The Evolution of Corruption

Game theory concerns the rational choice of strategy, in order to maximise utility, for individuals playing a well defined game against some opponents. A well informed and rational agent will choose the best response to play against an opponent; this is the choice that will maximise the agent’s utility in light of the opponent’s most rational choice. Invariably this will lead to the Nash equilibrium.

Evolutionary game theory instead concerns large populations of agents engaging in a game with strategies that are in a constant state of change. Now agents change their strategies based on imitation of agents playing other strategies with higher payoffs. The key difference is that the agents do not consider how changing their own choice will affect the 'fitness landscape'; the agents blindly copy other agents who received a payoff higher than them, even if it will lead to a lower payoff when they adopt the same strategy. This is in contrast to the idea of a best response as above.

Public Goods Games (PGGs) are a simple abstract representation of a common societal contract. Specifically, a number of players contribute some amount of money into a central pot. Some benevolent central authority, then multiplies the contributions and returns the inflated amount to the participants equally.

PGGs are abstractions of a society where the participants are citizens, the payments are taxes, the benevolent authority is a government and the inflated reward is some public service procured at good value by virtue of an economy of scale. However, in the absence of any further intervention, each player can maximise her own wealth by not contributing her share but benefiting from her share of everyone else's contributions. The logical outcome is that all players seek to 'free-ride' all others and no player contributes. This is known as theTragedy of the Commons

Sigmund et al investigated how to encourage cooperation by introducing agents who punish other agents who attempt to free-ride. Punishers of two types exist; those who 'outsource' punishment to a central punishing authority by simply paying a tax ('pool punishers') and those who pay a personal cost to inflict punishment directly ('peer punishers'). However, the temptation to free-ride on the peer punishers remains; leave it to someone else to do the costly punishment. Therefore, centralised pool-punishment emerges as the most stable means to maintain cooperation.

Yet this route to cooperation is susceptible, as with most centralised processes, to corruption. Introducing agents who are able to 'pay-off' the police by making a small payment to avoid the compulsory tax causes cooperation to break down again. However, the presence of a new type of 'hybrid' agent who can both participate in the centralised or state-sanctioned punishment as well as individual peer-punishment can keep the corrupt players in check.

Philip Ball (author of the excellent Critical Mass) described this in his excellent piece for Nature: Who should pay for the police. A tutorial in Python that I developed for a graduate level class in simulation explains the methods behind this in more depth. The Python code used to produce the results in this paper can be found on GitHub.