Question

Serena and Venus are playing Tennis. Consider a single point in which Serena is serving. She has to decide whether to serve to Venus’s forehand or backhand. Venus has to anticipate either a forehand or a backhand. The following table gives the success percentage for Serena.

Venus Anticipate Anticipate backhand forehand+ Serve to 80 20 Serena forehand? Serve to backhand

For instance, if Serena serves to the forehand and Venus anticipates a backhand, Serena is likely to win 80 percent of the time. Serena wants to maximize the probability that she wins, while Venus wants to minimize it.

1. What is Venus’s best response if Serena is serving to the forehand?
2. What is Serena’s best response if Venus is anticipating a forehand?
3. Is there a dominant strategy for Serena? If yes, what is it? If no, explain why not.
4. Is there a pure strategy Nash equilibrium in this game? If yes, what is it? If no, explain why not.
5. Find the mixed strategy Nash equilibrium of this gam

Answer 1

a). If Serena is serving to the forehand then there is 20%chance of Venus to anticipate it and make Serena loose. So it will be her best response.

b). Serena best response if Venus is anticipating a forehand would be hitting a backhand. Then she will wins the game.

c). There is a dominant strategy for this game to Serena. Because Venus game value of anticipating opposite to what Serena does is much higher than anticipating correct choice. Hence it is a dominant strategy for winning of Serena or favourable to serena.