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Dynamic Games and Applications

Erschienen in:

02.11.2020

Periodic Attractor in the Discrete Time Best-Response Dynamics of the Rock-Paper-Scissors Game

verfasst von: José Pedro Gaivão, Telmo Peixe

Erschienen in: Dynamic Games and Applications | Ausgabe 3/2021

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Abstract

The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game widely studied in terms of its theoretical analysis as well as in its applications, ranging from sociology and biology to economics. In this work, we show that the attractor of the discrete time best-response dynamics of the RPS game is a finite union of periodic orbits. Moreover, we also describe the bifurcations of the attractor and determine the exact number, period and location of the periodic orbits.

Vorheriger Artikel Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach

Nächster Artikel A Mean Field Approach for Discounted Zero-Sum Games in a Class of Systems of Interacting Objects

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In fact, the smallest period is \(3\left( \left\lfloor \frac{\log (a/b)}{\log (1-\varepsilon )}\right\rfloor +1\right) \sim \frac{3\log (b/a)}{\varepsilon }\) as \(\varepsilon \rightarrow 0\).

The inverse of the supergolden ratio.

For every \(x\in {\mathbb {R}}\), \(x\le \lfloor x\rfloor <x+1\) and \(x-1<\lceil x \rceil \le x\).

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Titel: Periodic Attractor in the Discrete Time Best-Response Dynamics of the Rock-Paper-Scissors Game
verfasst von: José Pedro Gaivão
Telmo Peixe
Publikationsdatum: 02.11.2020
Verlag: Springer US
Erschienen in: Dynamic Games and Applications / Ausgabe 3/2021
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-020-00371-y

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