Five lifeguard towers are lined up along a beach. The leftmost is Tower 1 and the rightmost is Tower 5. Two vendors, A and B, each have an ice cream stand that can be located at one of five towers (which they place simultaneously and independently). There are 20 people located near each tower, and each person will purchase ice cream from the stand that is closest to him or her. Each purchase yields a profit of $1. Any customers that are equidistant from the stands split their business. For example, if A puts his stand at Tower 2 and B at Tower 3, then A will make $40 (from Towers 1 and 2) while B will make $60 (from Towers 3, 4, and 5).

(a) Write a payoff matrix for this game

(b) Are there any strictly dominated strategies?

(c) Are there any dominant strategies?

(d) Is there an iterated elimination of dominated strategies equilibrium?

(e) How is this exercise relevant to two political parties vying for votes?

(f) How is this exercise relevant to car companies designing similar vehicles?

Answer rating: 100% (QA)

a The payoff matrix for this game can be represented as follows where the rows indicate the choice of vendor A and the columns indicate the choice of ... View the full answer