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. |
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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. |
“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.” |
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CONFLICT Buyer — Buyer |
Buyers compete to ensure access to quantity and type of diamonds. |
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COMMONALITY Buyer — Buyer |
Buyers wish to minimise the price level paid which can be achieved through collusion. |
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————————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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