Paul Samuelson's critique and equilibrium concepts in evolutionary game theory

Arbeitspapier

We present two new notions of evolutionary stability, the truly evolutionarily stable state (TESS) and the generalized evolutionarily stable equilibrium (GESE). The GESE generalizes the evolutionarily stable equilibrium (ESE) of Joosten [1996]. An ESE attracts all nearby trajectories monotonically, i.e., the Euclidean distance decreasing steadily in time. For a GESE this property should holds for at least one metric. The TESS generalizes the evolutionarily stable strategy (ESS) of Maynard Smith & Price [1973]. A TESS attracts nearby trajectories too, but the behavior of the dynamics nearby must be similar to the behavior of the replicator dynamics near an ESS. Both notions are defned on the dynamics and immediately imply asymptotical stability for the dynamics at hand, i.e., the equilibrium attracts all trajectories sufficiently nearby. We consider this the relevant and conceptually right approach in defining evolutionary equilibria, rather than defining a static equilibrium notion and search for appropriate dynamics guaranteeing its dynamic stability. Moreover, the GESE and the TESS take similar positions as the ESE and ESE do in relation to other equilibrium and fixed point concepts in general.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Papers on Economics and Evolution ; No. 0916

Classification and Topics

• Classification: Wirtschaft ; Relation of Economics to Other Disciplines ; Existence and Stability Conditions of Equilibrium ; Noncooperative Games ; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games ; Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
• Subject: evolutionary stability ; evolutionary game theory

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Joosten, Reinoud
• Event: Veröffentlichung
• (who): Max Planck Institute of Economics
• (where): Jena
• (when): 2009

Further information

• Handle: http://hdl.handle.net/10419/32669
• Last update: 10.03.2025, 11:42 AM CET