The table shows consumer valuations for two types of Callawa

The table shows consumer valuations for two types of Callaway golf shoes. Suppose Callaway prices the C-Tech shoes at $85 and the Xtreme shoes at $125. Show that this pricing scheme is incentive compatible. Suppose Callaway prices the C- Tech shoes at $70 and the Xtreme shoes at $125. Show that this pricing scheme is NOT incentive-compatible.

Solution

A mechanism or a process is known to be incentive-compatible (IC) if every participant can achieve the best outcome to him/herself just by acting according to his/her true preferences

a. In this option Callaway gives reduction in the prices of C-Tech shoes whereas increases the price of an X-treme shoe. A weekend Hacker will prefer an ordinary golf shoe against a golf champion. The C-tech shoes are priced less than that of Etreme shoes but they are priced way too high than the Xtreme golf shoes. Hence even if the C-Tech shoes are priced less than the Xtreme shoes, both the weekend hacker and the club champion will prefer the X-treme shoes as they are available for relatively cheaper price than the other shops. Hence the shop will be able to have good profits as well as the customers will be able to get good brand in reasonable price. Thereby allowing all participants to have good outcome based on their preference. Hence option a is incentive compatible.

b. In this option the first shoes are priced way too less and Xtreme shoes are retained at the same price. In this scenario people will only try to use the best of available offer. So customers will try to exploit the available discounts. Thereby the owner will not be able to gain profits. Hence the option b is not incentive compatible.