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 dominant strategy for Sheb is to place ________ sheep on the commons.

Question

Quizplus · Accepted Answer

A dominant strategy is the best strategy for a player, regardless of the strategies chosen by other players. Here, regardless of whether Monty grazes 4 or 5 sheep, Sheb benefits more from grazing 5 sheep. With 4 sheep from Monty, grazing 5 gives Sheb 85 (17*5) pounds of wool instead of 80 (20*4) pounds with 4 sheep. With 5 sheep from Monty, grazing 5 still gives Sheb 70 (14*5) pounds of wool, which is better than the 56 (14*4) pounds if only grazing 4. Thus, Sheb's dominant strategy is to graze 5 sheep.

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