# Question: There are two gas stations in a certain block and

There are two gas stations in a certain block, and the owner of the first station knows that if neither station lowers its prices, he can expect a net profit of $ 100 on any given day. If he lowers his prices while the other station does not, he can expect a net profit of $ 140; if he does not lower his prices but the other station does, he can expect a net profit of $ 70; and if both stations participate in this “price war,” he can expect a net profit of $ 80. The owners of the two gas stations decide independently what prices to charge on any given day, and it is assumed that they cannot change their prices after they discover those charged by the other.

(a) Should the owner of the first gas station charge his regular prices or should he lower them if he wants to maximize his minimum net profit?

(b) Assuming that the profit figures for the first gas station apply also to the second gas station, how might the owners of the gas stations collude so that each could expect a net profit of $ 105?

This “game” is not zero- sum, so that the possibility of collusion opens entirely new possibilities.

(a) Should the owner of the first gas station charge his regular prices or should he lower them if he wants to maximize his minimum net profit?

(b) Assuming that the profit figures for the first gas station apply also to the second gas station, how might the owners of the gas stations collude so that each could expect a net profit of $ 105?

This “game” is not zero- sum, so that the possibility of collusion opens entirely new possibilities.

## Relevant Questions

A statistician has to decide on the basis of one observation whether the parameter θ of a Bernoulli distribution is 0, 1/2 , or 1; her loss in dollars (a penalty that is deducted from her fee) is 100 times the absolute ...With reference to Example 9.10, for what values of Cw and Cd will Strategy 2 be preferred? Example 9.10 Suppose a manufacturer incurs warranty costs of Cw for every defective unit shipped and it costs Cd to detail an entire ...If X1, X2, . . . , Xn constitute a random sample from a population with the mean µ, what condition must be imposed on the constants a1, a2, . . . , an so that a1X1 + a2X2 + · · · + anXn is an unbiased estimator of µ? Show that for the unbiased estimator of Example 10.4, n + 1 / n ∙ Yn, the Cramer-Rao inequality is not satisfied. Verify the result given for var(n + 1 / n ∙ Yn) in Example 10.6.Post your question