ИСТИНА

The games of inspection and corruption are well developed in the game-theoretic literature. However, there are only a few publications that approach these problems from the evolutionary point of view. In previous papers of the author a generalization of the replicator dynamics of the evolutionary game theory was suggested for the inspection modeling, namely the pressure and resistance framework, where a large pool of small players is playing against a distinguished major player and evolving according to certain myopic rules. Here we develop this approach further in a setting of the two-level hierarchy, where a local inspector can be corrupted and is further controlled by the higher authority. Mathematical novelty arising in this investigation involves the analysis of the generalized replicator dynamics (or kinetic equation) with switching, which occurs on the 'efficient frontier of corruption'. We prove a result that can be called the 'principle of quadratic fines': We show that if the fine for violations (both for criminal businesses and corrupted inspectors) is proportional to the level of violations, the stable rest points of the dynamics support the maximal possible level of both corruption and violation. The situation changes if a convex fine is introduced. In particular starting from the quadratic growth of the fine function one can effectively control the level of violations.