SINGAPORE — A phone company disclosing a $7bn equity investment in a country just as its government gets ready to sell expensive spectrum is one of those clever tricks John Nash would have approved of.The maths genius whose life was depicted in the biopic A Beautiful Mind, and whose work underpins solutions to competitive games like the one Vodafone is playing in India, might have guessed that the British company’s latest move is also its dominant strategy — what it should be doing regardless of its rivals’ playbook.Here’s how it works: if the news that Vodafone has halved the debt burden of its India operation scares its more indebted competitors into submission, the company (which actually needs the airwaves more than any other large telecommunications company in India) gets to buy them without spending an arm and a leg in the $83bn auction that starts on September 29.And if the announcement brings out the warrior spirit in Indian billionaires, there will be an irrational bidding ...

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