Sheb and Monty, both sheep ranchers, share a pasture that is open to both. Each rancher faces the choice of grazing 4 or 5 sheep on the commons. With 8 sheep on the commons, the grass will be plentiful and each sheep will produce 20 pounds of wool per year. With 9 sheep on the commons, the grass will will be sufficient enough for each sheep to produce 17 pounds of wool per year. With 10 sheep on the commons, the grass will be sparse, and each sheep will only produce 14 pounds of wool each year.
-The Nash equilibrium occurs when Sheb places ________ sheep on the commons and Monty places ________ sheep on the commons.

Question

Quizplus · Accepted Answer

The Nash equilibrium occurs when neither player can benefit by unilaterally changing their strategy given the other player's strategy. If either Sheb or Monty chooses to graze only 4 sheep, the other can benefit by grazing 5, as the reduction in wool per sheep is outweighed by the benefit of having an additional sheep. Thus, both will choose to graze 5 sheep for a total of 10 on the commons, despite the lower wool yield per sheep, because neither can improve their situation by reducing their number of sheep while the other grazes 5.

Sheb and Monty, Both Sheep Ranchers, Share a Pasture That