English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study an optimal control problem arising from a generalization ofrock-paper-scissors in which the number of strategies may be selected from anypositive odd number greater than 1 and in which the payoff to the winner iscontrolled by a control variable $\gamma$. Using the replicator dynamics as theequations of motion, we show that a quasi-linearization of the problem admits aspecial optimal control form in which explicit dynamics for the controller canbe identified. We show that all optimal controls must satisfy a specific secondorder differential equation parameterized by the number of strategies in thegame. We show that as the number of strategies increases, a limiting caseadmits a closed form for the open-loop optimal control. In performing ouranalysis we show necessary conditions on an optimal control problem that allowthis analytic approach to function.

Control Problems with Vanishing Lie Bracket Arising from Complete Odd Circulant Evolutionary Games