A class of population dynamics for reaching epsilon-equilibria: Engineering applications

Abstract

Abstract-This document proposes a novel class of population dynamics that are parameterized by a nonnegative scalar . We show that any rest point of the proposed dynamics corresponds to an -equilibrium of the underlying population game. In order to derive this class of population dynamics, our approach is twofold. First, we use an extension of the pairwise comparison revision protocol and the classic mean dynamics for well-mixed populations. This approach requires full-information. Second, we employ the same revision protocol and a version of the mean dynamics for non-well-mixed populations that uses only local information. Furthermore, invariance properties of the set of allowed population states are analyzed, and stability of the -equilibria is formally proven. Finally, two engineering examples based on the −dynamics are presented: A control scenario in which noisy measurements should be mitigated, and a humanitarian engineering application related to wealth distribution in poor societies.

Atomicity and Non-Anonymity in Population-Like Games for the Energy Efficiency of Hybrid-Power HetNets

“…Furthermore, since decision maker i ∈ U cannot select the strategies B\B i,k , then for simplicity it is considered that the decision maker has no incentives to move to such a strategy -i.e., f i, ,k = 0, for all B\B i,k . The objective within the population is to achieve a local ε-equilibrium [49], as presented in Definition 3, which also provides notions about the local Nash equilibrium [50], [51].…”

Energy Efficiency of Hybrid-Power HetNets: A Population-like Games Approach

“…Furthermore, since the decision maker i ∈ U cannot select the strategies B\B i,k , then for simplicity it is considered that the decision maker has no incentives to move to such a strategy, i.e., f i ,k = 0, for all B\B i,k . The objective within the population is to achieve a Local ε-Equilibrium [17] as presented in Definition 3, which also provides notions about Local Nash Equilibrium [14], [15].…”

“…In particular, characteristics of atomicity and non-anonymity are considered to take into account that one user decision affects the global performance of the system. It is important to note that atomicity and nonanonymity are novel features of the population games approach proposed being this the main difference with previous works as presented in [5], [17]. For this reason, we refer to the proposed mechanism as population-like games.…”