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It is almost amusing. The world's central bankers face a classic prisoner's dilemma. Yet all those master economists are proving as inadequate at solving one of the great puzzles of game theory as the pitiful rational actors that appear in the textbooks.

A quick review: The prisoner's dilemma illustrates how normal people, acting in their self-interest, can actually make their situations worse. Two suspects from a gang are held by the police in isolation. Investigators lack evidence for a conviction, so offer each prisoner an opportunity to rat on the other in return for his or her freedom. The optimal thing for the prisoners to do is keep quiet: Both would be set free because the cops would have no case. But Prisoner A and Prisoner B have no idea what the other will tell the police. The self-interested response therefore is to squeal on the other. And then both go to jail.

The leaders of the world's major central banks are part of a gang. They gather regularly in Switzerland for meetings of the Basel Committee. They serve together on the Financial Stability Board, and they compare notes a couple of times a year under the guise of the Group of 20. But then they go home and operate as though they are setting monetary policy for island nations that have no part in the global economy and international financial markets. Central banks cling to their domestic mandates, which are like blinkers on a draft horse.

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The Basel Gang operates by a tough code: Once you go home, you are on your own. If one central bank opts to create hundreds of billions of dollars to buy bonds, it is up to all the other central banks to respond to whatever market distortions follow. As with the saps in the prisoner's dilemma, the self-interested response clouds the optimal response. The result is frequent chaos.

The 2013 "taper tantrum" that followed former Federal Reserve chairman Ben Bernanke's offhand statement that the U.S. central intended to ease its monthly purchases of bonds is the best example of how a central bank can cause harm by acting completely rationally. The frenzy of interest-rate cuts at the start of this year is another example. The recent volatility in bond markets also is a product of central banks acting in their own best interests. Some argue that the sudden and sharp appreciation in German bond yields was a reaction to shifting probabilities of whether Greece will remain in the euro zone. Maybe. But more likely, investors and traders simply lost confidence in an asset that was extremely overvalued, as reflected in yields of almost zero.

"The reality is that when 10-year bond yields are at 0.077 per cent, it doesn't take much to cause a sell-off," Avinash Persaud, non-executive chairman of Elara Capital, said in a commentary published this week in Mint. Bonds are overvalued because the Fed, the Bank of Japan, the Bank of England and now the European Central Bank have severely reduced the supply by vacuuming up safe assets to put downward pressure on interest rates.

There is one central banker who is trying to persuade his counterparts to think globally while they act locally. For more than a year, India's Raghuram Rajan, a former chief economist at the International Monetary Fund, has been building an argument for why central bank co-ordination should be more than semi-regular chats behind closed doors.

"The current non-system in international monetary policy is, in my view, a source of substantial risk, both to sustainable growth as well as to the financial sector," Mr. Rajan said this week in a speech at the Economic Club of New York. "We are being pushed towards competitive monetary easing and musical crises."

India was one of the victims of the taper tantrum. Mr. Bernanke's loose talk of higher interest rates in the United States sparked a rush of capital from emerging markets. India's rupee plunged, complicating Mr. Rajan's efforts to cure the country's inflation epidemic. The Reserve Bank of India seems to have things under control now, no thanks to the Fed. Mr. Rajan's job was made harder than it needed to be, and emerging markets were left with another reason to distrust the United States and the other established powers. Emerging markets have every incentive to pile up reserves so that they are ready for the next tantrum.

Mr. Rajan has some fairly developed thoughts on how to break the current dynamic. Central banks and their political masters should start acting like responsible global citizens, worrying as much about "spillovers" as "spill backs." Global lenders such as the World Bank and the Asian Development Bank should be given more capital to finance emerging-market infrastructure and create "new demand." The International Monetary Fund should be given the authority to police new rules of the game, shaming central banks and governments whose policies cause undue harm to other countries.

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Inexplicably, Mr. Rajan remains a lonely voice on these issues. His counterparts sniff at his suggestions and retreat to their domestic mandates. Rational, but as recent history has shown, suboptimal. Game theory suggests that we can do better.

Kevin Carmichael is a senior fellow at the Centre for International Governance Innovation, based in Mumbai.

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