State University is about to play Ivy College for the statetennis championship. The State team has two players (A andB), and the Ivy team has three players (X, Y, and Z). Thefollowing facts are known about the players’ relative abilities: X will always beat B; Y will always beat A; A will alwaysbeat Z. In any other match, each player has a12chance ofwinning. Before State plays Ivy, the State coach mustdetermine who will play first singles and who will play secondsingles. The Ivy coach (after choosing which two players willplay singles) must also determine who will play first singlesand second singles. Assume that each coach wants tomaximize the expected number of singles matches won bythe team. Use game theory to determine optimal strategies foreach coach and the value of the game to each team.
State University is about to play Ivy College for the state
tennis championship. The State team has two players (A and
B), and the Ivy team has three players (X, Y, and Z). The
following facts are known about the players’ relative abilities:
X will always beat B; Y will always beat A; A will always
beat Z. In any other match, each player has a
1
2
chance of
winning. Before State plays Ivy, the State coach must
determine who will play first singles and who will play second
singles. The Ivy coach (after choosing which two players will
play singles) must also determine who will play first singles
and second singles. Assume that each coach wants to
maximize the expected number of singles matches won by
the team. Use game theory to determine optimal strategies for
each coach and the value of the game to each team.
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