# Population dynamics of tax avoidance with crowding effects

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## Abstract

There are two ways for taxpayers to avoid paying taxes: *legal* tax optimization and *illegal* tax evasion. The government reacts by altering the law, and by conducting audits, respectively. These phenomena are modeled as a strategic interaction between all taxpayers: the more taxpayers optimize, the lower the optimization result as a consequence of the government tightening the tax law. The more taxpayers evade, the higher the risk of detection because of the tax agencies increasing the audit probability. It emerges that, in equilibrium, the population shares of optimizers and evaders are not interdependent; rather, they both increase to the detriment of the share of non-optimizing taxpayers. If the government reacts to changed optimization behavior with too large a delay, an equilibrium tax law cannot be reached. Tax codes should be updated rapidly in order to avoid a permanent change of the tax law, which is costly both for the legislator and the taxpayers facing legal uncertainty.

## Keywords

Tax evasion Tax avoidance Evolutionary game theory Crowding## JEL Classification

H26 C73 K34## Notes

### Acknowledgements

Many thanks to the participants of the 2015 Annual Congress of the European Accounting Association in Glasgow, and the participants of the 2015 Annual Meeting of the German Academic Association for Business Research in Vienna, especially Martin Fochmann, as well as two anonymous referees for helpful comments.

### Compliance with Ethical Standards

### Conflict of interests

The author declares that he has no conflict of interest.

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