How many pure strategy Nash equilibria are there? What is true about this game?

Question

How many pure strategy Nash equilibria are there?
What is true about this game? a) the Batter has a dominant strategy b) neither team has dominant strategy, but the batter has a dominated strategy c) the fielder has a dominant strategy d) neither team has a dominant strategy, but the fielder has a dominated strategy e) neither team has a dominant strategy or dominated strategy
Use the following information to answer questions 15-16. Now let's play baseball, this time with only three strategies. Probability of the Batter getting on base, given any two strategies, is given in the table below. Remember that the Fielder prefers a lower probability, while the Batter prefers a higher probability. Fielder Infield Right field Left field Bunt 0.300 0.300 0.350 Batter Swing Hard Opposite Field 0.350 0.250 0.100 0.100 0.200 0.150

Explanation / Answer

Answers:

1. How many pure strategy Nash equilibria are there?

None.

    The Pure Strategy means that a specific action of a player will follow in every possible attainable situation in a game and the Nash Equilibrium neither Player have anything to gain by changing only its own strategy unilaterally. Therefore, there is no pure strategy Nash equilibria in this case.

2. What is true about this game?

e) neither team has a dominant strategy or dominated strategy

The dominant strategy refers that the results in a higher pay off regardless of what strategy the opponent chooses. In this case, we can see neither team a dominant strategy in all pay offs.

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