It is 1850 during the days of the gold rush in california, and 100 miners are si

Question

It is 1850 during the days of the gold rush in california, and 100 miners are simultaenosuly deciding which of three plots to go to and mine for gold. In order to simplify matters, suppose it is known how much gold is in the ground at each plot. 1000 ounces in plot A, 600 ounces in plot B, and 400 ounces in Plot C. A miners payoff is the number of ounces he mines, which is assumed to equal the number of ounces at the plot he's chosen divided by the total number of miners at that plot; thus, miners at a plot are assumed to work equally effectively, so that they end up with equal shares of the amount of avalable gold. Find a nash equilibrium.

Explanation / Answer

Nash equilibrium = Total ounces of gold / Total number of miners. As the ounces are to to be divided equally.

Equilibrium = 2000 / 100 = 20 ounces per miner

Hence plot A will have 1000 / 20 = 50 miners

Plot B will have 600 / 20 = 30 miners

Plot C will have 400 / 20 = 20 miners

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