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Game strategy

  • Fredrik Odegaard
  • |
  • Jul 1, 2017
Game strategy

In 1971, Martin Shubik, of Yale University, published a paper describing “an extremely simple, highly amusing, and instructive parlor game which can be played at any party by arranging for the auction of a dollar.”

Sounds simple enough.

In the game, the auctioneer auctions off a dollar to the highest bidder, with this twist: both the highest bidder and the second highest bidder must pay the auctioneer their bids. So if George bids 10 cents, and Sunali bids 15 cents, Sunali gets the dollar, George is out 10 cents and the auctioneer gets 25 cents.

Now imagine you are bidding on an item valued at $10 with bids in $1 increments, and whatever you bid is a sunk cost. A critical point in the auction comes when you have bid $9 and another bidder decides to bid $10 – the agreed-upon value of the item. You could lose $9 if you don’t get the item, or you could bid $11, get the item for $10, and only lose $1.

“This is when the “paradox of escalation” takes over. Beyond this point, both bidders will be losing out on the item but may escalate their bids in order to cut down on their losses,” says Fredrik Odegaard, an associate professor in Ivey’s Management Science group whose recent research is investigating the game’s strategy.

There are several examples of this paradox in business.

Different groups in an organization could be vying for research and development money. They could use their own budget to build a prototype in the hopes of getting the greater amount of R&D funding at stake. It then becomes a race between groups to win the big budget and recoup their losses. A classic multi-national version includes the “Concorde fallacy” - the race between UK, France, USA, and USSR to produce supersonic airplanes.

The nuclear arms race during the Cold War is another example. Each country built up a nuclear arsenal that could destroy the other country many times over. But no country would back down.
More recent applications of the Dollar Auction include the open innovation challenges, such as the 2009 Netflix Prize and 2017 Zillow’s Prize – an online real estate database. In both challenges, participants attempt to improve various algorithms for the respective companies in an attempt to win $1 million.

The Netflix Prize was an open competition for the best collaborative filtering algorithm to predict user ratings for films, based on previous ratings without any other information about the users or films. The currently ongoing Zillow’s Prize is for individuals or teams to improve the Zestimate algorithm of real estate valuation.

The problem is that nobody seems to be able to overcome the seemingly arbitrage and escalation paradox without changing the original rules of the game.

Until now.

In a paper entitled Multilateral Deescalation in the Dollar Auction, Odegaard and his Western colleague, Economics Professor Charles Zheng, outline a number of ways to overcome the paradox without changing the rules of the game.

The main crux is that in each round bidders flip a coin to see whether to continue bidding or accept the sunk cost, i.e. “heads” I bid; “tails” I stop.

“This way, you don’t escalate the bidding with certainty,” said Odegaard. “The flip of the coin determines whether you should proceed or not. If you do this, you can stop this escalation. The conflict is then expected to end earlier and end in such a way as the seller won’t be able to extract more than the worth of the item.”

The idea of a coin toss is equivalent to the random shocks or events that can happen in business. And so the paradox is resolved by designing the coin such that the probability of “heads” is balanced with the expected outcome of the game.

For example, if you are in an R&D race in an organization, and there are external shocks such as the opportunity to develop another project or a change in leadership (which is equivalent to the flip of a coin) these random shocks can take you out of the bidding and deescalate the conflict.

“If you don’t get a shock, your incentives are always to continue, because rather than accept your sunk cost you’ll always want to raise it one more increment, in order to get that grand prize. Then at some point, we are beyond what the reward is actually worth. We need some shock to stop that behavior, where you say, ‘You know what, I’m just going to have to accept this sunk cost.’ ”


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