@article{Casajus2021,
  author    = {Andr{\´e} Casajus},
  title     = {Second-order productivity, second-order payoffs, and the Shapley value},
  series   = {Discrete applied mathematics},
  number    = {304 (December 2021)},
  issn      = {0166-218X},
  doi       = {10.1016/j.dam.2021.07.036},
  pages     = {212 -- 219},
  year      = {2021},
  abstract  = {We introduce the concepts of the players’ second-order productivities in cooperative games with transferable utility (TU games) and of the players’ second-order payoffs for one-point solutions for TU games. Second-order productivities are conceptualized as second-order marginal contributions, that is, how one player affects another player’s marginal contributions to coalitions containing neither of them by entering these coalitions. Second-order payoffs are conceptualized as the effect of one player leaving the game on the payoff of another player. We show that the Shapley value is the unique efficient one-point solution for TU games that reflects the players’ second-order productivities in terms of their second-order payoffs.},
  language  = {en}
}