Diamonds, dollars and deception

January 23, 2012

On a recent trip to his native Australia, John Asker heard an interesting story about diamonds, dollars and deception. It’s a fun story in itself; it also relates to some of the themes discussed in the Firms and Markets course (as well as Game Theory and Business Strategy). Here are the details.

In the northwest of Australia is an area the size of Texas called The Kimberly. About 30,000 people live there. It’s a vast, empty, barren and beautiful place. The main town in the eastern Kimberly is Kununurra, south of which lies the massive Lake Arglye created by the Argyle Dam.

Back in the early 1970s, the mining lease for the area south of (what is now) Lake Arglye, Australia, was owned by a South African company. This company engaged some Australia geologists to wander around their lease to see if there were any viable deposits there. The contract specifically engaged them to look for and report any uranium indications.

One of the geologists found some high quality diamonds lying in a creek bed. Being a bit cynical, she figured these had been dropped by her supervising geologists as a test to make sure she was doing her job. Going back to camp that night she told her supervisor that she found the “testers.”

The supervisor had no idea what she was talking about.

Once the confusion was clarified, they all got excited (understandably) and decided to look more carefully. The stones they’d found earlier were not a fluke: they came from an enormous diamond deposit upstream.

Then the fun started. The geology team looked carefully at the exploration contract and confirmed that they were only obliged to tell the South African mining company if they found uranium. So they kept it quiet.

The mining lease had about three years to run. It’s hard to keep a secret for three years. So by the time the lease is almost up, word is out that CRA (the Australian company leading the consortium that the geologists were now working with) had found diamonds somewhere near Kununurra.

The play was to wait for the original mining lease to expire and then snap it up. However, this wouldn’t happen if the mining lease was renewed.

So to trick the South African company, CRA hired every earth mover, and every spare bit of labor and moved them 100km west of Kununurra (the diamonds are south of Kununurra). The South African company went nuts and started buying up land west of Kununarra.

And let the original mining lease lapsed.

Meanwhile, CRA (now Rio Tinto) started the mine and made out like bandits.

For a “traditional” game theorist, this example of deception raises an interesting challenge. If it is commonly known among players what’s at stake, and if it is commonly known that the players are rational, then there exists no Nash equilibrium where the players choose “pure” strategies (that is, strategies that are not chosen randomly). To see why not, consider the following chain of thought: if the SA company expects CRA to deceive, then the SA company should not buy the area where CRA is working on; given this choice by the SA company, CRA is better off working on the diamond mine; but then there is no deception, which makes the SA company’s belief a non-Nash-equilibrium belief.

In order to reconcile theory and empirical observation, game theorists have considered “deception” games in a bounded-rationality setting (that is, assuming that players are not quite as “smart” as a “traditional” game theorist would). A good example is this paper by Ettinger & Jehiel. Still another possible solution is to consider a Nash equilibrium in “mixed strategies,” whereby players randomly choose between different strategies: CRA between deceiving and not deceiving, the SA company between following CRA’s location choice and not doing so. However, the facts from the story don’t seem quite consistent with this view.

The Kununurra example shows how the seemly abstract assumptions of models can really matter in practice. In particular, in this instance, to use economics to explain the strategic interactions between mining companies requires us to push against the very frontier of economic theory. That’s what research is for, after all…

Posted by John Asker and Luis Cabral, with thanks to various Stern colleagues for comments on an earlier draft.

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