Last year Takashi Hashiyama, the head of a Japanese electronics company, wanted to put his company’s art collection up for auction and could not make up his mind whether to sell through Christie’s or Sotheby’s.

Racked by indecision, in the end he asked the two auction houses, which between them have a lock on global fine art sales, to decide the outcome by playing the game Rock, Paper, Scissors – with the winner to sell the $20m collection.

“As both companies were equally good and I just could not choose one, I asked them to please decide between themselves,” he told reporters at the time.

The game was played and, having spent a frantic weekend researching strategies on how to play, Christie’s won. It put up the collection for auction a few months later.

His methods might have been unusual but Hashiyama is hardly alone in his indecision about which auction house to choose. The two highly competitive companies sometimes appear as the Tweedledum and Tweedledee of the art world, frequently pursuing the same collections and offering very similar terms to sellers. Both have big teams of specialists and are well versed in how to market an art collection to get the best price. And both are skilled at pointing out the other’s weaknesses. (The price-fixing scandal of a few years ago created the misleading impression that the staff of both houses were in collusion during the 1990s. In fact, most employees continued to compete fiercely, unaware of the deals their bosses had struck.)

Of course, other auction houses do exist. Bonhams, which is making a big push into the US, is the third biggest. Phillips de Pury, having recovered somewhat from its failed attempt to take on the big two, has settled into its niche. In Paris, there is the Hotel Drouot, and in each country there are specialist auction houses that can offer a targeted audience of buyers.

However, if a collector has a sizeable number of expensive artworks or antiques and wants to reach a global audience, Christie’s or Sotheby’s are usually the main options, and the two most commonly compete against each other for business.

Their work on snagging the big collections begins long before the gavel falls. As the supply of top-quality artworks becomes increasingly thin, the two houses work hard on building relationships with potential sellers, sometimes focusing for years on a particular family in the knowledge that at some point (usually through death or divorce), its collection will come up for sale. There are cocktail parties, lunches, exclusive previews, seats at invitation-only auctions, regular visits from the house specialists who help with appraisals, insurance and care of the artworks. And every buyer is, of course, a potential seller.

Warren Weitman, the chairman of Sotheby’s Americas, says: “People will consult with us even if they are going to sell elsewhere. Sometimes people are consulting with us as prospective buyers of an artwork, and I view that as an opportunity to increase our strength in finding the sellers. Sellers come to us because we not only understand their property but we know who might buy their collection”.

The first thing a seller must consider is who has the expertise in their collection’s particular genre. Christie’s historically has dominated jewellery sales, for example, and has recently pitched itself as the place to be for postwar and contemporary art. Sotheby’s has the edge in American art and furniture, and claims hegemony in Impressionist and Modern artworks.

However, those are generalisations that might not apply to particular cases.

Each house offers financial inducements to sellers, although they are reluctant to make the details of these public. They might offer to guarantee the price the collection will get at auction (the collector does pay for these guarantees but the payment can vary); offer to lend money to the consigner, using the artworks as collateral; or offer a reduced seller’s commission (for works worth more than $5m, the seller’s commission is entirely negotiable).

They might even make a donation to the family’s foundation or charity, though this is less common today than it was. Paul Provost, director of trusts, estates and appraisals at Christie’s, says: “We ask lots of questions to try and find out what is important to the seller. If their charity is important, we might host a fundraiser here. That would be part of a tailor-made plan (for the consigner).”

Both donate to museums, which helps grease the wheels when the museum comes to sell items.

“Guarantees are actually more talked about than done,” says Weitman. “Recently there was one particular work that we had estimated at up to $1m, and the other guys [Christie’s] had estimated it at $200,000, and the consigner said: ‘What can I believe?’ We said we’re prepared to give whatever financial incentive is necessary and guarantee it at that price if necessary. We didn’t guarantee it in the end but we were willing to do it. The client said that’s a compelling argument and we got the whole collection. It went for close to $3m.”

In some cases, a house might go out on a limb financially to land a trophy sale, although neither ever admit to this.

Weitman says: “It’s the hardest thing to do, to step aside, but I’ve stepped aside. I’ve been on the front lines competing since 1978. I stepped aside recently in one sale, which hasn’t been announced yet. I did it last year with a major group of properties. They were sold at Christie’s last year, they stepped up with hefty financial packages, offering guarantees that were inflated. My view was borne out by the results. Consigners will sometimes say, we’d love to work with you, but we’ve got a completely insane financial offer elsewhere”.

Provost says: “If we’re really interested in a collection, we are going to be more aggressive in the terms we offer. But people think the only thing that differentiates the two (auction houses) is the deal and I can’t stress enough that that’s only a small part of it.

“Financially it can be quite varied. A classic situation is where there’s an estate that has a variety of works of art, jewellery and furniture. What we provide is a tailored proposal that might offer, for example, a single-owner catalogue for the artworks, and putting the antiques in our house sale. If it’s a client that’s publicity-averse, then a single-owner catalogue would not be the best thing. If they are very publicity-averse, then a private sale might meet their needs more effectively”.

Provost points out that Christie’s is the dominant auction house (referring to the fact that it sold more than Sotheby’s did last year). “Given our market share, we win much more business than we lose,” he says. “But if our competitors are still in business, then by definition we’ve lost some business”.

Ultimately, most collectors are emotionally attached to their artworks and often place possibly the greatest value on the trust and connection they feel with their contacts at the auction house. In a revealing comment, one serious collector who has sold works through both houses says: “I think it really depends on whether I like the person I am dealing with. That, and how much attention they pay to me, and how much they seem to really appreciate my collection.”