Weak differential monotonicity and axiomatization of convex combinations of solutions to cooperative games

• Zeguang Cui ^[1] ; Erfang Shan ^[1] ; Wenrong Lyu ^[2]
  1. [1] Shanghai University

     Shanghai University

     China

     
  2. [2] Zhejiang Normal University

     Zhejiang Normal University

     China

     
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 33, Nº. 3, 2025, págs. 489-510
• Idioma: inglés
• DOI: 10.1007/s11750-024-00686-8
• Enlaces
  • Texto completo
• Resumen

  • The α-egalitarian Shapley values are convex combinations of the Shapley value and the equal division value. For cooperative games that contain more than three players, Casajus and Yokote (Int J Game Theory 48:979–997, 2019) propose a characterization of the α-egalitarian Shapley values by efficiency, weak differential monotonicity, and the average dummy player property. However, it remains an open question whether the characterization holds true for games with three players or not. In this paper, we answer this question in the affirmative. Furthermore, we establish a new axiomatization of the α-equal surplus division values, which are convex combinations of the equal surplus division value and the equal division value.

• Referencias bibliográficas
  • Casajus A, Yokote K (2017) Weak differential marginality and the Shapley value. J Econ Theory 167:274– 284
  • Casajus A, Yokote K (2019) Weakly differentially monotonic solutions for cooperative games. Int J Game Theory 48:979–997
  • Driessen TSH, Funaki Y (1991) Coincidence of and collinearity between game theoretic solutions. OR Spektrum 13:15–30
  • Harsanyi JC (1959) A bargaining model for cooperative n-person games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games IV....
  • Joosten R (1996) Dynamics, equilibria and values. Maastricht University, Maastricht
  • Shapley LS (1953) A value for n-person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games. Princeton University Press,...
  • van den Brink R, Funaki Y (2009) Axiomatizations of a class of equal surplus sharing solutions for TUgames. Theory Decis 67:303–340
  • Xu G, Dai H, Shi H (2015) Axiomatizations and a noncooperative interpretation of the α-CIS value. Asia Pac J Oper Res 32:1550031
  • Yokote K, Casajus A (2017) Weak differential monotonicity, flat tax, and basic income. Econ Lett 151:100– 103
  • Young HP (1985) Monotonic solutions of cooperative games. Int J Game Theory 14:65–72