Updated: October 19, 2020 8:54:36 am
There is a direct linkage between the RBI governor’s statement on October 9 and the Nobel Prize in economics that was awarded to Robert Wilson and Paul Milgrom on October 12. The statement by the governor that yield curve control and financial market stability are public goods is a stark reminder of the treatment of the same in game theory, where defection among individuals/market players is random, often resulting in least payoffs. Interestingly, Wilson and Milgrom are also proponents of game theory. It is an irony that the application of game theory in macroeconomics in India is minimal and, thus, it is always a matter of great elation whenever we can find a link.
First, a little titbit from this year’s Nobel prize award in economics. This is, perhaps, the fourth instance of a student and teacher getting the award in the same year. The first instance was in 2004, when Finn Kydland and Edward Prescott were chosen for the honour. Robert Wilson, besides being the winner of the economics Nobel this year, has three Nobel-winning PhD students — Alvin E. Roth, Bengt Holmstrom and Paul Milgrom.
In economic parlance, public goods are defined as non-excludable and non-rivalrous in nature, such as law enforcement. There is plenty of literature on the use of public good in financial markets — if agents cooperate well, all players have the opportunity to benefit; if agents work in isolation, all are likely to suffer. Hence, all should have a common interest in reforms that will improve the system for public benefit.
Garrett Hardin’s famous essay, “The Tragedy of the Commons,” published in Science magazine in 1968, was the earliest example of this argument. The farmer who added an extra cow gained an advantage over other farmers in his village, but it also led to an overgrazed pasture.
In the Indian context, let me provide an even earlier example to illustrate the idea of public goods. One day, Emperor Akbar told Birbal that he was planning to take a bath in milk and that all his ministers should cooperate and get milk to fill the bathtub. However, each minister decided that since milk was costly, he would get the water, while the others get milk. The end result was that all the ministers brought water. When this experiment was done subsequently with proviso of a punishment, everyone cooperated and got milk. In a similar vein, the RBI governor communicated through the policy that market players should always be competitive and not combative so as to get the best results. Central banks can only act to oversee the market.
Against this background, it is important to understand how the breakdown of trust across agents in the use of public goods often results in minimal payoffs. Both agents have two options between them — either cooperate or defect. Thus, we effectively have four policy options, and each of the options will have a particular benefit/payoff. Our endeavour is to find out which policy option can result in a Nash equilibrium, which occurs when neither of the agents can increase their payoff by unilaterally changing their actions. Thus there are four options — both Player 1 and Player 2 cooperate, both Player 1 and Player 2 defect, Player 1 cooperates while Player 2 defects, and, lastly, Player 1 defects while Player 2 cooperates.
The payoff scenarios are hypothesised as benefits accruing to Player 1 and Player 2 separately, when they are deciding on either of the policy options: Cooperate or defect. Specifically, both of them cooperating cannot be a Nash equilibrium, as both the players unilaterally will always have an incentive to defect because they will get a higher payoff in such an eventuality. Since the situation is the same for everyone, both the players will thus ultimately defect and receive a payoff of 0. This is the Nash equilibrium for this game. But this is sub-optimal as both players get zero payoffs because of uncoordinated behaviour. The bottomline is an outcome that the regulator will never want.
Let us now extend this analogy to the Indian debt markets. The Bank of Japan was, perhaps, the first central bank to proclaim that the yield curve is a public good and it is heartening to see the RBI echo the same.
In the Indian markets, it is common to find debt market players behaving differently. For example, if one set of players act pro-cyclically, selling government securities with the RBI’s monetary policy stance, the other set of players act counter-cyclically, buying government securities — sometimes both the players are combative. While there is nothing wrong in taking two way positions in the market, the problem arises when such buying/selling far outstrips selling/buying that the RBI would prefer. This also results in a yield structure not in sync with macro fundamentals. For example, during 2017-18, the spread between the overnight repo rate and the 10-year G-Sec yield had increased to 169 basis points in February. Till that time, such a large spread was seen only during a financial crisis.
Can we avoid such a problem of defection? The economist Elinor Ostrom had an answer (the only woman apart from Esther Duflo to have won a Nobel in economics). The only way groups can avoid such a breakdown is by adhering to conditions in the form of eight core design principles.
In a similar vein, the concept of public goods can be experimentally put to good use in the current pandemic for a social cause. Suppose the government were to frame a policy of incentivising well-off households (say, through a certification from the PM) to co-operate and support at least one poor household. Such incentives are extremely important as otherwise individual households can always defect unilaterally because it gives them a higher payoff and thus both could end up defecting. This is a clear example of Jan Bhagidhari.
Similarly, wearing masks is a perfect example of a public good, as there is always a proviso that the person not wearing a mask could benefit and hence, again, both defecting and not wearing masks could be an eventuality. In this case, we, however, need a harsh punishment for those not wearing masks. This is a clear example of Jan Chetna.
Clearly, adhering to Jan Bhagidhari and Jan Chetna, as the Prime Minister has been espousing, requires an intelligent application of game theory in policy making.
This article first appeared in the print edition on October 19 under the title “How to Make You Wear a Mask”. The writer, group chief economic advisor, State Bank of India, is thankful to Sudipta Sarangi and Indranil Bhattacharya for useful comments. Views are personal
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