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Casajus, André; Kramm, Michael

Asymptotic stability in replicator dynamics derived from TU games. (English) Zbl 1525.91041

Oper. Res. Lett. 50, No. 6, 650-654 (2022).
Summary: We study the asymptotic stability in replicator dynamics derived from TU games using the dual Lovász-Shapley value and the Shapley\(^2\) value for non-negatively weighted games. In particular, we provide a complete description of asymptotically stable population profiles in both dynamics. In the dual Lovász-Shapley replicator dynamic, for example, asymptotically stable populations for simple monotonic games correspond to their minimal blocking coalitions.

MSC:

91A22 Evolutionary games
34D20 Stability of solutions to ordinary differential equations
91A12 Cooperative games

Keywords:

evolutionary game theory; Lovász-Shapley value; dual Lovász-Shapley value; Shapley\(^2\) value; CES production function
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References:

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