Game Theory Draft

draft to my analysis of MF using GT
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  Game theory draft Group-lending has proved to be an effective method of countering the issues that are faced by financial institutions [reference] . Adverse selection and moral hazard are ... [why is group-lending good] I present a developed model from [amelie brune's]. The base (?) model assumes that lending is made simultaneously to all group members, where player 1 is the MFI and player 2 is the group. The group is not disaggregated into individual members for simplicity. The design involved a trigger strategy, whereby if one member of the group defects, then all members defect. The model is developed as it needs to reflect the risk of the groups. With the movement toward self-sufficiency, many efficiency suggestions ()? Have been proposed [footnote: Note that the thesis does not intend to answer questions on the effectiveness of certain changes in the operations of MFI's, but to reflect these changes in a game-theoretical model. See xxx for more on the effectivness of MFI's.]. My model incorporates risk, by allowing the payoffs to the bank differ (and, therefore the group), by risk. For each co-operate pay-off, a term 'b2-log(x)' is deducted from the player, and given to the bank. This acts as a safe-guard. (note this is not deisgned to be a deterrent from entering, still no requirement for physical collateral etc). The risk is determined by what criteria MFI use. The Grameen Bank (xx) and BRAC (X) determine credit-worthiness by a history of savings, focus on health, education and family etc. X (belongs to the set of 1 and 10, but not including 1 and 10) X  1 represents total trustworthiness. i.e. the group has a good history of savings etc. This is the srcinal base model. x   10 represents untrustworthiness. For a group that is more untrustworthy, they have a higher pay-off deducted and given to the bank. This has been designed to see how the incentives might change for the individual to defect when banks require an extra pay off (can it be like a lump-sum tax ?).  For robustness, we further assume that the groups are allowed to choose themselves. It doesn't work as well if borrowers also lack good infomration on each other - particularly in sparsely populated areas (chapter 4). Ahlin 2009 and gine' et all 2009 shows that when groups are formed non-randomly, the risk is relatively homogonised comapred to a random assorting. Borrowers cluster together by risk. Hence the overall variability/variance in risk is reduced.  Choosing people represents a reduction in the variability of risk (not quite homogenised) but still To reflect changes in practices (such as Grameen Bank 2), the pay off's for defecting no longer reflect alternative income (in previous model, if the group defected, the MFI defected forever as a trigger strategy). Instead it reflects a lowering of loan - either to the same group, or with one different member) [Footnote: this is to reflect the new leniance, as groups used to be punished as a whole when it was one individuals fault (regardless of whether it was an anomolee or higher risk-taking that didn't pay off. Loan guards are now encouraged to seek out the reason for defecting (the cost in which is in part paid by the new/extra pay off) [REFERENCE TO GRAMEEN BANK 2] Grameens reinvention as greemeen bank 2, introdues mechanisms that loan officers may address problems of individual borrowers without invoking punishments for the entire group. Yunus 2002, dowla and barua 2006. The same inequality and reasoning apply. The sum of the discounted profits for co-operating must be greater than the sum of the discounted profits for co-operating until T, and the profits for defecting starting from T+1. If this does not hold, then long-term co-operation and repayments of loans will not occur as the group has an incentive to defect, as they realise a higher profit (and thus utility). A graphical representation is shown below: The profits from always co-operating are reflected as : The profits for co-operating until T-1, defecting at T (whilst the bank still co-operates, and then the profits for defecting after T (up until T+k). T -1 T T -1 T   [a 1  + b 2  lg(x)] , [a 2  - b 2  lg(x)] [b 1  + b 2  lg(x)] , [b 2  - b 2  lg(x)] [c 1  + d 2  lg(x)] , [c 2  - d 2  lg(x)] [d 1  + d 2  lg(x)] , [d 2  - d 2  lg(x)] Defect Cooperate Cooperate Defect Player 2 (Group) Player 1 (MFI)
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