a True or False Let mi be a mixed strategy for player i It i

a) True or False: Let mi be a mixed strategy for player i. It is possible that mi is strictly dominated, but each pure strategy si for which mi(si) > 0 is not strictly dominated. Either provide a proof or a counter-example.

b) Let a mixed strategy m i be a best response for player i to mi i.e. m i BRi(mi). •

(i) Show that if si is a pure strategy such that m i (si) > 0, then si BRi(mi). •

(ii) Let s 1 i , . . . , sk i BRi(mi). Let mi be a mixed strategy that only randomizes among the pure strategies s 1 i , . . . , sk i . That is Pk j=1 mi(s j i ) = 1. Show that mi BRi(mi).

Solution

a) True or False: Let mi be a mixed strategy for player i. It is possible that mi is strictly dominated, but each pure strategy si for which mi(si) > 0 is not strictly dominated. Either provide a proof or a counter-example.

FALSE