André Casajus, Michael Kramm

• Casajus, Kramm, and Wiese (2020, J. Econ. Theory 186, 104993) study the asymptotic stability in population dynamics derived from finite cooperative games with transferable utility using the Lovász-Shapley value (Casajus and Wiese, 2017, Int. J. Game Theory 45, 1-16) for non-negatively weighted games, where the players are interpreted as types of individuals. We extend their analysis to the population dynamics derived using the dual Lovász-Shapley value and the Shapley² value for non-negatively weighted games (Casajus and Kramm, HHL Working Paper 196, HHL Leipzig Graduate School of Management, Leipzig, Germany). As the former, we provide a complete description of asymptotically stable population profiles in both dynamics. In the dual Lovász-Shapley replicator dynamic, for example, any asymptotically stable population profile is characterized by a coalition: while the types in the coalition have the same positive share, the other types vanish. In the dual of the game, the per-capita productivity of such a stable coalition must be greater than the per-capita productivity of any proper sub- or supercoalition. In simple monotonic games, this means that exactly the minimal blocking coalitions are stable.