There are two ice-cream stores, each of whom chooses a position from ten spots along the beach: spot 1, 2, 3, . The ten spots are lined up and...

There are two ice-cream stores, each of whom chooses a position from ten spots along the

beach: spot 1, 2, 3, …10. The ten spots are lined up and separated 100 meters from each other:

1 2 3 4 5 6 7 8 9 10

The consumers are equally distributed across these ten spots. Consumers buy from the store

whose spot is closest to theirs. If the two stores are equidistant from a given spot, the consumers

at that position split their consumption equally. The aim of the ice-cream stores is to maximize

their share of the total ice-cream consumption.

a. Is there any dominated strategy? If so, spell out explicitly how one strategy is dominated by

another strategy.

b. What is the Nash Equilibrium of this game?