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.

This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels.

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.