Game theory and police

Introduction
The exposure of recent U.P.Police recruitment scam as has been brought out in the print and the electronic media, has once again, stirred the deep seated anguish, apathy and frustration. It has evoked mixed response of ridicule, astonishment and shame. It is the police which have brought bad name but let us not disregard the fact that it is the same police which has unearthed the very scam. True, it is the police which have indulged in to those misdeeds but once again, it is the same police which have engineered the process of bringing those black sheep to justice. One side of the police is so frightening, but at the same time, the other side is equally comfortable and assuring. It is high time to ponder over this dichotomy; whether there are two set of police falling on two sides of the divide or police is of the same color working essentially with the same mindset though bringing out different outcome under different socio-political context?
we are what we are
Before analyzing police and its actions let us look at and think about ourselves; what we are? After all police is just a subset of the bigger set comprising of us all. We frown when we see a traffic cop extracting money from a traffic violator but when we ourselves get stuck up having violated a traffic rule, we look for an easy way out and proudly proclaim our victorious deed as to how we bribed a paltry sum to an ever greedy traffic cop. We make rules after very long deliberations and all possible considerations thinking that all the loopholes have been effectively plugged and pat our backs, but when the very rules come our own way, it is we, who again struggle to invent strategies to circumvent them. We tolerate injustice when meted out to others thinking why to bother when it does not concern us but, when we ourselves become victim, we furiously condemn the indifference of others. When our own kith and kin get recruited as a police constable or a sub inspector by questionable means, with our connivance and consent, we justify it by saying that so is the way world functions. When other fellow gets selected the same way, we vehemently protest and cry foul. We never fathom courage to champion any issue and always leave it to others to take the initiative. The others, in turn, do exactly the same, that is, leave it to someone else. So we are left with a thousand issues facing the country and no champion in sight. We always find fault with others and try to prove how others have failed in their job but when someone similarly points fingers at us, we quarrel. When police treats a suspect with third degree we make hue and cry, and rightly so, for human rights violation but, when a suspect is caught who is accused of robbing my house, and police adheres to books this time, I accuse police of soft peddling with criminals. We expect justice here and accept injustice there. In essence we are neither this nor that. We are hard core selfish, always calculative, always playing game desiring always to win at the expense of others. Imagine the plight of the referee and the game when either of the side would not accept the decision declaring opponent, a "winner". We will have allegations and counter allegations, arguments and counter arguments, statements and counter statements, then will follow spate of enquiries, commissions and recommendations to be debated further in the name of justice and fair play. Ultimately, confusion and chaos will prevail leaving the spectators totally baffled as to whether aftermath of the game was the actual game originally intended to be played or otherwise. No one would remember in the end, what the rules of the game were. Might is right or show me the face and I will show you the rule, would guide the activities in the arena. This appears to be hard ground reality. We are, just what we are.
game theory
In our day to day life, in our social interactions, in our business life, we take decisions; make moves in view of the move which the other party is likely to make. There is always the “other”. So, whenever we take a decision, in a way, we play game. It would be worthwhile to have a glance over the game theory:
Game theory can be defined as the study of how people interact and make decisions. This broad definition applies to most of the social sciences, but game theory applies mathematical models to this interaction under the assumption that each person's behavior impacts the well-being of all other participants in the game. These models are often quite simplified abstractions of real-world interactions. While many game theorists certainly enjoy playing games, a "game" is an abstract representation of many serious situations and has a serious purpose.
A major issue with game theory is that is is necessary to make assumptions. Any model of the real world must make simplifying assumptions because the real world is too messy to analyze with any precision. There is a constant tradeoff between realism and solvability. Even if one could write down a model that accurately describes how people make decisions in general, no amount of computers would be able to calculate it.
What assumptions are made normally? The most common ones are:
- rationality (people take whatever actions are likely to make them more happy - and they know what makes them happy), and
- common knowledge (we know that everyone else is trying to make himself or herself as happy as possible, potentially at our expense).
The most widely known example of game theory is probably the prisoner's dilemma: A zero-sum cooperation game that got its name from the following hypothetical situation. Suppose that the police have arrested two people whom they know have committed an armed robbery together. Unfortunately, they lack enough admissible evidence to get a jury to convict. They do, however, have enough evidence to send each prisoner away for two years for theft of the getaway car. The chief inspector now makes the following offer to each prisoner: If you will confess to the robbery, implicating your partner, and she does not also confess, then you'll go free and she'll get ten years. If you both confess, you'll each get 5 years. If neither of you confess, then you'll each get two years for the auto theft.
. The dilemma resides in the fact that each prisoner has a choice between only two options, but cannot make a good decision without knowing what the other one will do[i].

Game theory presupposes that each individual is a rational being which in turn means that each one wants to be happy and would take a decision which would yield maximum return to him and secondly, each one knows that everyone else is thinking the same way. Going back to prisoners dilemma (PD), the dilemma is as follows: if she confesses against him and he does not confess against her, she goes scot free and he lands up in jail for 10 years ,so he should confess against her , and if she is so naïve as not to confess against him and he confesses against her, he goes scot free. Being a rational being, he would like to take such a decision which would give maximum return (scot free in this case or at least she does not go scot free) so he confesses against her. She being equally rational takes a similar decision and confesses against him. As a result, both end up in jail for 10 years. This is defect – defect situation where one perceives getting immediate gain but ultimately both end up being losers. Had both kept quiet (cooperate), both would have got only 2 years.
police and prisoners dilema
As we have discussed, we are hard core selfish, so the selfishness would be main driving force for our rational decisions (yielding maximum return even at the cost of others). Common knowledge (that others are also rational) makes one insecure ( because others are also similarly motivated) and this would make every one suspicious of everyone else (others are likely to defect to derive advantage at our expense). Ultimately, it creates defect - defect situation. Loaded with such a mind set when one joins police, as a police man, he would be no different than we.
Let us examine what amounts to a return for a police man which he or she would strive to maximize. One is organizational gains which are mainly aimed at public at large and other is personal gain in terms of money as well as position and power. If policemen are driven by selfish motives, he thinks maximizing his personal gain even at the expense of organization. He isolates himself both from the organization (from where he earns his bread and butter) and the society (he is recruited to serve).

[i] Inserted from <http://www.valuebasedmanagement.net/methods_game_theory.html> & <http://plato.stanford.edu/entries/game-theory/>