Mixed strategy equilibrium The table below shows success rates for the receiver
ID: 1121912 • Letter: M
Question
Mixed strategy equilibrium The table below shows success rates for the receiver in returning a serve in a tennis match. Table 9.11 Receiver's success rates Receiver's move Forehand 20%, 80% 80%, 20% Backhand 75%, 25% 30%, 70% Forehand Server's aim Backhand a) Is this a zero-sum game? b) Explain why a 50/50 randomization strategy is non-optimal for each player. c) Determine the optimal strategy for each player. d) Determine the overall success rates for server and receiver, assuming each is using an optimal strategyExplanation / Answer
Answer a) No, this is not a zero sum game as in a zero sum game the gain or loss by one party is offset by some loss or gain of the other party. In this situation there is not such offset thus it is not an example of zero game theory.
Answer b) 50-50 randomization strategy is non-optimal for each player as it would result in no loss or gain of either of the players and in the game of tennis it is not always true to copy the other party's move . A 50-50 strategy would result in no benefit at all.
Answer c) Optimal staregy in case of server would be forehand when receiver's move is backhand and backhand when receiver's move is forehand.
Similarly the optimal strategy for receiver would be forehand when server's aim is forehand and backhand when server's aim is backhand.
Answer d) If both of them uses the optimal strategy then success rate for server when he uses forehand to compete with receiver's backhand would be 75% and 80% when server uses backhand when receiver's move is forehand.
Similarly, success rate for receiver when he uses forehand to compete with server's forehand would be 80% and 70% when receiver uses backhand when serverr's move is backhand.