computable ones and noncomputable ones. This strongly… CONTINUE READING

    Topics from this paper.

    References

    SHOWING 1-10 OF 38 REFERENCES
    Computability of Simple Games: A Characterization and Application to the Core
    • 7
    • PDF
    The Nakamura numbers for computable simple games
    • 6
    • PDF
    Nonanonymity and sensitivity of computable simple games
    • H. Mihara
    • Mathematics, Computer Science
    • Math. Soc. Sci.
    • 2004
    • 4
    • PDF
    Arrow's Theorem and Turing computability
    • 37
    • PDF
    On computational complexity of membership test in flow games and linear production games
    • 29
    Computable preference and utility
    • 9
    On the Complexity of Cooperative Solution Concepts
    • 507
    • PDF
    A Simple Introduction to Computable Analysis
    • 15
    • PDF
    Game Theoretic Analysis of Voting in Committees
    • B. Peleg
    • Mathematics, Political Science
    • 1984
    • 255
    • PDF