One of my friends suggested that "only common man will have to improve and refrain from paying bribe to anybody. If one common man is already honest, he should try to influence others to be honest and that's it. Just by doing so will take care of the whole problem of corruption. No need of any special law."
We were not sure why this does not work in a social context. So, I kinda did this analysis to find out what really happens. I welcome your suggestions and comments. Please read the detailed analysis below:
Game theory application to bribing scenario
Lets say two peace loving common men(Common Man 1 - CM1 and Common Man 2 - CM2) are there in a society. They have their own businesses.
We were not sure why this does not work in a social context. So, I kinda did this analysis to find out what really happens. I welcome your suggestions and comments. Please read the detailed analysis below:
Game theory application to bribing scenario
Lets say two peace loving common men(Common Man 1 - CM1 and Common Man 2 - CM2) are there in a society. They have their own businesses.
If both of them pay bribe to the government, they both make a profit of 
10 as shown in red below.
10 as shown in red below.If CM1 pays bribe to the government, and CM2 does not, then CM1 makes 30 profit and CM2 loses the deal and hence goes in a loss of 5.
30 profit and CM2 loses the deal and hence goes in a loss of 5.If CM1 does not pay bribe to the government, and CM2 pays, then CM2 makes 30 profit and CM1 loses the deal and hence goes in a loss of 5.
30 profit and CM1 loses the deal and hence goes in a loss of 5.If both of them do not pay bribe to the government, they both save the bribe money and make a total profit of 13 as shown in green below.
13 as shown in green below.| Common Man 2 | |||
|---|---|---|---|
| Pay Bribe | Don't Pay Bribe | ||
| Common Man 1 | Pay Bribe | 10, 10 | 30, -5 |
| Don't Pay Bribe | -5, 30 | 13, 13 | |
The nature of the game can be summarized as follows.
It is an infinitely repeated game with no known final period (and thus no end-of-period problem)
Two strategies are available to each man, “Don’t Pay Bribe” and “Pay Bribe”.
Dominant Strategy: The dominant strategy for both men is “Pay Bribe”. To see this, note that
- For CM1,
- If CM2 chooses “Pay Bribe”, the best choice by CM1 is “Pay Bribe”. That way he ensures that he earns at least 10 profit rather than losing 5.
- If CM2 chooses “Don’t Pay Bribe”, the best choice by CM1 is “Pay Bribe”. That way he ensures that he gets the total profit of 30.
- In other words, regardless of whether CM2’s strategy is “Pay Bribe” or “Don’t Pay Bribe”, the best choice by CM1 is “Pay Bribe”. Hence, “Pay Bribe” is Dominant strategy for CM1.
- For CM2,
- If CM1 chooses “Pay Bribe”, the best choice by CM2 is “Pay Bribe”. That way he ensures that he earns at least 10 profit rather than losing 5.
- If CM1 chooses “Don’t Pay Bribe”, the best choice by CM2 is “Pay Bribe”. That way he ensures that he gets the total profit of 30.
- In other words, regardless of whether CM1’s strategy is “Pay Bribe” or “Don’t Pay Bribe”, the best choice by CM2 is “Pay Bribe”. Hence, “Pay Bribe” is Dominant strategy for CM2.
Nash Equilibrium: The Nash equilibrium would be “Pay Bribe”-”Pay Bribe”. Since both men have the dominant strategy of “Pay Bribe”, it is obvious that the Nash Equilibrium is in the “Pay Bribe”-”Pay Bribe” quadrant when both men earn a profit of 10. To prove this,
10. To prove this,- While in “Pay Bribe”-”Pay Bribe” quarter, CM1 can not improve his profit given CM2 is in “Pay Bribe” (vertical) column. The only two options for CM1 in “Pay Bribe”(vertical) column is 10 profit(by being in “Pay Bribe”) or 5 loss(by being in “Don’t Pay Bribe”). Hence CM1 will have to stay in “Pay Bribe” to earn profit.
- While in “Pay Bribe”-”Pay Bribe” quarter, CM2 can not improve its profit given CM1 is in “Pay Bribe” (horizontal) row. The only two options for CM2 in “Pay Bribe”(horizontal) row is 10 profit(by being in “Pay Bribe”) or 5 loss(by being in “Don’t Pay Bribe”). Hence CM2 will have to stay in “Pay Bribe” to earn profit.
Collusion: Now suppose, CM1 influences CM2 to collude with him so that both will be able to earn 13 profit by both not bribing the govt rather than 10 that they earn in current Nash equilibrium. CM1 and CM2 do not pay any bribe in that year. But for next year, if CM2 decides to "cheat" CM1 and pay bribe to government. Then CM1 will be caught off-guard and suffer 5 loss and CM2 will earn a profit of 30. The outcome of that cheating will be that, henceforth CM1 will not cooperate with CM2 in "not paying bribe". In other words, the collusion will not work forever. So what? by cheating once CM2 earned 17 more than what he would earn by being in collusion. So, in other words, there is considerable incentive for the person who is a cheat. For both the men to be in collusion forever, they should make a legal agreement that the cheater will pay the other man 17 every time he cheats. This would deter the cheater from cheating and both men will happily earn 13 per year forever. This in other words proves that the collusion never works without any legal agreement between the colluding parties. This also depends on the present value of the future profits, but I will not drill down into those details in this post. This post was prepared only to prove how two common men cannot survive in a collusion where they decide not to pay bribe to government.
If you introduce a third player "government" in the game and then evaluate all the scenarios, the outcome of that game also will be "having a strong law to keep another collusion working for the benefit of all the players".
So, if you doubt the credibility of a strong law like "Lokpaal Bill", think again. I know it needs to be crafted very carefully as have been our "Election Commission" and "Judiciary". If you see both of these have powers which are not granted to any politician. They are independent systems and work so very efficiently that our democracy is still running well despite having so many social issues.
13 profit by both not bribing the govt rather than 10 that they earn in current Nash equilibrium. CM1 and CM2 do not pay any bribe in that year. But for next year, if CM2 decides to "cheat" CM1 and pay bribe to government. Then CM1 will be caught off-guard and suffer 5 loss and CM2 will earn a profit of 30. The outcome of that cheating will be that, henceforth CM1 will not cooperate with CM2 in "not paying bribe". In other words, the collusion will not work forever. So what? by cheating once CM2 earned 17 more than what he would earn by being in collusion. So, in other words, there is considerable incentive for the person who is a cheat. For both the men to be in collusion forever, they should make a legal agreement that the cheater will pay the other man 17 every time he cheats. This would deter the cheater from cheating and both men will happily earn 13 per year forever. This in other words proves that the collusion never works without any legal agreement between the colluding parties. This also depends on the present value of the future profits, but I will not drill down into those details in this post. This post was prepared only to prove how two common men cannot survive in a collusion where they decide not to pay bribe to government.If you introduce a third player "government" in the game and then evaluate all the scenarios, the outcome of that game also will be "having a strong law to keep another collusion working for the benefit of all the players".
So, if you doubt the credibility of a strong law like "Lokpaal Bill", think again. I know it needs to be crafted very carefully as have been our "Election Commission" and "Judiciary". If you see both of these have powers which are not granted to any politician. They are independent systems and work so very efficiently that our democracy is still running well despite having so many social issues.
