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Asymptotic stability in the dual Lovász-Shapley and the Shapley² replicator dynamics for TU games

  • 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.

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Document Type:Working Paper
Author:André CasajusORCiD, Michael KrammORCiD
Chairs and Professorships:Chair of Economics and Information Systems
Full text/ URN:urn:nbn:de:0217-28517
Parent Title (English):HHL Working Paper
Series (Serial Number):HHL-Arbeitspapier / HHL Working paper (197)
Issue:January 2022
Year of Completion:2022
Page Number:13 pages
Tag:CES production function; Dual Lovász-Shapley value; Evolutionary game theory; Shapley² value; ovász-Shapley value
Content Focus:Academic Audience
Licence (German):License LogoUrheberrechtlich geschützt