Escort function definitions for feasible region flexibility in applications of Replicator-like dynamics with constraints
Résumé
This paper proposes an extension to a family of evolutionary game dynamics called Escort Replicator Dynamics (ERD), defined in [1] based on information-geometric concepts. Specifically, the objective of this paper is to propose three types of convenient so-called escort functions and 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, non-negative. From an engineering application perspective, these proposed escort functions are convenient since they allow to extend replicator-like dynamics applications to engineering problems with feasible regions more general than the standard simplex or the non-negative 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.
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