Game of Theories: A Policy of Bribery and Punishment

Theoretical study suggests that encouraging complaints from citizens may be the most effective way of reducing incidents of bribery



Data analysis is critical for the formation of any robust policy. But reliable data in economics is not always available, since unlike in the natural sciences, controlled experiments at the population level are not possible.  Moreover, present data may not have sufficient predictive power, since population behavior changes over time. Economists use theoretical models to account for variables and parameters to predict end-results in such situations. These models can serve as prototype systems on which to test the possible consequences of a new policy.

In this particular study, the authors use evolutionary game theory to approach bribery, a prevalent problem in may societies.

What is Game Theory?

Economics, broadly defined, is the science of human behavior. And much like in the natural sciences, economists look for “bottom-up” explanations of phenomena, where simple underlying rules give rise to complex behavior. The rules generally take the form of mathematical equations, the solutions to which are expected to capture (and predict) the essential features of social dynamics.

A central theory which has proved useful is game theory. A more accurate name for it is “multi-person decision theory” – because that’s exactly what it is. It deals with situations where multiple players engage with each other, each armed with a repertoire of possible strategies, and the outcome (or “payoff”, as it is called) for each player depends on the strategy adopted by all the players.  The aim of each player is to choose the strategy that maximizes her payoff. As you can see, the theory potentially covers a very broad range of human interactions, and thus the widespread application of game theory in economics is hardly surprising.

But how do we adopt and revise our strategies over time? A set of perfectly rational beings with complete information would quickly reach a unique equilibrium situation (provided such a situation is allowed by the dynamics of the game). But in the real world, people are neither perfect computing machines, nor do they have perfect information. So the strategies we use, and the way we update them with further experience, depends a lot on the context.

What game does this article study?

The study employs different players and their corresponding strategies; an honest officer, a bribe-taking officer, an honest citizen, a bribe-paying citizen who doesn’t report on the crime, and a bribe-paying citizen who reports on the crime. The advantage to reporting, of course, is that you have a chance of getting your bribe refunded. These players (citizens and officers) interact at random and such interactions can potentially involve a corrupt transaction (depending on the strategies of the interacting players) leading to payment of a bribe. Like Kaushik Basu, the authors focus on the problem of harassment bribes. These are bribes paid by citizens to corrupt officers for getting access to a service they are legally entitled to (such as acquiring a passport or getting a driver’s license)

The authors also consider two different ways in which the citizens and officers may update their strategies over time. First is the Replicator model, where an officer or citizen randomly chooses a fellow officer or citizen, and tends to imitate their strategy if they have been more successful. In the second scenario, called the Alternative Strategy Exploration model, they first make their moves and receive their payoffs, then consider whether the possible alternatives may have given them a higher payoff, and if so, update their strategies accordingly. In both the cases, it is found that the population finally reaches a fixed frequency distribution of the various strategies.

What is the question?

The authors consider two major punishment models:

1. Symmetric punishment, where both bribe taker and bribe giver are punished

2. Asymmetric punishment, where only the bribe taker is punished.

In fact, a major motivating point for the study was the claim by economist Kaushik Basu that bribe-giving, as opposed to bribe-taking, should be legalized for harassment bribes, as this would increase the frequency of complaints and help bring down bribery.

The authors numerically simulate the evolution of strategies under both kind of punishment models to find out which might be better in curbing bribery incidents. They further analyze conditions under which a decrease in incidents of harassment bribery might be possible.

What do they find?

Contrary to the claims by Basu, they find that the effect of asymmetric punishment depends on the update strategies used by the players, and cannot be considered a universal solution. Lowering the cost of complaint, however, seems to work under both the asymmetric and symmetric punishment models. However, the extent of bribery reduction depends on other parameters as well.

What are the conclusions?

Bribery is a very complex and dynamic issue. While there can be no single way to get rid of it, the authors suggest that bringing down the cost of complaint to negligible might be important in an overall reduction in incidents of bribery, irrespective of the punishment model. On the other hand, what happens under more complicated updated strategies is still an open question. As the authors say in their article, “It would perhaps be more pragmatic to look at a combination of technological fixes and public policies targeting the myriad underlying causes of bribery in order to effect reduction in bribery and ease the toll it takes on public finances.”

It is interesting to note that even in relatively idealized economic models, a simple and universal solution may prove to be elusive. This should make us more skeptical of quick fixes suggested by policy leaders that seem to make intuitive sense, and look for solutions that are customized to individual scenarios.


Bribe and Punishment: An Evolutionary Game-Theoretic Analysis of Bribery,Prateek Verma, Supratim Sengupta, PLoS One. 2015 Jul 23;10(7):e0133441.

An interview with Dr. Supratim Sengupta

Q. Basu (2011) had submitted a report to the Government to inform on policy for bribery punishment. Why did you choose to study this report using game theory and which facets of this report have your study addressed in more depth?

When this report came out, a literature search revealed that there was practically no quantitative analysis of the issues raised and claims made in the report. The principle claim was that incidents of harassment bribery could be substantially reduced if only the bribe-taker but not the bribe-giver was penalized for the crime. It was also evident to us that the problem was ideally suited to be analyzed using evolutionary game theory since it presented a very well-defined scenario of social conflict with mutually exclusive interests of the principle parties (bribe-giver and bribe-taker) involved. Our main objective was to quantitatively examine in great detail the principle claim of Basu’s report (mentioned above) and understand how reduction in incidents of bribery depend on factors like the amount of bribe demanded, the cost of complaining about a bribery incident, the penalty to a bribe-taker if caught. We also examined how the manner in which individuals updates their strategies in response to a bribery incident affect the prevalence of bribery in the population. None of these aspects had been examined in such detail using the framework of evolutionary game theory and our work (carried out with my PhD student Prateek Verma) is the first to do so.

Q. Your models indicate that low cost of complaint may eradicate bribery. In countries with low bribery, are there platforms which make registering complaints easier?

Yes, most western European countries and places like USA, Canada etc., have efficient grievance redressal systems and harassment bribes are practically non-existent for basic services provided by the government. Even in India, a website called started by an NGO in Bangalore has made it easy to report incidents of bribery and bring grievances to the notice of public officials. Such steps have led to positive outcomes which suggest that reducing the cost of reporting bribery incidents and establishing an efficient grievance redressal system by using technology can be quite helpful. If there is one policy proposal that we could advocate to reduce incidents of bribery, it would be this.

Q. Countries with low corruption indices seem to have a higher national income and lower inequality. But these factors do not seem to be explicitly incorporated in your model. Would you like to comment on that?

Bribery is a multi-faceted social problem and has many underlying causes including (but not restricted to) high levels of income inequality, as you have pointed out. However it is quite difficult to quantify the impact of such income inequality on the problem of harassment bribes. We took into consideration the most relevant factors that directly affect harassment bribery and that could be incorporated into a tractable mathematical model that would enable us to obtain insights into the problem and identify steps that can be taken to reduce such incidents of bribery.

Q. Why did you choose the two strategies: Replicator dynamics and alternative strategies dynamics for the study? What other scenarios might have been considered?

We wanted to highlight the difference in outcome when individuals choose two completely different methods to update their strategies over the course of time. We found that in the alternative strategy exploration case, the reduction in incidents of bribery was far less pronounced even when we followed Kaushik Basu’s proposal. However, these two methods are not the only ways individuals can choose to update their strategies and hence the outcome would indeed depend on the method followed. For instance, different individuals in the population could choose different methods to update their strategies and that would affect the outcome.

Q. Since collecting bribery data is difficult due to the secretive nature of the phenomenon, how do we check if some bribery-related policy has worked?

Collecting bribery data may not be as difficult as it seems. The government can ask citizens to fill out a simple questionnaire given by the service provider to report incidents of bribery. For example, the regional passport office can ask citizens applying for a passport to submit their feedback online by filling out an online questionnaire at the end of the process. Statistics based on such documents can be a very useful indicator of the prevailing levels of bribery in different services. It would also provide clues on how to allocate resources to reduce incidents of bribery in different services provided by the government.

Q. Do you expect your study or other related studies to have an impact on government policy?

It is difficult to predict whether any study of this kind will impact public policy. This is a topic of great public interest and Kaushik Basu’s original proposal certainly garnered a lot of attention. But that was in no small measure due to the important position he held at that time (Chief Economic Advisor to the PM) as well as his influence as a well-known economist. However, many (but not all) of the responses to that article in the press at that time were simplistic, knee-jerk reactions. Moreover, they were not grounded on objective analysis. We hope our work along with those of others have contributed towards a critical analysis and will at least rekindle the debate and stimulate new proposals on how to reduce harassment bribery. Despite the controversial nature of the proposal, we believe there are concrete and simple steps that can be taken that may have an impact. As I mentioned in my previous response, using web-based technology to streamline access to services, gather critical feedback and reduce the cost of complaining can definitely have a positive impact. However, we also acknowledge that technological fixes alone cannot and will not get rid of such a complex social problem that is definitely affected by income-inequality, the efficiency of the public justice system etc.

Q. In general, how much do you think game theory models accurately capture real world dynamics?

Evolutionary game theory is employed when the effectiveness of a strategy depends on the presence of other competing strategies in the population. It relies on specifying the net gain or loss (referred to as “payoffs”) to each strategy when it interacts with different strategies. It is very useful in analyzing how the number of individuals employing different strategies change over time and the conditions under which a specific strategy can out-compete all other strategies and take over the population. Unlike conventional game theory used by economists, which is involved only in finding equilibrium solutions (the so-called Nash equilibrium), evolutionary game theory allows us to see how the population gradually progresses towards an equilibrium state by tracking the change in number of individuals employing different strategies over time. The usefulness of evolutionary game theory in accurately capturing real world scenarios depends on the question being asked. There have been some criticisms (valid in my opinion) of using game theory to understand how cooperative behavior can spread or be sustained among groups of individuals. Experiments have revealed that people have an intrinsic tendency to cooperate more than game theoretic analysis predicts, despite cooperation being costly. In such scenarios, it is necessary to be cautious in drawing conclusions based on game theory. However, in the current scenario, such concerns do not apply since the primary interests of the principle players are at cross-purposes. We therefore feel that evolutionary game theory is well suited to accurately address the bribery problem. Nevertheless, some words of caution are in order. Our models employ quantities like the prosecution rate and penalty when prosecuted to understand the effects of punishment and its deterrence on bribery. In reality, these depend on the efficiency and integrity of the public grievance redressal systems and justice systems. These can vary a lot not just across countries but also across jurisdictions within the same country. These factors need to be given serious consideration before framing any public policy dealing with bribery.

Q. What do you think is the role of theory in economics, in general terms? I come from a background in theoretical physics (says Jabali) and now work in biology. And I and others like me sometimes wonder about whether we are making the right kind of assumptions in our models, or whether the phenomena we are describing are really reducible to a mathematical description, given the current state of knowledge. Does a theoretical study in economics contain the same kind of concerns? Or is the picture there very different?

You raise a very pertinent point here that I will not be able to satisfactorily address. I am not an economist by training. Like you, I am a theoretical physicist interested in analyzing complex social and biological systems using quantitative tools inspired by Physics and Mathematics. I am therefore not qualified to comment about the real-world relevance and drawbacks of theoretical models in Economics in general. However, the concerns you raise are surely relevant to studies of this kind and any honest scientist/economist needs to ponder about them. These concerns certainly informed our formulation of the problem and we tried to make the model as realistic as possible. But we also admit that some simplification was inevitable and we could not incorporate every single factor (like income-inequality for example) that may play a role in the prevalence of harassment bribes. Sometimes, even the factors incorporated, like prosecution rate, penalty for taking bribes etc. may not reveal the true complexity of the real world problem where such quantities depend on the efficiency and integrity of the police and justice systems. In some cases, the simplifications (like our assumption of a mixed population) can be addressed by studying the effects of a structured population of citizens and officers, as we are currently doing in an ongoing work (with Prateek Verma and Anjan Nandi) which is being written up. It is therefore important to acknowledge the potential consequences of the underlying assumptions and the associated simplifications while proposing new public policy based on such studies. It is also important for us (the community of social and natural scientists) to continue to strive to develop more realistic models by improving on existing ones whenever possible. Finally, I believe it is necessary for policy makers to pay attention to such studies and start a dialogue with social scientists to critically examine the consequences of such studies on public policy.