Game theory in the rough diamond market – buy the box?

The mechanism to buy and sell rough diamonds is bizarre. Diamonds are sold in “boxes”, collections of diamonds with similar characteristics, where values ranging from $100,000 to $1.5 million. Approximately 5,000 boxes are available for sale at 10 occasions per year which are known as “sights”. At these transaction points, a competitively large number of customers, (approximately 80 “sightholders”) to accept or reject the box allocated to them by the seller at a price specified by the seller. No negotiation occurs and there is no cross access between boxes assigned to other customers.

This strange structure triggers lots of questions – When should a buyer reject? What price should the seller set? How do these choices change over time? Why did the structure end up like this? To help us understand these aspects, Game Theory is a useful framework in order to assess the interaction and sheds light into the strategies undertaken by the buyer and the seller.

————————THE GAME————————

Each single sight is part of a larger game between buyer and seller. The repeated element to the game develops relationships with different payoffs to the one shot game.

a.        Term Contracts (1-3 years of estimated future goods from a mine)

  • Seller Forecasts Quantity (from each production asset)
  • Buyer Lobbying (seller signal preferences to buyer)
  • Seller Allocates Forecast Quantity

b.        Multiple Sights (10 sights per year of actual goods)
c.        Single  Sight (single interaction between buyer and seller)

  • Seller Recovers Material (sold 3 months after getting dug up)
  • Buyer Lobbying (seller signal preferences to buyer within term agreement)
  • Seller Allocates Material to Boxes (within term contract specifications)
  • Seller Sets Price (price book with a level and relative premiums and discounts between diamond categories)
  • Buyer Inspects Box
  • Buyer Accept or Reject (within Minimum Purchase Volumes of term contract)

 ————————OBJECTIVES & STRATEGIES————————

Ultimately participants want to maximise profits available over the lifetime of the game and not just in the one shot arena, creating areas of common ground and not just conflict.

Based on the set of game rules, objectives and payoffs for players – a set of strategies can be developed. It is a game plan for all possible ways that the interactions might play out and how a party would best respond to another’s course of action.

INTERACTION

OBJECTIVE

SELLER STRATEGY

BUYER STRATEGY

CONFLICT

Buyer — Seller

Prices paid for boxes will directly impact the margins achieved for both players. Surplus is divided in a zero sum game.
  • Restrict supply to raise prices (within elasticity constraints) using market power.
  • High price – low quantity setting tracks market demand. The slowdown in 2009 led to a 25% reduction in production volume.

 

  • Option for seller to exclude a buyer from participating in the market.
  • Asymmetric exclusion payoffs – much worse for the buyer who receives nothing.
  • Credible threat as the seller impact is small with the volume likely to be re-distributed to other buyers.

 

  • Captive nature of the agreements in place creates short run incentives for seller to recover additional margins if required (e.g. management targets etc.).
  • A reject box strategy should only be used if the value saved from one off rejection is greater than the value lost from harming the long run relationship.
  • Costs to the relationship include the increased probability of future exclusion (removing all future profits) + expected loss from poorer stone allocation.
  • Empirically, rejection rates are low – suggested to be around 10%, rising to 20-25% under difficult market conditions.
  • Buyer rationality anticipates the strategies of the seller – the small but positive payoff provided for buyers and the use of exclusion – and realise they need to toe the line as set by the seller.

COMMONALITY

Buyer — Seller

A stable repeated game needs to ensure that both sides of the market still want to play.Players optimise the timing of transactions and security of supply.
  • Repeated games drive the seller to offer a price for the buyer so they still play the game.
  • Price for small but positive buyer margins
  • Comments by a managing director of De Beers confirm the strategy of sufficient buyer return to play the game over the long run.

“We look at the actual polished price .. take into account the labor costs, other expenses and economic factors like interest and box quotes… We are looking for our clients to make money, because there’s very little point in our clients not making money… are trying to get to a price that is a sustainable market price.”

  • Buyers are engage in mutually beneficial term structure contracts to ensure access to supply.
  • Removal of quantity risk for both parties
  • Improved material planning
  • Buyers are price takers by game design leading to limited cost to this strategy apart from minimum quantity requirements imposed by the term contract.

CONFLICT

Buyer — Buyer

Buyers compete to ensure access to quantity and type of diamonds.
  • The seller wants to foster competition within the buyers to minimise buyer power.
  • Strategies might include preferential treatment on a rotating basis to avoid favouring buyers.
  • If the willingness to pay varies enough between buyer’s then it might be a preferable strategy to permit buyer-buyer conflict through bidding for stones (high demand goods are likely to go up in price but poorer stones may go below their typical fixed price leaving an uncertain total effect).
  • Extent of conflict depends upon the homogeneity of buyers’ stone preferences
  • Similar preferences lead to strong conflict to secure access to stones because all buyers chase the same stones.
  • If preferences vary then the competition weakens because buyers chase the categories they prefer.
  • Market evidence of two market buyer types; cut & polishers and intermediary suppliers to secondary markets.
  • Cut and polishers typically specialise in a category of diamonds increasing heterogeneous preferences. Intermediaries lead to homogenous preferences in the market because each player chases the same arbitrage trades.

COMMONALITY

Buyer — Buyer

Buyers wish to minimise the price level paid which can be achieved through collusion.
  • Sellers explicitly forbid communication between buyers as part of the contract to become a sightholder.
  • The threat to exclude a buyer is less credible as the proportion of buyers colluding increases because payoffs to the seller start to become increasingly costly and painful to act upon.
  • Buyers can benefit from to collusion to lower prices but it comes at the risk of being excluded by the seller from the game.
  • A uniform cost structure lowers the risk of being long run unprofitable without all other companies being similarly impaired.
  • Risks of rejecting an unprofitable box become smaller because a buyer knows it will also be unprofitable for the others leading to multiple rejections
  • Evidence suggests some economies of scale exist given the large working capital requirements (to manage this cash flow mismatches) – an estimated 30 percent of the clients receive up to 70 percent of goods.

————————PAYOFFS IN EQUILIBRIUM————————

The current payoffs within the diamond value chain indicate that the sellers of rough diamonds are the clear winners with typical operating margins of 16-20%. The rough diamond buyers, the middle market players with direct access achieve operating margins of 6-8%. Both parties are earning positive returns with the surplus being split at almost 3:1.

There is a clear stable equilibrium in the interaction between buyers and sellers, with many of the sightholding companies participating in the market for over 30 years. The mutual profitability within the relationship stabilises the game.

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