Mineral Conundrum
The two mining companies of Argon Co. and Bismuth Inc. are exploiting a rare mineral from a single mine and selling it for an equal profit of 50 billion dollars each. An expansion opportunity has opened up for both corporations, and they would like to know if they should take it.
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If Argon Co. ( Bismuth Inc. ) takes the expansion opportunity while Bismuth Inc. ( Argon Co. ) does not, then Argon Co. ( Bismuth Inc. ) will have a new profit of 80 billion dollars, while Bismuth Inc. ( Argon Co. ) will have a new profit of 40 billion dollars, having been out-competed.
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If both companies take the expansion opportunity, then the quantity of available mineral will become exhausted and both companies will have a new profit of 0 dollars.
Which choice should they make to optimize their expected individual profit?
Assume that both companies are rational and self-interested.
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1 solution
By symmetry, we may only consider the perspective of Argon Co. There are two possible decisions A could make:
Case (1): A does not take the opportunity. If B does not take the opportunity, then A has a payoff of 50. If B takes the opportunity, then A has a payoff of 40. The expected payoff is then P 1 = 2 4 0 + 5 0 = 4 5 .
Case (2): A takes the opportunity. If B does not take the opportunity, then A has a payoff of 80. If B takes the opportunity, then A has a payoff of 0. The expected payoff is then P 2 = 2 8 0 + 0 = 4 0 .
As P 1 > P 2 , both companies should not take the opportunity.