Escort Function Definitions for Feasible Region Flexibility in Applications of Replicatorlike Dynamics With Constraints

• Published in: IEEE transactions on automatic control Vol. 66; no. 11; pp. 5414 - 5421
• Main Authors: Ovalle, Andres, Hably, Ahmad, Bacha, Seddik
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Dynamic equilibrium; Dynamics; Evolutionary computation; Game theory; Lapunov methods; Lyapunov methods; Stability analysis; State vectors
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3065010

This articleproposes an extension to a family of evolutionary game dynamics called escort replicator dynamics (ERD), defined by (Harper, 2011) based on information-geometric concepts. Specifically, the objective of this article is to propose three types of convenient so-called escort functionsand evaluate the stability of ERD under the use of these functions. Since it is proven that ERD is stable using the proposed definitions, ERD is able to confine trajectories of the state vector in regions defined by upper and lower boundaries which can be, but are not required to be, nonnegative. From an engineering application perspective, these proposed escort functions are convenient since they allow to extend replicatorlike dynamics applications to engineering problems with feasible regions more general than the standard simplex or the nonnegative orthant. From a population dynamics perspective the proposed escort functions are useful to represent upper and lower limits on the share of a population that is allowed to play a given pure strategy of the underlying symmetric game.