Corruption is
one of the most talked about topics today.
This article attempts to connect game theory to corruption and tries to
theorize what the market structure, demand and supply of corruption would
possibly be.
The effectiveness of the bribing system now depends on
the elasticity of demand. If the demand
is very elastic, there will be very huge decrease in the quantity demand when
the price increases and if the demand is inelastic, there will be a very small
decrease in the quantity demanded.
What about the long run? What would happen if we simulate the scenario millions of times? Would the same condition prevail? This, in game theory is known as the iterative prisoner’s dilemma. The goal here is to find out the optimal strategy in the long run.
I did no actively record every article/paper I read. However, I took a few ideas from some of the background reading I did for the article:
What some people
miss is the fact that we may very well be the root for all corruption.
When I say that
we are the root of all corruption, I am not blaming us. I am just merely stating that we took the most rational decision with the information we had at that point. Be it bribing a policeman to get
out of going to court or bribing a peon to skip a line, we as individuals are
trying to act in self interest and try to maximize our utility over the
society’s. The amount of money we can
save and the time we would have spent in court is the additional utility we
gain from bribing a policeman while the amount of time we gain by not standing
in line is the utility gained by bribing the peon.The loss to the exchequer due
to the fines not reaching the government in case 1 and the loss of time to
other people because you cut the line in case 2 is what the society in general
would have gained from us not acting in our own self-interest. Society, of course, has a different meaning in
each context.
This post is to
try and analyze how close this statement is to the truth. This post will not analyze how to reduce corruption;
rather, I will try to put forth a theory on the market structure of
corruption. Kindly note that this is my conjecture
(I have not found literature on this…I am searching for literature as we speak)
and is subject to inaccuracies (after all, I am an amateur economist). The theory is based on an interpretation of
what I have read till now and what I have experienced in India.
Read on …
Game theory and Nash Equilibrium:
In order to
understand the next portion of the article (you will have to bear with me
here), it is vital to understand the concept of Game theory and Nash
Equilibrium in Economics (People who know the theory can skip this section).
Let us assume
that you and I are accomplices in a crime.
We get caught and the police are holding us in two separate rooms. We do not know each other (this was a black
bag job apparently) and currently face the following (this scenario is known as
a Faustian Bargain):
Scenario A: Both of
us deny the charges. We both get 1 year
each in jail
Scenario B: One of
us denies and the other confesses. The
one who confesses is released and the one who denies the charges gets 10 years
in Jail
Scenario C: Both of
us confess. We both get 3 years each in
Jail
What is the
optimal strategy that we can follow here?
Clearly, the
strategy that has the maximum utility (otherwise read as combined minimum jail
time) is scenario A (we both deny the charges, we both get a year in
jail). However, all rational individuals
(who generally consider only self-interest) in situations such as this would
betray each other even though the most optimal solution here would be to
co-operate.
Nash Equilibrium
basically explains that in such a scenario, it is in the best interest for an
individual to take a decision after taking
into account the other person’s decision.
Thus, the Nash equilibrium for this situation would be for us to betray
each other.
How does this connect with Corruption in our
country?
As I mentioned
earlier, we are always trying to act in ways that maximize our own
self-interest by doing what we deem as the most rational decision. When we make the decision, we are also taking
the decision made by other players. When
we decide to bribe the policeman, we assuage ourselves by saying “so many
people have done this. I am not the
first” and decide that this is the
most rational decision and bribe the policeman.
When a
politician comes to our homes and asks for votes (by giving us money), we assume that other people have also
accepted the money and take it. In every
scenario where we are offering bribes, we are involuntarily taking into account
the decision of the society in general and accepting that this is the most rational decision that we can take. In each scenario, we are not taking the decision
that would give the society maximum benefit.
The supply and demand for corruption in the short
run(From hereon in, these are my thoughts and hence, there is a chance I could
be wrong. Please read with a pinch of
salt (which incidentally is really costly if you live in Bihar or the
North-east for now):
I spent a huge
amount of time thinking on the market for corruption. What do we mean by market here? What is the definition of demand and
supply? Are we suppliers because we shell
out money and are the officials consumers because they accept the money? Or are we consumers because we pay for a
special service from the supplier of that service? The latter makes more sense as we can now say
that bribes are a premium that we pay when we want a service from an
official. The market here is the market for giving and accepting a bribe for a service. The service is not the commodity in question here. The act of giving the bribe and the act of receiving it is the "commodity". Thus, the demand for the commodity is the affinity of a person to give bribes and the supply for the commodity is the affinity of an agent to accept bribes.
Thus, as a
consumer, your decision to “buy” the service (bribe the official) will now be
dependent on the total price (total price = price of service + additional
bribe). However, the decision is also
subject to a variety of other factors now.
Factors such as the amount of time (which would determine whether we
want to give the bribe) would now come into play as well. For the sake of simplicity, let us assume
that we will take a binary decision (to either pay for the service with the
bribe or not take it at all).
The more
interesting question is how the market structure for corruption would be
like. Would it be like a free market
(where the price a.k.a. Bribe would be determined by the invisible hand of the
market)? Would it be like a monopoly (where
the official a.k.a. supplier sets the price and we as consumers become price
takers?
From my point of
view, a monopoly seems to make more sense.
Though there are a huge number of potential people who supply services
for bribes (similar to a free market), the actual number of people who are
responsible for a service is one person (if you want a license in a particular
location, you have to bribe one RTO official. Similarly, if you get caught by the traffic
police on the road, you have to bribe one
policeman (or a group of policmen acting as one unit) to get out of a ticket).
In the
explanations going forward, price is a function of many parameters (of which
time spent doing an activity/service and money spent on that service are
factors). Let us say call this as
“utility” (for lack of a better term).
The quantity demanded/supplied will be the number of people willing to
pay this “utility” and the number of people that the agent can service in a
given time period.
Thus, the
supplier/agent is now offering the service (the service of priority treatment
for accepting a birbe) at an increased utility/price (to the individual, this
means paying a premium to reduce the amount of time taken to get the service
done while to the agent, it means an increase in his monetary capacity).
People will have
a threshold for the amount of bribe that they are willing to pay. For instance, my limit to bribe a policeman
might by Rs. 100 but yours might be Rs. 150.
Thus, the “demand” for giving into bribes should be a typical demand
curve.
Let us now come
to the costs associated (to the person accepting the bribe). The cost here would be the cost that is
associated with the agent getting caught by the authorities. This is, again, a function of a lot of
factors (including but not limited to government intervention, tolerance towards
corruption and the person’s risk appetite).
For a risk
loving person, the marginal cost (the cost incurred in accepting a bribe from
an extra person) would be lesser than that of a risk averse person (who would
get scared about taking excessive bribes).
Thus, the demand and supply curves for this scenario would represent
something similar to this. This made most logical sense to me. A risk averse person will be willing to accept bribes from multiple people while a risk loving agent will be willing to accept bribes from fewer people. The risk aversion here is caused due to the fear of getting caught.
What I infer
from this is that the elasticity of demand can now be used as a proxy to measure our tolerance to corruption. The advent of
corruption in the sale of a good or service will shift the elasticity of demand (depending
on the necessity of the product). If we,
as a society are intolerant towards corruption, the demand becomes
more elastic (as more people choose not to go against their wishes) while if we
become tolerant to corruption, the demand stays the same (if not becoming more
inelastic due to us valuing our convenience over the society’s loss in utility).
In the short run
therefore, what I am trying to say here is that corruption is a bigger problem
than we have previously debated, especially in a country like India where it has penetrated to the grass root level. Policy
changes and stricter laws on government officials can have only so much effect
on curbing corruption. The time taken for policies against corruption to trickle down to the grass root level, in my opinion, is an important factor that needs to be considered (a long trickle time will ultimately end up in the grass root (us) corrupting the top (government officials). There needs to be
an enactment to curb corruption from both the supply and the demand side of the
corruption spectrum. A new government at
the center might not necessarily ensure the curbing of corruption
overnight. At the end of the day, it
needs a combined effort of the government (to enact accurate policies), the
judiciary (to monitor the policies effectively) and the citizens (the most
crucial cog in the wheel – The group that acts to maximize social utility) to
reduce and eradicate corruptionby becoming more intolerant towards it.
Long run Ramifications:
What we
discussed till now here all in the short run.
We have, till now assumed that the corruption has trickled down to the
grass-root level and therefore, the Nash equilibrium here would be to
effectively give in to bribing.
What about the long run? What would happen if we simulate the scenario millions of times? Would the same condition prevail? This, in game theory is known as the iterative prisoner’s dilemma. The goal here is to find out the optimal strategy in the long run.
Would the entry
of clean agents into the market (change of government/enforcement of strict
government policies) shift the nash equilibrium to a cleaner system? This simulation will help us understand the
effect that the grass-root has on the top and vice versa.
I will discuss
the modelling of various strategies in the next post! J
References:
I did no actively record every article/paper I read. However, I took a few ideas from some of the background reading I did for the article:
1. Corruption - Supply Side and Demand Side solutions By Avinash Dixit (Princeton University)
3. Underdevelopment and the Economics of Corruption - A Game Theory approach by John Macrae
4. The Economics of Corruption - By Susan Rose-Ackerman
Acknowledgements:
I would like to thank the following people for taking time out of their busy schedules to help me:
1. Dr. Amarnath Ananthanaraynan (For guiding me on the concepts of Nash equilibrium and explaining his prior work)
2. Aravind Krishnan and Ananthapadmanabhan Ramkumar (for proof reading)
3. Padma Goda - For all the above :)
