Verma, Prateek (2014) *Is the Bribe Free World Possible? An Evolutionary Game Theoretical Analysis.* Masters thesis, Indian Institute of Science Education and Research Kolkata.

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## Abstract

We start with a general harassment game with five strategies in chapter 2. After some simplification of the generalized harassment game, we study the evolutionary dynamics of the model using replicator equations. We plot the bifurcation diagrams for two varying parameters at time for various cases and contrast the results obtained for „symmetric liabilities‟ and „asymmetric liabilities‟. We found that a bribe free world is more likely to attain in „asymmetric liabilities‟ case. High punishment and prosecution rate and low value of bribe demand assists in achieving utopia. An Agent Based Simulation (ABS) for the same five strategy model was done with Moran process as the population update rule. We found the same dependence on various parameters with respect to attaining utopia as we had found in case of replicator equations. Though we found that there is no conformity of attaining utopia for finite population size, there is always some probability with which population reaches utopia for a given parameter set. In chapter 3, the five strategy model was removed to a four strategy model for better understanding and scope for accommodating more complexity. We draw bifurcation diagrams and velocity vector diagrams for the four strategy model. There was a sudden emergence of utopia after a certain critical value of parameters is reached. We also observes some interesting features of the system in „with refund‟ and „no refund‟ scenario. One observation was for imitation dynamics „with refund‟ case, bribe amount should to be judiciously set by the corrupt officer in order to survive in the population. A general observation was high punishment, high prosecution rate, low value of bribe demand, low cost of complain and incentives for having refund helps in attaining bribe free world. We also test the Basu‟s „proposed policy‟ with the „present policy‟ in the limits of high cost of complaining and low prosecution rate. We found that success of „proposed policy‟ depends on having significant proportion of citizen who „pay and complain‟ and officers who „does not take bribe‟. Next we investigate the effect of allowing officers to take up the roles of citizens on the long term evolutionary fate of the population structure. No qualitative different result was observed from the modified model. In chapter 4, we change the mode of updating the population from „imitation‟ to „alternative strategy exploration‟. The results of bifurcation diagram shows that unlike „imitation‟ model there was no sudden emergence of strategies but a spontaneous emergence in the parameter space. The possibilities of reaching a complete bribe free world were very rare except for some extreme parameter regime. There was a coexistence of different strategies in the population for most of the parameter space. Next we investigate the effect of empathy on the part of corrupt officer when he is victimized as citizen during an interaction with another corrupt officer. It was observed that presence of empathy leads to a reduction in the number of officers who „demand bribe‟. Chapter 5 and 6 is not related to the evolutionary game modeling of bribery scenario. These are two general formalism or techniques that can be applied in variety of context in evolutionary game theory. In chapter 5 we form a technique with which one could find the scores of the competing players in an infinitely iterative one-memory based game when players are prone to behavioral and perception errors. The results of the analysis show an exact match with the known results of some competitions between different strategy pairs. In chapter 6 we tried to apply the technique of solving master equation using generating functions in context of a general two player evolutionary game with local update imitation as the rule for population update. We feel that more investigation is required to fully understand the hidden connections and validity of implementation of the technique in the generalized evolutionary game models.

Item Type: | Thesis (Masters) |
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Additional Information: | Supervisor: Dr. Supratim Sengupta |

Uncontrolled Keywords: | Bribe; Bribery; Bribe Free World; Evolutionary Dynamics; Game Theory; Imitation Dynamics |

Subjects: | Q Science > QC Physics |

Divisions: | Department of Physical Sciences |

Depositing User: | IISER Kolkata Librarian |

Date Deposited: | 15 Jan 2015 10:05 |

Last Modified: | 15 Jan 2015 10:05 |

URI: | http://eprints.iiserkol.ac.in/id/eprint/203 |

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