Question

Cheng Lee of Singapore and Josh Andrews from the United States are the odds-on favorites to win the 100-meter butterfly at the 2020 Olympic games in Tokyo. Each swimmer is tempted to enhance his chances of winning the event by doping. The Singapore Olympic Committee awards $1 million to gold medal winners, $500,000 to silver medal winners, and $250,000 to bronze medal winners. The United States Olympic Committee awards $37.500 to gold medal winners, $22,500 for silver medal winners, and $15,000 for bronze medal winners. Each individual must decide whether or not to dope. We will assume that if one person dopes and the other does not, the doper will win the gold medal and the other person will win the silver medal. If both dope (or neither dopes), the odds that each person will win the gold is 50%, which implies that the odds of winning the silver is also 50%. a. Draw a matrix that shows each person's decision and the associated payoffs.

Answer 1

Anc): (a) The payoff matrix is as follows: Josh Andrews Dope Does not dope | 6750,000, $30,000) |($1,000,000, $ 22,500) Dope Ching ($500,000, $ 37,500). 1 ($750,000, $ 30,000) Does not dope

In case if both dope (or neither dopes) , we find the payoff of each player by the following method:

Lee's payoff- 0.5x1,000,000 + 0.5x500,000 = $750,000

Andrews' payoff- 0.5x37,500 + 0.5x22,500 = $30,000

(b) Lee has the dominant strategy "Dope" because it gives him a higher payoff no matter what Andrews chooses.

(c) Andrews has the dominant strategy "Dope" as well because it gives him higher payoff no matter what Lee chooses.

(d) The Nash equilibrium in this case is (Dope, Dope). The playoffs of Lee and Andrews are $750,000 and $30,000 respectively.