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ABSTRACT: This article analyses corruption policy through  game theory analysis of the choices of two players, the briber and the bribee. It finds that public policy initiatives of harsh penalties to deter corruption are not sufficient. These rely on decision theory and have empirically shown to have failed. Through  game theory analysis, this article suggests the direction policy to deter and punish corruption to take. 


All the world’s a stage,

And all the men and women merely players

November 8, 2016 saw the demonetization announcement by the NDA government in India, which was done to eliminate black money, lower cash circulation in the country and curb the rising corruption.   According to the estimates of the World Bank, 1 Trillion US Dollars are paid worldwide in bribes. Estimates in Kenya suggest that out of 10 interactions with public officials, 8 require bribes and that the average Kenyan pays bribes 16 times a month. Denmark in contrast has the lowest level of corruption and an average Dane may never have to pay a bribe. Corruption is present all over the world and as an economic phenomenon is symptomatic of rational behaviour and choices of people in society.  

Corruption is defined by the World Bank as “the abuse of public officers for private gain”.   It has an immense detrimental effect on the economy. It affects investment, development and growth in the economy. Income distribution is adversely affected, and public resources are put to unproductive use. There are deadweight costs of corruption that cause entrepreneurs to pay huge sums of money towards bribes that cause them to give up profitable investments. Corruption has costs and  negative externalities such as lowered legitimacy of the government, implicit tax, red tape etc. The costs of corruption are immensely heavy, be it reduction in anti-poverty programmes or deaths because of collapsed buildings. Corruption is also risky because it is not legally enforceable. There is no guarantee of service or good and there is even the chance of blackmail after the transaction. 

Finding a solution to corruption has led to academics searching for the cause. One explanation for corruption is the Rational Choice Theory, i.e. an individual making a rational decision leading to a predetermined outcome. Central to this theory, is the individual corrupt official who aims to maximise his or her utility. This is premised on the simple logic that the perceived potential benefits exceed the potential costs of corruption. The consequences of this theory are that anti-corruption regulations try to make sure that the benefits of corruption are minimised. By increasing the chances of getting caught and imposing harder penalties, the costs can, therefore, be increased. But just solely imposing harder penalties have often not given the desired results. 

Moving from a micro level of corrupt agents to a more meso level of organisations, there is the ‘Organizational Culture Theory’. This theory propounds that it is public machinery, and not faulty agents that lead to corruption. It talks about a certain group culture, that leads to a certain mental state of individuals. This takes into consideration social context. The argument is that group behaviour rooted in extreme practices and established arrangements embedded within structures and cultures of organisations explain the culture of corruption. Other theories are for example, the ‘Bad Apple Theory’ which blames the few people who do it for being immoral and the ‘Clashing Moral Values Theory’ that says that corruption is natural and just how society works. Public policy efforts made as a consequence of these theories have not worked. Following is a game theoretical analysis of corruption, with further explanation of the Nash Equilibrium and the implications of the result of such analysis on public policy.

A bribe is a result of players choosing optimal strategies. In the game, there are two players, A and B. A is the public officer who is the bribee and B is the company/entrepreneur who is the briber. The following are the variables used in the analysis;

  1. a is the bribe amount, the payoff for accepting bribe
  2. b is the psychological and moral security which the bribee gets by not accepting the bribe, or being honest 
  3. c is the additional revenue that B gets more than competition because of giving the bribe
  4. d is the psychological effect, moral consequences and material risks of the bribe
  5. e is the cost to B if B bribes A and A doesn’t take the bribe

If then, B goes through legitimate ways of procuring from the public officer, without the bribe, then d and c will be zero for B. Both players want to maximise their own utility. When Player B attempts to bribe Player A, Payer A has two choices, either accept the bribe or decline it. If A chooses not to take the bribe, he gets psychological and moral satisfaction, b. If A chooses to accept the bribe, there is the bribe amount a that A receives, but there is also the insecurity as a result of accepting the bribe -b. In the former, Player B gets c, the additional revenue earned due to the bribe and –d, because of the negative consequences of taking the bribe; and in the latter e, the costs incurred because A refused the bribe which are for example, the risk of being revealed or the costs incurred in getting the bribe ready and attempting to bribe A like transportation, time wasted on it etc. If neither Player A nor Player B attempt the bribe, there is zero utility for both of them. If Player A wants the bribe, but Player B makes no attempt to give one, then there again there is zero utility for both of them. This is seen in the game matrix below.                                                                                                                                                         


                           Player A

            No Bribery

Payer B             

(c-d, a-b)

(-e, b)

No Bribery

(0, 0)

(0, 0)

a, b, c and d have to be greater than 0 because both players want the greatest utility available.  If B does take the bribe, B will only take it in a circumstance where c > d.  In the current circumstance, the pay-off from ‘bribery’ is greatest for A, a-b> b and 0=0 whether Player B chooses ‘Bribery’ or ‘No Bribery’. For B, the pure strategy ‘bribery’ is better because c – d> 0 and 0=0. Thus, the dominant strategy is ‘Bribery’. The Nash Equilibrium of this game, therefore is (bribery, bribery). This Pareto optimal solution leads to corruption. The above game leaves us with the observation that players choose (bribery, bribery) when a>2b and c>d. Their benefits are much higher than the costs in this particular analysis. While this is a cost-benefit analysis based on rational players, it is not strictly the Rational Choice Theory because the results of this game theoretical analysis give us the exact markers that will allow change in the dominant strategy and the behaviour of both players is taken into consideration. Basically, for A, the pay-off that A receives a, has to be greater than two times security received from not taking the bribe b. And d has to be greater than c, i.e. the risks and costs of giving a bribe have to be more than the additional revenue received for players not to choose the strategy (bribery, bribery).  

Imposing strict penalties for corruption, or increasing the cost and risk of corruption is a method that has been used worldwide. China has a wide range of rules and regulations covering an extensive range of corrupt activities. China even imposed the death penalty for criminals who are convicted of corruption. However, empirical evidence suggests that due to harsher penalties the corruption has only grown more sophisticated and involves larger amounts. The rule of law has failed in deterring corruption. In most Western countries like Mexico and the USA, fines are imposed on those caught being corrupt. In the USA, fines and imprisonment are forms of punishment. Problems with harsher punishments range from ineffective law enforcement, loose implementation of policies and corrupt officials imposing anti-corruption measures.

A similar situation is spoken about by Tsebelis in his classic 1989 essay, The Abuse of Probability in Political Analysis: The Robinson Crusoe Fallacy. The method of deterrence treats the crisis of corruption like one of decision theory and not one of game theory. This is a Robinson Crusoe Fallacy. What’s important to remember is that both the parties involved are rational and intelligent agents who can change their behaviour. While people respond to incentives, those who create and enforce these incentives also respond to changes. Thus, the people who enforce the harsh punishments also respond to the change and change their behaviour. This could give rise to a Principal-Agent problem. The agent,  here the enforcers of the harsh penalties, will ignore the interests of the principal  (the government) leading to moral hazard and conflict of interest. There is a need to overcome the fallacy of applying decision theory for what is essentially game theory i.e. the Robinson Crusoe Fallacy.  This can be done by linking the pay-offs of the officials in charge of the enforcement with the punishment, so they don’t defect and work against the interests of the government. The incentives of the officials who are enforcing the anti-corruption rules need to be increased. This will also increase their determination to achieve a corruption free society. The premise of the Principal-Agent problem is information asymmetry. Therefore, another effective public policy solution can be transparency. Research suggests that larger access to information causes lower corruption levels across nations. If increasing the risk and costs of the bribe does not work, the game theoretical analysis tells us that public policy must increase the reward of the person who takes the bribe because all that is required for the players to not choose the dominant strategy is defection by one player, which would be, in this case, the bribe-taker if sufficient incentives are given. 

Corruption is not a contemporary phenomenon. Some form of it has existed since time immemorial. Enlightenment thinkers have historically taken different views on corruption. Adam Ferguson and other classical authors like Rousseau and Montesquieu conceived corruption as a problem of virtue. Similar to Machiavelli who saw it as a ‘deterioration in the quality of the government’. Adam Smith, on the other hand, saw any interference with the market, what he saw as the natural and spontaneous order of nature, to be corrupt. He condemned poor laws, restrictions on trade, corporation privileges and other such regulations as a violation of people’s natural rights. Even though Smith saw this as a result of commercialisation, he saw commercialisation as inevitable, natural and positive. He, in fact, saw privatisation, civic quiescence and breakdown of social categories as solutions to the corrupt state. As the world develops, so do corruption practices and methods. What also develops however, are the methods of analysis and study that can be used to curb corruption. One of them being, game theory. 

Muskan Tibrewala is a fourth year law student at Jindal Global Law School.


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