Question

Microsoft and a smaller rival often have to select from one of two competing technologies, A and B. The rival always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. If the two companies select different technologies, Microsoft’s payoff is 2 units of utility, while the small rival suffers a loss of utility of 1. If the two companies select the same technology, Microsoft suffers a loss of utility of 1 while the rival gains 1 units of utility.
Using the given information, fill in the payoffs for each cell in the matrix, assuming that each company chooses its technology simultaneously.

Microsoft
Technology A Technology B
Rival Technology A Rival ___, MS ___ Rival ____, MS ____
Technology B Rival ____, MS ___ Rival ____, MS ____
There is an equilibrium for this game in pure strategies. ___True ___False

Answer 1

Answer: true, there is an equilibrium.

Explanation:

the above game is a pure strategy. A pure strategy occur when the game is strictly determined. the criteria used to determine the pure strategy is maxi-min and min-max. max-min means selecting the least case from all best cases and min-max means selecting the best from all least cases.

Base on the criterion, the least out of all best for max-min is 1 unit and the best out of all least cases for min-max is 1 unit. the max-min is equal to the min-max,hence it strictly determined and therefore a pure strategy.