Grameen Bank and John Nash

Here is an exercise on Grameen Bank's sustainability through the Game Theory of Nobel laureate mathematician John Nash, who, along with his wife Dr. Daniel Kabet, died in a car accident on May 23 last.
In Grameen's context, sustainability refers to being able to continue banking operations. Since Grameen brings financial services to the poor, it can only sustain its operations as long as its borrowers remain loyal.
However, its proponents, such as Hillary Clinton, suggest that a non-cooperative game or a marriage of inconvenience does not necessarily have to be 'doomed.' They claim that this 'non-cooperative' business would endure because all rational players (e.g., Grameen and the borrowers) will choose the Nash Equilibrium (NE) strategy to protect their material interests. The proponents of Grameen would give examples to support their claim: the relationship between King Henry and Queen Eleanor was based on material interests. This article applies John Nash's Game Theory to determine whether such a claim is credible. A marriage of inconvenience similar to that of King Henry and Queen Eleanor would be a more appropriate description of a union in which partners are incompatible in many respects and yet are welded indissolubly together.
 It is true that over the course of three decades, many Grameen borrowers have become rebellious, yet they made weekly repayments. In fact, Grameen and its 8.0 million borrowers are similar to King Henry and Queen Eleanor who cannot live happily together yet cannot live apart, almost in the same way as a thief loves his jewelry not because of romantic attachment, but merely because of its worth. These arguments should lead us to conclude that the relationship between Grameen and its borrowers is non-cooperatively based. Yet, both players still try their best to maintain this odd relationship. By doing so, they help ensure economic development.
Most of the time, borrowers reluctantly agree to go through Grameen Bank's rigorous process: making groups, attending weekly meetings, chanting 16 Decisions, learning to write signatures, doing physical drills, making repayments, helping fellow members to overcome radical Islam, denouncing dowries, and keeping families small.
Like borrowers, Grameen also reluctantly makes compromises when it must. It should be noted that Grameen used to have a strict strategy to recover the loans, but it did not work. During the 1980s, for example, the bank doubled its pressure on lazy group members who failed to save money for their own pension funds and other types of funds for emergency. However, they became rebellious and protested against this pressure. "They were protesting Grameen's handling of a fund it created for each group, using 5.0 per cent of each loan and additional mandatory deposits," wrote Daniel Pearl, "The group fund was meant for emergencies, but many borrowers wanted to withdraw money from the group fund." Grameen gave borrowers easier access to the funds at the peak of a big protest movement. Why did both players make such compromises? The reason is that no player can benefit by changing its Nash Strategy when the other player does not. This could be further understood through John Nash's Nobel Prize-winning concept of equilibrium. Nash pioneered Game Theory, which led him to discover the non-zero-sum situation. In this situation, people cooperate to reach a position of mutual benefit.
For example, Taslima and Grameen are in Nash Equilibrium (NE) if she is making the best decision she can without violating Grameen's rules, while Grameen's decision remains unchanged and Grameen is making the best decision it can by taking into account Taslima's decision. If this continues, then both players (Grameen and the borrower) approach the Nash Equilibrium. When Grameen was awarded the Nobel Prize in 2006, for example, the Bank chose Taslima to represent Grameen at the Nobel Prize ceremony in Oslo. If we multiply Taslima by 8.0 million borrowers, we get a sense of how Grameen successfully empowers women and how borrowers strengthen Grameen financially.
Thus, a perfect rational player's strategy abides by the Nash Equilibrium because it leads to the best cumulative payoff for Taslima and Grameen. Grameen Bank and its borrowers are at NE. No player wants to change their strategy because NE is a happy outcome for both. It is a non-zero-sum game, where NE is a 'win-win' outcome for Grameen as well as for borrowers, such as Taslima. This is why Grameen does not increase its interest rate and why borrowers do not stop making payments. As a result, the drop-out rate is almost zero, while the loan repayment rate is 98.6 per cent. In fact, Grameen Bank borrowers have accumulated enough savings to finance almost 80 per cent of its loans outstanding.
Grameen and the borrower are in NE because the former made the best decision (which is helping the latter) it possibly could, taking into account her decision, and she made the best decision (following the former's terms) she could. It should also be noted that no strictly dominant play could ever be made in the Grameen system because a strictly dominant strategy is not the best response to anything; in particular, it cannot respond to things being played in NE.  In fact, Nash and his mathematics help us understand why all efforts fail to unleash Grameen borrowers against Yunus. John Nash's mathematics also helps us realise why attempts to utilise even the bad players of Grameen (e.g., rebellious borrowers) to go against the Bank and its founder have failed. Such discussions lead us to conclude that Grameen has and will continue to sustain itself due to Nash Equilibrium, forcing both players to make mutually beneficial decisions.
And for this reason, for over three decades, Yunus and his borrowers have been able to work together, pray together, struggle together, attack poverty together and even win the Nobel Peace Prize together.
The writer, a biographer of Muhammad Yunus, is a CRISP scholar at New York University.  [email protected]