# To Corrupt or Not to Corrupt

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To Corrupt or Not To Corrupt: Game Theory Model of Corruption in the Philippines:

Introduction

Why Janet Napoles did it?

Game theory is a mathematical modeling of strategies. Every deal or transaction involves players or agents whose

aim foremost are maximizing their gains or utilities out of a given game. Reference [1] presents a gametheoretical model of corruption, mainly on the premise of economic gains. Reference [2] details the game theorymodel of why professional athletes indulge into doping in order to gain advantage or maximize their economic

utility.

Corruption in the Philippines is a cancer. For centuries, we know it exists but it seems theres no antidote for it.This paper aims to explain why people in the government or not continue to do corruption using game theory.

Assumptions

1. Small time corruption means small time connections and has heavier penalties like getting in jailtherefore.

2. Big time corruption means big time connections and has lighter penalties like getting treated in highlevel medical hospitals or house arrest in a luxurious mansion located in a high end village or eludesarrest since you can be tipped off and protected by your connections in government and lawenforcements.

3. Probability of getting exposed being involved in corruption is equal with perpetrators of small timecorruption and big time corruption and very high )0.1( since Filipinos are really, really, really (likereally) tired of this cancer of corruption plus social media savvy Filipinos let the news fly quickly.

4. Game is simultaneous as players or agents choose among strategies (to do honest and cleantransactions, to participate in a small time corruption, or to engage in a big time corruption deal).

In economics, firms aim to maximize their utilities or financial benefits from any transaction they are involved

with. Economic utilities for players or agents in the corruption game would be:

>=

>>=

>>=

>=

=

0,)(

,)(

,)(

0,)(

)(

ddPu

bccBu

abbSu

aaHu

u

i

i

i

i

(1)

where:HPlayeri deals honestlyS Playeriparticipates in a small time corruption activityBPlayeriparticipates in a big time corruption activityPPlayerispenalty due to getting caught in participating in a corruption activity

a is the economic benefit of an honest government official or an ordinary citizen, this may be a regular salary ora normal profit from a project or a transaction

b is the economic benefit of a government official or an ordinary citizen engaging in a small time corruption, forexample LTO licensingc is the economic benefit of a government official or an ordinary citizen engaging in a big time corruption, for

example pork barreld is the economic loss of a government official or an ordinary citizen engaging in corruption but get exposed

and caught for corruption

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From this equation , c>>b>>a, meaning that the economic incentives to participate in big time corruption likepork barrel scam is much bigger than being involved in small time corruption like city hall departmental fund

malversation. As always, the financial incentives to play clean and honest is very much lesser than being corruptfor the benefit may be your regular salary or spending the funds for the betterment of livelihood of Filipinos. The

utility for being caught and penalized as a corrupt official or citizen is negative since this would mean economicloss upon playeri.

For the probabilities, applying the present scenario in the Philippines,pS is equal topB, meaning there is an equalchance of being exposed as engaging in corrupt practices since Filipinos are very very very tired of corruption.

Though in this analysis the economic loss dB will be lesser than economic loss dSwhich means when dealing withbig time corruption, a person would have significant political connections thus less financial or economic losscompared to indulging into small time corruption. In this case, the big time political partner in a big time

corruption will protect you since this will protect them whereas when involved in a small time corruption theeconomic loss is greater since no big time personality is involved to support you or to save their face thus you get

caught and may go to jail.

Consider players or agents (player 1 and player 2) choose to indulge in big time corruption, the assumption is aplayer will get equal economic benefit and equal economic loss as his partner, therefore equal to 0.5 or half. Inthis case, the payoff of each player would be:

( )

0.1also

2

1

2

1then,remember

2

1

2

1

2

1

2

1

2

1

2

1

2

1

>>>>>>>

===+

B

BB

BBBBBB

p

dcdcdpcdpac

(2)

From equation (2), the payoff of a player involved in a big time corruption activity would be equal to the half ofutility c minus the financial loss dB due to getting caught since utility a would be diminutive and the probability of

getting caught is high and equal to 1. If the probability of getting caught is small (

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Player 1

B S H

Player2

B ( ) ( )BB dcdc 2

1,

2

1 ( ) ( )BS dcdb , ( ) ( )Bdca ,

S ( ) ( )SB dbdc , ( ) ( )SS dbdb 2

1,

2

1 ( ) ( )Sdba ,

H ( ) ( )adc B , ( ) ( )adb S , ( ) ( )aa ,

Figure 1. Payoff matrix for the corruption game.

Nash Equilibrium

Nash equilibrium is defined as an action profile with the property that no single player can obtain a higher payoff

by deviating unilaterally from this profile [3]. Recalling that c>>b>>a and dB >(b-dS)>>a,the Nash equilibrium of the corruption game is the action profile or payoff where each player chooses B. In here,the dominant strategy of the game would be both players choosing to participate in big time corruption since nomatter what the other players course of action is, a player would be better off choosing column B or row B.

Ifa>>b>>c then corruption would never be committed for clean and honest government dealings is rewarded withenough economic benefits. However, that is not the reality. The reality is that payoff is too large when commitingcorruption and for a very minimal penalty even when exposed or caught as a corrupt person. Another sensitivity

is, ifc>b>a but the penalties dB and dS are very high enough that would negate the utility gains, then the Nashequilibrium of this game would be [(a), (a)].

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Conclusion

This paper presents a game theory model of corruption practices in the Philippines. Currently, for peoplecommiting corruption, financial or economic incentives are too high when their penalties are very low. If

corruption is to be solved, if it is solvable, keeping corrupt officials in jail and heavy financial penalties must begiven to persons who squander the nations resources thus exponentially increasing the utility of economic loss ofcorruption penalty. Also, aside for economic benefits, moral incentives must be considered by parties like rewards

like honoring and recognition or promotion of honest public servants to increase utility for being honest ingovernment transactions.

References

[1] John Macrae, Underdevelopment and the Economics of Corruption: A Game Theory Approach, WorldDevelopment, Vol.10, No.8, pp.677-687, 1982, available on-line:http://conferences.wcfia.harvard.edu/files/gov2126/files/macrae_1982.pdf

[2] Kjetil K. Haugen, "The Performance-Enhancing Drug Game", Journal of Sports Economics February2004 vol. 5, no. 1, pp. 67-86, available on-line: http://www.suu.edu/faculty/berri/JSE2004Haugen.pdf

[3] Nash Equilibrium, available on-line: http://www.columbia.edu/~rs328/NashEquilibrium.pdf