Presentation on YouTube.

Games of inspection and corruption are well developed in the game-theoretic literature. In author's paper "Inspection -corruption game of illegal logging and other violations: generalized evolutionary approach" (Mathematics MDPI 2021, 9(14), 1619) a generalised evolutionary approach was developed based on the general framework of the pressure -resistance games of author's paper "The evolutionary game of pressure (or interference), resistance and collaboration" (Mathematics of Operations Research), 42 (2017), no. 4, 915 - 944). An evolution of a two-level hierarchy was constructed, where a local inspector can be corrupted and is further controlled by the higher authority. Concerning a mathematical novelty, the model led to a switching generalised replicator dynamics (kinetic equations), where switching occurred on the effective frontier of corruption.

In this framework the "principle of quadratic fines" was discovered stating that the quadratic growth of the fine function allows one to effectively control the level of violations. In the talk we present these ideas together with some recent developments showing the robustness of the principle of quadratic fine by extending the model in various directions.