# Evolutionary Dynamics of Gig Economy Labor Strategies under Technology, Policy and Market Influence

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Overview

#### 2.2. Evolutionary Dynamics of Gig Economy Labor Preferences

#### Replicator Equations for Asymmetric Bi-Matrix Games

## 3. Results

#### 3.1. Key Concepts and Theoretical Analysis of the Evolutionary Game Theory Model

#### 3.1.1. System Equilibria

#### 3.1.2. Saddle Points

#### 3.1.3. Saddle Point Geographies

- Quadrant
- I: ${a}_{l}<{d}_{l}$ and ${a}_{f}<{d}_{f}$;
- Quadrant
- II: ${a}_{l}<{d}_{l}$ and ${a}_{f}>{d}_{f}$;
- Quadrant
- III: ${a}_{l}>{d}_{l}$ and ${a}_{f}>{d}_{f}$;
- Quadrant
- IV: ${a}_{l}>{d}_{l}$ and ${a}_{f}<{d}_{f}$.

#### 3.1.4. Attractor Arc, Driven Oscillation and Trapping Zones

#### Attractor Arc

#### 3.1.5. Shepherding Attractors, Driven Oscillation and Trapping Zones

#### Escape and Implications

#### Selection of Initial Conditions

#### Attractor Arc Drift and Tilt

#### 3.2. Market Influences on Firm and Laborer Gig Preference

#### 3.2.1. Interpretations of Market Influenced Dynamics

#### Market Influence on Labor Dynamics, Example No. 1

#### Market Influence on Labor Dynamics, Example No. 2

#### 3.2.2. Generalized Framework for Market Influenced Oscillatory Dynamics

#### 3.2.3. Payoff Generation

#### 3.3. Technology Influences on Firm and Laborer Gig Preference

#### 3.3.1. Technology and the Neoteric Growth of the Gig Economy

#### 3.3.2. Technological Implications on the Future of the Gig Economy

#### 3.4. Policy Influences on Firm and Laborer Gig Preference

#### 3.4.1. The Impact of Regulation on Labor Strategy Sensitivities

#### 3.5. A Treble of Evolutionary Dynamics under Technology, Policy and Market Influence

#### 3.5.1. An Evolving Orbit of Forced Dynamics

#### 3.5.2. Implications for the Modern Gig Economy

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Evolutionary Model

#### Appendix A.1. System Equilibria

#### Appendix A.1.1. Fixed Points

#### Appendix A.1.2. Stability Analysis

**Saddle Points**

**Unstable Fixed Points**

**Stable Fixed Points**

#### Appendix A.1.3. Concept Visuals

**Figure A1.**Evolutionary behavior for $n=0$, $\dot{n}=0$ with theoretical GameState payoff, see Figure 1. In this visualization, green represents initial condition, yellow represents the evolutionary path and red represents the final system position at an ESS. Two evolutionary journeys are visualized with initial conditions ($\frac{1}{4}$,$\frac{1}{4}$) and ($\frac{3}{4}$,$\frac{3}{4}$).

#### Appendix A.2. Oscillating Replicator Dynamics

#### Appendix A.2.1. Computational Notes

#### Appendix A.2.2. Trapping Zone Orbit

**Figure A3.**Trapping zone oscillation with initial conditions $(0.45,0.40)$, $\omega =0.005$ and $n=1$ and theoretical GameState pair, see Figure 1. (

**a**) Mismatching oscillatory behavior in trapping zone. (

**b**) Trapping zone orbit. We illustrate the trapping zone orbit in yellow. A reference attractor arc is plotted in purple and attractor positions at $n=0$ and $n=1$ are represented in orange and blue, respectively. The opaque black ellipse is a background element for visual contrast.

#### Appendix A.2.3. Escape Demonstration with Different Initial Conditions

**Figure A4.**Escape demonstration with initial conditions $(0.45,0.40)$, $\omega =0.1$ and $n=1$ and theoretical GameState pair, see Figure 1.

**Figure A5.**Escape demonstration with initial conditions $(0.45,0.40)$, $\omega =0.1$ and $n=0$ and theoretical GameState pair, see Figure 1.

## Appendix B. Payoff Matrices

**Figure A7.**Payoffs for vertical attractor arc demonstration. (

**a**) Bear market, $n=0$; (

**b**) Bull market, $n=1$.

**Figure A8.**Payoffs for horizontal attractor arc demonstration. (

**a**) Bear market, $n=0$; (

**b**) Bull market, $n=1$.

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**Figure 1.**Theoretical GameState pair payoff matrices used in demonstrations. (

**a**) Bear market GameState; (

**b**) bull market GameState.

**Figure 2.**Saddle point geographies with theoretical GameState payoffs, see Figure 1. (

**a**) Bear GameState, $n=0$; (

**b**) bull GameState, $n=1$; (

**c**) quadrant legend. ${x}_{1}$ and ${y}_{1}$ denote laborer and firm preference for gig work, respectively, where the value of $1.0$ represents a universal gig strategy and the value of $0.0$ represents a universal employee strategy.

**Figure 3.**2D attractor arc mapping on superimposed theoretical GameState payoff when $n=0$ and $n=1$, see Figure 1. The attractor arc represents the entirety of possible attractor positions given $n\in [0,1]$. Reference points on the attractor arc demonstrate attractor positions when $n=0$, $n=0.25$, $n=0.5$, $n=0.75$ and $n=1$.

**Figure 4.**3D attractor arc. The 3D arc is represented in yellow with reference attractor positions when $n=0$, $n=0.25$, $n=0.5$, $n=0.75$ and $n=1$. The projected 2D arc is represented in purple, consistent with the antecedent diagram, see Figure 3. Nullclines for $n=0$ and $n=1$ are illustrated in green and red, respectively.

**Figure 5.**Concept visuals: Shepherding attractors and driven oscillation. (

**a**) Evolution in bear market; (

**b**) evolution in bull market; (

**c**) driven oscillation. In (

**a**,

**b**), we plot the evolutionary trajectories for a bear and bull market. For each phase diagram, green denotes initial condition, red denotes ending destination and yellow denotes the evolutionary path. In (

**c**), a reference attractor arc is plotted in purple and attractor positions at $n=0$ and $n=1$ are represented in orange and blue, respectively. The trapping zone orbit is plotted in yellow. The opaque black ellipse is a background element for visual contrast. This oscillation models $\omega =0.5$ and initial conditions $n=1$ and $(0.45,0.4)$, the attractor position when $n=0.5$. In this figure, we use a relatively large $\omega $ for the purpose of visualizing the evolution in (

**a**,

**b**). In (

**c**), nullclines for $n=0$ and $n=1$ are illustrated in green and red, respectively. The central region demarcated by the nullclines is an attraction zone where trapping behavior is possible.

**Figure 6.**Concept visuals: Attractor arc drift and arc tilt. (

**a**) Attractor arc drift $\dot{A},\dot{B}\ne 0$; (

**b**) attractor arc tilt $\dot{A},\dot{B}\ne 0$. In (

**a**), the green arc applies the theoretical GameState pair payoff, see Figure 1, and the red arc applies a high employee payoff matrix operation, see Figure 12. In (

**b**), the green arc applies the theoretical GameState pair payoff, see Figure 1, and the red arc applies a lenient policy matrix operation, see Figure 14.

**Figure 7.**Theoretical market demonstration No. 1: Evolution of strategy densities under market influence with initial conditions $(0.45,0.40)$, the attractor position at $n=0.5$, an approximation for a point in the trapping zone; $n=1$, a bull market; $\omega =0.01$; and theoretical payoff matrices from Figure 1. (

**a**) Trapping zone orbit. (

**b**) Attractor arc. (

**c**) Labor strategy oscillation over three market periods. In (

**a**), the trapping zone orbit is plotted in yellow, and attractor positions at $n=0$ and $n=1$ are represented in orange and blue, respectively. Directional dynamics during bear and bull markets are represented by the orange and blue arrows, respectively. In (

**b**), we plot a reference attractor arc in purple with attractor positions when $n=0$, $n=0.25$, $n=0.5$, $n=0.75$ and $n=1$. (

**c**) visualizes the fluctuation in firm and laborer preferences for gig strategies over three market cycles.

**Figure 8.**Theoretical market demonstration No. 2: Evolution of strategy densities under market influence with initial conditions $(0.55,0.40)$, the attractor position at $n=0.5$, an approximation for a point in the trapping zone; $n=1$, a bull market; $\omega =0.01$; and theoretical payoff matrices from Figure A6 in Appendix B. (

**a**) Trapping zone orbit. (

**b**) Attractor arc. (

**c**) Labor strategy oscillation over three market periods. In (

**a**), the trapping zone orbit is plotted in yellow, and attractor positions at $n=0$ and $n=1$ are represented in orange and blue, respectively. Directional dynamics during bear and bull markets are represented by the orange and blue arrows, respectively. In (

**b**), we plot a reference attractor arc in purple with attractor positions when $n=0$, $n=0.25$, $n=0.5$, $n=0.75$ and $n=1$. (

**c**) visualizes the fluctuation in firm and laborer preferences for gig strategies over three market cycles.

**Figure 9.**$n=1$ payoffs represented in terms of $n=0$ payoffs. (

**a**) Bear market, $n=0$. (

**b**) Bull market, $n=1$. We rephrase bull market payoffs in terms of bear market payoffs and a market $\delta $, which captures how labor preference varies from a bear to bull market. For simplification purposes, we assign all mismatching strategies a payoff of 0 as no mutual labor agreement is made between firm and laborer.

**Figure 10.**Directional framework for market influenced dynamics with normalized bear market payoffs. Directional dynamics are presented through the lens of a normalized $n=0$ payoff. The attractor position at $n=0$ is represented in orange. Four theoretical attractor positions at $n=1$, represented in blue, are depicted in quadrants I through IV. Directional dynamics during bear and bull markets are represented by the orange and blue arrows, respectively. A single attractor arc is illustrated in purple to demonstrate when the attractor position at $n=1$ is located in quadrant II in respect to a normalized attractor position at $n=0$. Here, directional dynamics are similar to our first theoretical example, see Figure 7.

**Figure 11.**High gig payoff, matrix operation. (

**a**) High gig payoff, $n=0$; (

**b**) high gig payoff, $n=1$.

**Figure 12.**High employee payoff, matrix operation. (

**a**) High employee payoff, $n=0$; (

**b**) high employee payoff, $n=1$.

**Figure 13.**Attractor arc drift transformations. (

**a**) Arc transformation with high gig payoff matrix operation, see Figure 11; theoretical GameState pair, see Figure 1; and $\delta {a}^{q}=\delta {d}^{q}=10$. (

**b**) Arc transformation with high employee payoff matrix operation, see Figure 12; theoretical GameState pair, see Figure 1; and $\delta {a}^{q}=\delta {d}^{q}=10$. (

**c**) Reference attractor arc with theoretical GameState pair, see Figure 1. (

**d**) Composite diagram with arcs (

**a**–

**c**).

**Figure 14.**Lenient policy, matrix operation. (

**a**) Lenient ordinance, $n=0$. (

**b**) Lenient ordinance, $n=1$.

**Figure 15.**Strict policy, matrix operation. (

**a**) Strict ordinance, $n=0$. (

**b**) Strict ordinance, $n=1$.

**Figure 16.**Attractor arc drift transformations. (

**a**) Arc transformation with lenient policy matrix operation, see Figure 14; theoretical GameState payoff pair, see Figure 1; and $\delta {a}^{p}=3$. (

**b**) Arc transformation with strict policy matrix operation, see Figure 15; theoretical GameState payoff pair, see Figure 1; and $\delta {a}^{p}=3$. (

**c**) Reference attractor arc with theoretical GameState payoff pair, see Figure 1. (

**d**) Composite diagram with arcs (

**a**–

**c**).

**Figure 17.**Vertical and horizontal attractor arc and trapping zone slopes. (

**a**) Attractor arc using theoretical payoff pair, see Figure A7 in Appendix B. When the attractor arc is oriented vertically, the slope of the trapping zone becomes horizontal and perpendicular to the arc. (

**b**) Attractor arc using theoretical payoff pair, see Figure A8 in Appendix B. When the attractor arc is oriented horizontally, the slope of the trapping zone becomes vertical and perpendicular to the arc. The opaque yellow ellipse is a background element to indicate the general region of the trapping zone. The evolutionary trajectories in both (

**a**,

**b**) trapping zones are orthogonal to their respective arcs.

**Figure 18.**Treble of dynamics. (

**a**) Market driven oscillatory dynamics. (

**b**) Technology driven arc drift. (

**c**) Policy driven arc tilt.

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Hu, K.; Fu, F.
Evolutionary Dynamics of Gig Economy Labor Strategies under Technology, Policy and Market Influence. *Games* **2021**, *12*, 49.
https://doi.org/10.3390/g12020049

**AMA Style**

Hu K, Fu F.
Evolutionary Dynamics of Gig Economy Labor Strategies under Technology, Policy and Market Influence. *Games*. 2021; 12(2):49.
https://doi.org/10.3390/g12020049

**Chicago/Turabian Style**

Hu, Kevin, and Feng Fu.
2021. "Evolutionary Dynamics of Gig Economy Labor Strategies under Technology, Policy and Market Influence" *Games* 12, no. 2: 49.
https://doi.org/10.3390/g12020049