Mistakes can stabilise the dynamics of rock-paper-scissors games

A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium.

Download Full-text

Mistakes can stabilise the dynamics of rock-paper-scissors games

10.1101/2020.12.02.407957 ◽

2020 ◽

Author(s):

Maria Kleshnina ◽

Sabrina S. Streipert ◽

Jerzy A. Filar ◽

Krishnendu Chatterjee

Keyword(s):

Evolutionary Dynamics ◽

Stable Equilibrium ◽

Mixed Strategies ◽

Strategy Execution ◽

Cyclic Pattern ◽

Behavioural Patterns ◽

Observed Behaviour ◽

Pure Strategies

AbstractA game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium.Author summaryA game of rock-paper-scissors is more than just a children’s game. This type of interactions is often used to describe competition among animals or humans. A special feature of such an interaction is that none of the pure strategies dominates, resulting in a cyclic pattern. However, in wild communities such interactions are rarely observed by biologists. Our results suggest that this lack of cyclicity may stem from imperfectness of interacting individuals. In other words, we show analytically that heterogeneity in behavioural patterns may break a cyclic relationship and lead to a stable equilibrium in pure or mixed strategies.

Download Full-text

Evolutionary Stable Strategies for Supply Chains: Selfishness, Fairness, and Altruism

Journal of Systems Science and Information ◽

10.21078/jssi-2018-532-20 ◽

2018 ◽

Vol 6 (6) ◽

pp. 532-551 ◽

Cited By ~ 1

Author(s):

Caichun Chai ◽

Hailong Zhu ◽

Zhangwei Feng

Keyword(s):

Supply Chains ◽

Evolutionary Dynamics ◽

Replicator Dynamics ◽

Management Strategies ◽

Individual Preference ◽

Short Term ◽

Evolutionary Stable Strategies ◽

Pure Strategies ◽

The Stability

Abstract The management strategies of a firm are inevitable affected by individual behavior preferences. The effect of individual preference on the evolutionary dynamics for supply chains is studied by employing replicator dynamics. Each firm has three behavior preferences: selfishness, fairness, and altruism. Firstly, the case that the strategy set of manufacturers and retailers including two pure strategies is considered and the effect of preference parameter on the equilibrium outcome in the short-term interaction is discussed. Secondly, the equilibrium state in the short-term is always disturbed because the change of the environment, firm’s structure, and so forth. Using the replicator dynamics, the evolutionary stable strategies of manufacturers and retailers in the long-term interaction are analyzed. Finally, the extend case that the strategy set of manufacturers and retailers include three pure strategies is investigated. These results are found that the strategy profile in which both manufacturer and retailer choose fairness or altruism, or one player chooses fair or altruistic strategy and the other player chooses selfish strategy may be evolutionary stable, the stability of these equilibria depends on the the preference parameters.

Download Full-text

Probabilistic participation in public goods games

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2007.0673 ◽

2007 ◽

Vol 274 (1625) ◽

pp. 2639-2642 ◽

Cited By ~ 36

Author(s):

Tatsuya Sasaki ◽

Isamu Okada ◽

Tatsuo Unemi

Keyword(s):

Public Goods ◽

Evolutionary Dynamics ◽

Voluntary Participation ◽

Dynamical Regime ◽

Mixed Strategies ◽

Public Enterprises ◽

Interior Equilibrium ◽

Public Goods Games ◽

Special Cases ◽

Pure Strategies

Voluntary participation in public goods games (PGGs) has turned out to be a simple but effective mechanism for promoting cooperation under full anonymity. Voluntary participation allows individuals to adopt a risk-aversion strategy, termed loner. A loner refuses to participate in unpromising public enterprises and instead relies on a small but fixed pay-off. This system leads to a cyclic dominance of three pure strategies, cooperators, defectors and loners, but at the same time, there remain two considerable restrictions: the addition of loners cannot stabilize the dynamics and the time average pay-off for each strategy remains equal to the pay-off of loners. Here, we introduce probabilistic participation in PGGs from the standpoint of diversification of risk, namely simple mixed strategies with loners, and prove the existence of a dynamical regime in which the restrictions no longer hold. Considering two kinds of mixed strategies associated with participants (cooperators or defectors) and non-participants (loners), we can recover all basic evolutionary dynamics of the two strategies: dominance; coexistence; bistability; and neutrality, as special cases depending on pairs of probabilities. Of special interest is that the expected pay-off of each mixed strategy exceeds the pay-off of loners at some interior equilibrium in the coexistence region.

Download Full-text

Analyzing the Stability Properties of Kaleidocycles

Journal of Applied Mechanics ◽

10.1115/1.4032572 ◽

2016 ◽

Vol 83 (5) ◽

Cited By ~ 13

Author(s):

C. Safsten ◽

T. Fillmore ◽

A. Logan ◽

D. Halverson ◽

L. Howell

Keyword(s):

Stable Equilibrium ◽

Equilibrium States ◽

Stored Energy ◽

Cyclic Pattern ◽

Stability Properties ◽

The Stability

Kaleidocycles are continuously rotating n-jointed linkages. We consider a certain class of six-jointed kaleidocycles which have a spring at each joint. For this class of kaleidocycles, stored energy varies throughout the rotation process in a nonconstant, cyclic pattern. The purpose of this paper is to model and provide an analysis of the stored energy of a kaleidocycle throughout its motion. In particular, we will solve analytically for the number of stable equilibrium states for any kaleidocycle in this class.

Download Full-text

Microtwinning Evidence For The Apparent Five-Fold Symmetry in T2(Al6Li3Cu)

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125178 ◽

1987 ◽

Vol 45 ◽

pp. 24-25

Author(s):

Kenneth S. Vecchio ◽

David B. Williams

Keyword(s):

Stable Equilibrium ◽

Equilibrium Phase ◽

Convergent Beam Electron Diffraction ◽

Icosahedral Structure ◽

Cubic Crystals ◽

Icosahedral Phases ◽

Heat Treated ◽

Zero Layer ◽

Convergent Beam ◽

Zr Alloy

Since the discovery in 1984 by Shechtman et al. of crystals which display apparent five-fold symmetry, extensive effort has been given to establishing a theoretical basis for the existence of icosahedral phases (eg.2.). Several other investigations have been centered on explaining these observations based on twinning of cubic crystals (eg.3.). Recently, the existence of a stable, equilibrium phase T2Al6 Li3Cu) possessing an icosahedral structure has been reported in the Al-Li-Cu system(4-6).In the present study an Al-2.6wt.%Li-l.5wt.%Cu-0.lwt.%Zr alloy was heat treated at 300°C for 100hrs. to produce large T2 precipitates. Convergent Beam Electron Diffraction (CBED) patterns were obtained from two-fold, three-fold, and apparent five-fold axes of T2 particles. Figure 1 shows the five-fold symmetric zero layer CBED pattern obtained from T2 particles.

Download Full-text

Evolutionary dynamics and chromosomal distribution of repetitive sequences on chromosomes of Aegilops speltoides revealed by genomic in situ hybridization

Heredity ◽

10.1046/j.1365-2540.2001.00891.x ◽

2001 ◽

Vol 86 (6) ◽

pp. 738-742 ◽

Cited By ~ 7

Author(s):

Alexander Belyayev ◽

Olga Raskina ◽

Eviatar Nevo

Keyword(s):

In Situ Hybridization ◽

Evolutionary Dynamics ◽

Repetitive Sequences ◽

Genomic In Situ Hybridization ◽

Aegilops Speltoides ◽

Chromosomal Distribution

Download Full-text

Evolutionary Dynamics of Plant-Pathogen Interactions

10.1017/9781108625517 ◽

2019 ◽

Cited By ~ 13

Author(s):

Jeremy J. Burdon ◽

Anna-Liisa Laine

Keyword(s):

Plant Pathogen ◽

Evolutionary Dynamics ◽

Plant Pathogen Interactions

Download Full-text

Sequential Difficulty Effects During Strategy Execution

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169/a000157 ◽

2012 ◽

Vol 59 (5) ◽

pp. 295-301 ◽

Cited By ~ 35

Author(s):

Kim Uittenhove ◽

Patrick Lemaire

Keyword(s):

Computational Models ◽

Preceding Trial ◽

Human Cognition ◽

Strategy Execution ◽

Strategy Performance ◽

Empirical Implications

In two experiments, we tested the hypothesis that strategy performance on a given trial is influenced by the difficulty of the strategy executed on the immediately preceding trial, an effect that we call strategy sequential difficulty effect. Participants’ task was to provide approximate sums to two-digit addition problems by using cued rounding strategies. Results showed that performance was poorer after a difficult strategy than after an easy strategy. Our results have important theoretical and empirical implications for computational models of strategy choices and for furthering our understanding of strategic variations in arithmetic as well as in human cognition in general.

Download Full-text