(a) Consider a game with three players 1, 2 and 3. The players' sets of pure strategies are respectively S1 = {L, M, R}, S2 = {U, D}, S3 = {T, B}. In the box below are shown player l's payoffs to each of his three pure strategies conditional on the pure-strategy choices of players 2 and 3. These are shown in the form of triples (ul(L), ul(M), ul(R), so that, for example, the payoff to player 1 when he plays M, player 2 plays U and player 3 plays T is 1. T B U 6,1,0 | 0,4,6 D 6,4,0 0,1,6 (i) Show that for player 1 the pure stragegy M is not strictly dominated by either of the pure strategies L or R. Can M be strictly dominated by any mix of L and R?
(a) Consider a game with three players 1, 2 and 3. The players' sets of pure strategies are respectively S1 = {L, M, R}, S2 = {U, D}, S3 = {T, B}. In the box below are shown player l's payoffs to each of his three pure strategies conditional on the pure-strategy choices of players 2 and 3. These are shown in the form of triples (ul(L), ul(M), ul(R), so that, for example, the payoff to player 1 when he plays M, player 2 plays U and player 3 plays T is 1. T B U 6,1,0 | 0,4,6 D 6,4,0 0,1,6 (i) Show that for player 1 the pure stragegy M is not strictly dominated by either of the pure strategies L or R. Can M be strictly dominated by any mix of L and R?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:(a) Consider a game with three players 1, 2 and 3. The players' sets
of pure strategies are respectively S1 = {L, M, R}, S2 = {U, D}, S3 = {T, B}.
In the box below are shown player l's payoffs to each of his three pure
strategies conditional on the pure-strategy choices of players 2 and 3.
These are shown in the form of triples (ul(L), ul(M), ul(R), so that, for
example, the payoff to player 1 when he plays M, player 2 plays U and
player 3 plays T is 1.
T
B
U 6,1,0 | 0,4,6
D 6,4,0 0,1,6
(i) Show that for player 1 the pure stragegy M is not strictly
dominated by either of the pure strategies L or R. Can M be strictly
dominated by any mix ofL and R?
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