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# The player’s dilemma

Game theory suggests that your best option, when surrounded by others you cannot trust to not cheat, and when the chance of getting caught is small, is to cheat as well

The real dilemma about the recent cheating scandal in the Indian Premier League is, well, there’s more than one. Let’s try this again. One puzzle about the scandal is how few players were caught and punished. Another is why these guys, well-paid as they are, try to cheat at all. A third is how few of us fans seem to care enough to turn our backs on the league circus. A fourth is an ancient one: how easy to punish the pawns—in this case, cricketers—yet how hard to even shame the real powers, the game’s administrators.

Maybe you have more.

What does this have to do with a column about mathematics? This much: there’s some fascinating recent mathematical research into the phenomenon of cheating in sports. Specifically, it addresses doping, the taking of performance-enhancing drugs—think Ben Johnson, Lance Armstrong—but it could apply to cricket’s fixing scams too.

In an ideal world, nobody would cheat. Well, scratch that. You’re a sportsman, and you suspect your teammates and competitors are cheating—whether with drugs to boost their performance or with money to boost their wealth. What do you do?

This is the classic prisoner’s dilemma from the field of mathematics known as game theory, pioneered by the Nobel laureate John Nash. (He’s the subject of the book and film A Beautiful Mind). It suggests that your best option, when surrounded by others you cannot trust to not cheat, and when the chance of getting caught is small, is to cheat as well. Otherwise your colleagues gain an edge over you.

But, of course, the players are not the only people in the circus. So game theorists study the role of authorities; in this case, sports administrators, whose role is to check for cheating and punish those who are caught. The fear of such punishment, goes the reasoning, should keep others clean. But somehow it doesn’t. Punishments to Hansie Cronje, Mohammad Azharuddin and Ajay Jadeja some years ago, for example, clearly did not deter S. Sreesanth and Ajit Chandila from their misdeeds. Now what?

The mathematical economist Berno Buechel, of the University of Hamburg, thinks he has an answer. In a paper earlier this year (Nobody’s Innocent—The Role of Customers in the Doping Dilemma), he and his colleagues “build on the previous game-theoretic work on doping but take the analysis...further by introducing customers as an additional player into the game. Customers are highly important because they finally make professional sports economically viable."

Customers, meaning you and I, paying altogether too many rupees for IPL tickets or cheering every slo-mo six on our TVs. How the players behave, Buechel argues, has a lot to do with our presence in the equation—for the simple reason that you and I ultimately pay their salaries. “The public perception of (a) clean sport," wrote Buechel, “seems crucial for customers...to keep their support... Their critical role is the potential withdrawal of support."

Yet about that withdrawal, Buechel and his colleagues found something surprising: that this “behaviour of critical customers accentuates the (players’) fraudulent behaviour."

Look at it like this: if when some cheaters are found and punished, we turn away from the sport, that will tend to make administrators back off on their monitoring of cheating, such as it is. This is because they want to preserve the economic value of their sports package: case in point, IPL. The more the cheats exposed, the harder it is to sell the show—that’s what it is, right?—to sponsors. Therefore, don’t expose too many cheats. The result is a return to the classic prisoner’s dilemma: since there’s not much chance of being found out and since others are likely doing it anyway, it pushes players towards cheating.

Buechel’s solution to this conundrum is full testing, of everyone. But also, full reporting of the results, whether of honest players or cheats. This way, we slice through the prisoner’s dilemma, because cheats know they will be exposed. This way too, you and I can better comprehend both how much cheating goes on and what’s being done to fight it. Gives us more faith in sports we love.

All right, I’m not holding my breath waiting to see Buechel’s solution implemented. It’s an expensive one. And after all, administrators routinely claim their sports are both clean and adequately tested (Ha).

And so the connection to my last column. As The Economist commented about such claims, the “human capacity for self-deception is infinite."

We deceive ourselves into the destructive wastelands of nationalism; we deceive ourselves into a reverie about squeaky-clean sports. Some of us even manage to conflate the two: like the man who told me I should support India’s Shikhar Dhawan’s mocking of Australia’s Shane Watson’s injury in a cricket match, because this was “nationalism".

All of which only persuades more players to bend rules. So, who are the real cheats? Let me submit: all of us. You and I, deceiving ourselves.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers will explore the joy of mathematics, with occasional forays into other sciences. To read Dilip D’Souza’s previous columns, go to www.livemint.com/dilipdsouza-

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