a) In the game Matching Pennies, two players with pennies simultaneously choose whether to play Heads or Tails. If the two pennies match (HH or TT), then Player 1 wins. If the two pennies don't match (HT or TH), then Player 2 wins. This is essentially the same as what happens when someone serves in a game of tennis. Try to find all of the Nash Equilibria in the game shown below. Payoffs are listed in terms of profits to Venus (TV) and to Serena (Ts). Serena's Return Choice Forehand Backhand Forehand ITy = -1, As = 1 ITy = 1, As = -1 Venus' Service Choice Backhand JTy = 1, Ts = -1 ITy = -1, As =1

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2. FAMOUS 2X2 GAMES: TENNIS SERVES
a) In the game Matching Pennies, two players with pennies simultaneously choose whether to play Heads or Tails. If the two
pennies match (HH or TT), then Player 1 wins. If the two pennies don't match (HT or TH), then Player 2 wins. This is
essentially the same as what happens when someone serves in a game of tennis. Try to find all of the Nash Equilibria in the game
shown below. Payoffs are listed in terms of profits to Venus (TV) and to Serena (Ts).
Serena's Return Choice
Forehand
Backhand
Forehand
Ty = -1, As = 1
ITy = 1, As = -1
Venus' Service Choice
Backhand
JTy = 1, Ts = -1
JTy = -1, Ts = 1
b) Put yourself in the shoes of Venus, who is deciding where to serve. If you serve many times during a match, what would
expect to happen if you systematically served to one side more often? What seems to be the ideal way to choose between
Forehand and Backhand?
you
Transcribed Image Text:2. FAMOUS 2X2 GAMES: TENNIS SERVES a) In the game Matching Pennies, two players with pennies simultaneously choose whether to play Heads or Tails. If the two pennies match (HH or TT), then Player 1 wins. If the two pennies don't match (HT or TH), then Player 2 wins. This is essentially the same as what happens when someone serves in a game of tennis. Try to find all of the Nash Equilibria in the game shown below. Payoffs are listed in terms of profits to Venus (TV) and to Serena (Ts). Serena's Return Choice Forehand Backhand Forehand Ty = -1, As = 1 ITy = 1, As = -1 Venus' Service Choice Backhand JTy = 1, Ts = -1 JTy = -1, Ts = 1 b) Put yourself in the shoes of Venus, who is deciding where to serve. If you serve many times during a match, what would expect to happen if you systematically served to one side more often? What seems to be the ideal way to choose between Forehand and Backhand? you
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