@techreport{Casajus2020,
  type      = {Working Paper},
  author    = {Casajus, Andr{\´e}},
  title     = {Second-order productivity, second-order payoffs, and the Shapley value},
  series    = {HHL Working paper},
  institution = {Chair of Economics and Information Systems},
  series    = {HHL-Arbeitspapier / HHL Working paper},
  number    = {187},
  pages     = {19},
  year      = {2020},
  abstract  = {We show that the Shapley value is the unique efficient one-point solution for cooperative games with transferable utility that reflects the players' second-order productivities in terms of their second-order payoffs. 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.},
  language  = {en}
}