Abstract
A simple model of corruption that takes into account the effect of the interaction of a large number of agents by both rational decision making and myopic behavior is developed. Its stationary version turns out to be a rare example of an exactly solvable model of mean-field-game type. The results show clearly how the presence of interaction (including social norms) influences the spread of corruption by creating certain phase transition from one to three equilibria.
Highlights
Analysis of the spread of corruption in bureaucracy is a well-recognized area of the application of game theory, which attracted attention of many researchers
A model we introduce is an instance of the finite state space mean-field games of [15,16]
We shall say that in a solution to the stationary MFG consistency problem the optimal individual behavior is corruption if uC = 0, u H = 1: If you are corrupt stay corrupt, and if you are honest, start corrupted behavior as soon as possible; the optimal individual behavior is honesty if uC = 1, u H = 0: If you are honest stay honest, and if you are involved in corruption try to clean yourself from corruption as soon as possible
Summary
Analysis of the spread of corruption in bureaucracy is a well-recognized area of the application of game theory, which attracted attention of many researchers. We develop a concrete mean-field-game model with a finite state space of individual players describing the distribution of corrupted and honest agents under the pressure of both an incorruptible governmental representative (often referred to, in the literature, as ‘benevolent principal’; see, e.g., [2]) and the ‘social norms’ of the society.
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