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Supervised tax compliance and evasion from a spatial evolutionary game perspective

Qin Li, Ting Ling, Minyu Feng, Attila Szolnoki

Abstract

Taxation constitutes a fundamental component of modern national economic systems, exerting profound impacts on both societal functioning and governmental operations. In this paper, we employ an interdependent network approach to model the coevolution between citizens and regulators within a taxation system that fundamentally constitutes a public goods game framework with complex interactive dynamics. In a game layer, citizens engage in public goods games, facing the social dilemma of tax compliance (cooperation) versus evasion (defection). Tax compliance supports the sustainability of public finances while tax evasion presents markedly stronger short-term incentives. In a regulatory layer, fair regulators punish tax evaders, while corrupt regulators keep silent due to bribes. Governmental regulatory interventions introduce critical institutional constraints that alter the traditional equilibrium of the game. Importantly, there exists a strategy update not only among citizens but also among regulators. Our results indicate that strengthening penalties can effectively curb tax evasion, and the influence of bribery on both tax compliance rates and the proportion of fair regulators is nonlinear. Additionally, increasing regulators' salaries and intensifying the crackdown on corrupt regulators can foster the emergence of fair regulators, thereby reducing tax evasion among citizens. The results offer practical policy implications, suggesting that balanced deterrence and institutional fairness are essential to sustaining compliance, and point to the need for future empirical validation and model extensions.

Supervised tax compliance and evasion from a spatial evolutionary game perspective

Abstract

Taxation constitutes a fundamental component of modern national economic systems, exerting profound impacts on both societal functioning and governmental operations. In this paper, we employ an interdependent network approach to model the coevolution between citizens and regulators within a taxation system that fundamentally constitutes a public goods game framework with complex interactive dynamics. In a game layer, citizens engage in public goods games, facing the social dilemma of tax compliance (cooperation) versus evasion (defection). Tax compliance supports the sustainability of public finances while tax evasion presents markedly stronger short-term incentives. In a regulatory layer, fair regulators punish tax evaders, while corrupt regulators keep silent due to bribes. Governmental regulatory interventions introduce critical institutional constraints that alter the traditional equilibrium of the game. Importantly, there exists a strategy update not only among citizens but also among regulators. Our results indicate that strengthening penalties can effectively curb tax evasion, and the influence of bribery on both tax compliance rates and the proportion of fair regulators is nonlinear. Additionally, increasing regulators' salaries and intensifying the crackdown on corrupt regulators can foster the emergence of fair regulators, thereby reducing tax evasion among citizens. The results offer practical policy implications, suggesting that balanced deterrence and institutional fairness are essential to sustaining compliance, and point to the need for future empirical validation and model extensions.
Paper Structure (15 sections, 5 equations, 8 figures)

This paper contains 15 sections, 5 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Model
  3. Game Model
  4. Payoff Calculation
  5. Strategy Evolution
  6. Simulation results and analyses
  7. Methods
  8. Effect of penalty $\alpha$ on tax compliance and fairness
  9. Effect of bribery ratio $\beta$ on the $f_C$ and $f_F$
  10. The landscapes of tax compliance and regulator fairness on punishment-bribe parameter space
  11. The effect of regulatory fee $m$ on $f_C$ and $f_F$
  12. The effect of monitoring cost $\gamma$ on $f_C$ and $f_F$
  13. The tax compliance and fairness landscapes on $m-\gamma$ parameter space
  14. Coevolutionary pattern formation of tax compliance and regulator fairness
  15. Conclusions and Discussion

Figures (8)

  • Figure 1: Evolutionary game model with regulators.The lower layer represents the stage of a taxation dilemma, where taxpayers (cooperators) and evaders (defectors) engage in interactions through a spatial public goods game. The upper layer comprises regulators who oversee the evolution of strategies. Fair regulators punish tax evaders, while corrupt regulators accept bribes and help the evaders from being punished. At the same time, to hide their proper behavior, corrupt regulators should pay an additional cost of monitoring.
  • Figure 2: Tax compliance rate and fair regulators density as a function of synergy factor at different fine values. Panel (a) illustrates the proportion of taxpayers in the game layer as the synergy factor $r$ increases, with the values of fine $\alpha$ for evaders marked in the legend. Panel (b) displays the proportion of fair regulators in the regulatory layer. We set the bribery ratio $\beta=0.3$, the supervision fee $m=0.1$ and the cost of monitoring $\gamma=0.1$. Each data point is averaged from the last 500 steps of 3000 total steps and averaged over 10 independent simulations.
  • Figure 3: The tax compliance rate and the proportion of fair regulators in dependence of synergy factor and bribery ratios. The left panels show the color-coded portion of taxpayers in the game layer on the $\beta-r$ parameter plane. The right panels show the color-coded density of fair regulators in the regulatory layer at the same $\beta-r$ parameter pairs. The remaining parameters, the penalty $\alpha=1.2$, the supervision fee $m=0.1$ and the cost of monitoring $\gamma=0.1$ are fixed. All results are averaged from the last 500 steps of 3000 total steps and averaged over 10 independent simulations.
  • Figure 4: The influence of parameter pairs ($\alpha$, $\beta$) on individual behaviors. The left panels show the color-coded portion of taxpayers in the game layer on the $\alpha-\beta$ parameter plane. Right panels show the color-coded density of fair regulators in the regulatory layer at the same parameter pairs. The top row shows the case obtained at supervision fee $m=0.1$ and corruption cost $\gamma=0.1$, while the bottom row indicates when $m=0.2$ and $\gamma=0.2$. The synergy factor is fixed at $r=1.5$ for all cases. The stationary values are calculated from the last 500 steps of 3000 total steps and averaged over 10 independent simulations.
  • Figure 5: Degree of tax compliance and fairness level among regulators in dependence of synergy factor at different regulatory fees. Panel (a) shows the fraction of taxpayers in the game layer as we increase the synergy factor $r$, while panel (b) depicts the fraction of fair regulators in the regulatory layer. The values of regulatory fees that all regulators can obtain are marked in the legend. We set the penalty $\alpha=1.2$, the bribery ratio $\beta=0.3$, and the cost of corruption $\gamma=0.1$. Each result is obtained by averaging the last 500 steps out of 3000 total steps, and the average is taken over 10 simulations.
  • ...and 3 more figures