Quinteros, M. J., & Villena, M. J. (2022). On the Dynamics and Stability of the Crime and Punishment Game. Complexity, 2022, 2449031.
Abstract: We study the dynamics and stability of the economics of crime and punishment game from an evolutionary perspective. Specifically, we model the interaction between agents and controllers as an asymmetric game exploring the dynamics of the classic static model using a replicator dynamics equation, given exogenous levels of monitoring and criminal sanctions. The dynamics show five possible equilibria, from which three are stable. Our results show that a culture of honest agents is never stable; however when the penalty is high enough, the system will neutrally tend to an equilibrium of honest agents and a monitoring firm. By contrast, when the probability of detecting wrongdoing is small, the system, in some cases, will remain in a transient state, in which it is impossible to predict the proportion of honest agents.
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Quinteros, M. J., Villena, M. J., & Villena, M. G. (2022). An evolutionary game theoretic model of whistleblowing behaviour in organizations. IMA J. Manag. Math., 33(2), 289–314.
Abstract: We present a theoretical model of corruption in organizations. Our specific focus is the role of incentives that aim to encourage whistleblowing behaviour. Corruption is modelled as a social norm of behaviour using evolutionary game theory. In particular, the dynamics of whistleblowing behaviour is captured using the replicator dynamics equation with constant and quadratic monitoring costs. We formally explore the local asymptotic stability of the equilibria. Our findings indicate that the traditional recommendations of the Beckerian approach are usually too expensive and/or unstable. We argue that an efficient mechanism for controlling corruption can be achieved by maintaining efficient salaries and imposing high rewards for whistleblowers when they detect wrongdoing. In the long term, employees can only be honest, or corrupt, or corrupt and whistleblowers; honest and whistleblowing behaviour will not coexist in the long run, since one of these two strategies is always dominated by the other.
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