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Game theory in practice

Game theory in practice

Game Theory An extensive form game
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Software that models human behaviour can make forecasts, outfox rivals and transform negotiations

FOR a man who claims to lack expertise in the field, Bruce Bueno de Mesquita, an academic at New York University, has made some impressively accurate political forecasts. In May 2010 he predicted that Egypt’s president, Hosni Mubarak, would fall from power within a year. Nine months later Mr Mubarak fled Cairo amid massive street protests. In February 2008 Mr Bueno de Mesquita predicted that Pakistan’s president, Pervez Musharraf, would leave office by the end of summer. He was gone before September. Five years before the death of Iran’s Ayatollah Khomeini in 1989, Mr Bueno de Mesquita correctly named his successor, and, since then, has made hundreds of prescient forecasts as a consultant both to foreign governments and to America’s State Department, Pentagon and intelligence agencies. What is the secret of his success? “I don’t have insights—the game does,” he says.

Mr Bueno de Mesquita’s “game” is a computer model he developed that uses a branch of mathematics called game theory, which is often used by economists, to work out how events will unfold as people and organisations act in what they perceive to be their best interests. Numerical values are placed on the goals, motivations and influence of “players”—negotiators, business leaders, political parties and organisations of all stripes, and, in some cases, their officials and supporters. The computer model then considers the options open to the various players, determines their likely course of action, evaluates their ability to influence others and hence predicts the course of events. Mr Mubarak’s influence, for example, waned as cuts in American aid threatened his ability to keep cronies in the army and security forces happy. Underemployed citizens then realised that disgruntled officials would be less willing to use violence to put down street protests against the ailing dictator.

Mesquita & Roundell, Mr Bueno de Mesquita’s company, is just one of several consulting outfits that run such computer simulations for law firms, companies and governments. Most decision-making advice is political, in the broadest sense of the word—how best to outfox a trial prosecutor, sway a jury, win support from shareholders or woo alienated voters by shuffling a political coalition and making legislative concessions.

But feeding software with good data on all the players involved is especially tricky for political matters. Reinier van Oosten of Decide, a Dutch firm that models political negotiations and vote-trading in European Union institutions, notes that forecasts go astray when people unexpectedly give in to “non-rational emotions”, such as hatred, rather than pursuing what is apparently in their best interests. Sorting out people’s motivations is much easier, however, when making money is the main object. Accordingly, modelling behaviour using game theory is proving especially useful when applied to economics.

Follow the money

Modelling auctions has proved especially successful, says Robert Aumann, an academic at the Hebrew University of Jerusalem who received a Nobel prize in 2005 for his work in game-theory economics. Bids, being quantified, facilitate analysis, and predicting the right answer can be very lucrative. Consulting firms are popping up to help clients design profitable auctions or win them less expensively. In the run-up to an online auction in 2006 of radio-spectrum licences by America’s Federal Communications Commission, Paul Milgrom, a consultant and Stanford University professor, customised his game-theory software to assist a consortium of bidders. The result was a triumph.

When the auction began, Dr Milgrom’s software tracked competitors’ bids to estimate their budgets for the 1,132 licences on offer. Crucially, the software estimated the secret values bidders placed on specific licences and determined that certain big licences were being overvalued. It directed Dr Milgrom’s clients to obtain a patchwork of smaller, less expensive licences instead. Two of his clients, Time Warner and Comcast, paid about a third less than their competitors for equivalent spectrum, saving almost $1.2 billion.

Advances in game theory have “picked up dramatically” in recent years as it has become apparent that failing to do a proper analysis can be costly, says Sergiu Hart, a colleague of Dr Aumann’s at Hebrew University. For example, a few years ago Israel’s government added a novel twist to an auction of oil-refinery facilities. To encourage more and higher bids, the government offered a $12m prize to the second-highest bidder. It was an expensive mistake. Without the incentive, the highest bid would have been about $12m higher, an analysis showed—participants bid low because the loser would strike it rich. Combine that sum with the prize payout, and the government’s loss amounted to roughly $24m. The conclusion, then, is “don’t presume you know what the solution is” without help from modelling software, says Brad Miller, senior modeller at Charles River Associates, a consultancy in Boston. It designs game-theory software to model industrial auctions and the plotting of corporate mergers and acquisitions.

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