Game theory has been much in the news of late, mostly due to the visit to India of John Nash, of A Beautiful Mind fame. Nash was in the country to participate in a conference on game theory, where much was made of its applications in areas like conflict resolution and telecom spectrum auctions.
To managers, cases like these might seem interesting, but they're hardly something they encounter on a regular basis at work. Yet game theory situations do occur constantly, even if they aren't recognised as such. One of the most striking examples of this comes with the dollar auction, a distinctly unsettling variation on classic game theory situations. The dollar auction was first described by game theory pioneer Martin Shubik in a paper he published in 1971. Shubik was trying to incorporate the principle of addiction in a game, which he did by adding a twist to the rules for classic bidding auction. Playing the dollar auction is simple. Bring a group of people together and tell them a fixed sum of money, originally a dollar (but let's say Rs 20) is up for bidding. Anyone can bid what they want, even just fifty paise, and if there's no bid topping it, the winner will get the full Rs 20. But if there’s more than one bid, the person who bids highest pays — and so does the person who bid second highest. The difference between the bids, of course, is that the winner will at least get the Rs 20 in return for his bid, while the second highest bidder also pays but gets absolutely nothing. And bidding can continue indefinitely, until no one is willing to top the last bid. Shubik wrote that the dollar auction is best played with a large crowd: "Furthermore, experience has indicated that the best time is during a party when spirits are high and the propensity to calculate does not settle in until at least two bids have been made. Once that happens, the auction very rapidly goes out of control. Since the second highest bidder always loses — and loses totally — it always seems in his interest to top the last bid. If the top two bids are Rs 5 and Rs 4, for the winner it means at least he gets Rs 15, but for the second highest bidder it's a straight Rs 4 loss. It's hardly surprising then that he’ll bid Rs 6 and now the positions are reversed. For him it means he gets Rs 14, while the other bidder loses Rs 5. Very rapidly with dollar auctions one reaches the point where one is bidding the auction amount. At Rs 20 the top bidder is not making any gain, but at least he's avoiding a loss. The problem, of course, is that the second bidder feels the same way. At this moment in the game, it's usually reported there is a momentary pause — and then the second bidder bids higher than the auction amount. At Rs 21 he's losing Rs 1, but he's better off than the other bidder who's losing the full Rs 20. Once this psychological point is breached, dollar auctions usually go spectacularly out of control. The two bidders — after a point it’s nearly always two bidders battling it out (and anecdotal evidence indicates the bidders are usually male!) — keep topping each other in frenzy, even though now there’s no gain for either, just a relatively smaller loss for the 'winner'. The contest only ends when one player finally drops out, usually having lost far more than he anticipated. One actual example of a dollar auction being played, for a $100 stake, ended with a final bid of $3,000! The dollar auction may seem like the sort of insanity that would never be encountered in real life. In fact, says Robert Weber, professor of management and decision sciences at Kellogg University, it happens all the time. "I teach the dollar auction in my course as an example of how disputes can easily go out of control in companies." A common example is with strikes. Management and unions get into a dispute and it rapidly goes out of control because neither can bring themselves to step down and lose face. And a refusal to lose face is one of the essential factors behind the dollar auction. Game theory shows that the strategy for a dollar auction is probably just not to take part, since taking part leads to unprofitable escalation. Yet stepping down is seen as an unacceptable loss of face, so people go ahead and make that second bid — and then face the consequences. So who wins in a dollar auction? "A dollar auction is a war of attrition, and is ultimately won by whoever has the larger resources and becomes willing to commit them," says Weber. Yet, as in all wars of attrition, the victory can become an increasingly dubious one if the cost paid by the winner is almost as much as the loser's. "The best way to play a dollar auction might be to make a realistic assessment of the resources one can commit, or to fix a period for how long you will play," says Weber. And once you reach that limit, you walk away, regardless of how much money — or face — you have lost.
Management will argue that this is a strategy of defeat in negotiating with a union. In a vicious sort of way, the dollar auction can be an equaliser, favouring weaker parties who are willing to go to the max, because they have nothing else to lose. Would a Margaret Thatcher have defeated the unions if she had followed a dollar auction strategy and backed down? But one point with game theory is that rules change over games, and the same is true with union-management negotiation. A union can use a dollar auction strategy and win once, twice, maybe three times. But over time, the balance of power shifts, and the management becomes more desperate. Thatcher calculated the country was becoming ungovernable because of strikes, so she could risk chaos anyway by staging a showdown. She did, and she won.
Dollar auctions often crop up in project development as well. A management invests money in a project, which then requires more money. The management may not want to put in more, but if they pull the plug the earlier investment is wasted. So they pump in more, which raises their involvement — they are essentially playing the dollar auction against themselves. This has been called the Concorde Fallacy, after the way the British and French government kept pouring money into the prestigious project for a supersonic airliner, long after it was quite evident that even if technically successful, the project was not commercially viable.
Weber points out that the dollar auction crops up in the most unexpected contexts. "Biologists have found it in nature," he says. "It's when male deer getting into confrontations to win mates, or with some types of birds when the males compete to build increasingly elaborate nests to entice females." And deer can show a better understanding of the dollar auction than many people, he notes. They confront each other to display their resources — like antlers — and the weaker one backs off and leaves without fighting. That's one way of coming out of a dollar auction. "People often assume that game theory gives them ideal solutions," says Weber. "In fact the biggest benefit with game theory is that it can help you recognize when you're getting into a type of game with particular outcomes. Having recognised that, you can then alter the rules before you get into the game to prevent that happening."
It's an insight that is probably most relevant with dollar auctions. If you see yourself getting into a dollar auction situation, just walk away without making that second bid.
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