Question

Instead of assuming that a player randomizes over his or her pure strategies, an alternative way to interpret mixed strategies is to assume that there are many identical players, each playing a pure strategy. Under this interpretation, one can compute the share (i.e., a number between 0 and 1) of players that play a given pure strategy and interpret that share as the frequency by which (or the probability that) that pure strategy is played. This is just a matter of interpretation, so that this problem will be framed using both interpretations. Assume that a worker’s performance is decreased by the use of social media in the workplace and that this has a negative impact on the employer’s profits. A worker who does not use social media (NS) while working produces output of value π > 0 for the employer. The value generated by a worker who uses social media (S) is 0. A worker is paid w > 0 if he is not discovered using social media, but otherwise is paid 0. The use of social media gives a utility of s > 0. The employer can decide to monitor (M) the workers but this is costly. Monitoring 2 a worker costs c > 0. Let α ∈ [0, 1] be the share of employees who use social media and let β ∈ [0, 1] be the probability that a worker is monitored.

1) Write down the matrix corresponding to the normal-form of this game.

2) Assume that w > c and w > s. How large should the share of workers who use social media in the work force be for random monitoring to be optimal?

3) With what probability should a worker be monitored to be indifferent between using social media or not? Find the Nash equilibrium in mixed strategies. Imagine now that the Nash equilibrium in mixed strategies you just found is at play but that the government is concerned about the low productivity of the work force. In particular, the government wants to reduce the use of social media on the job and is choosing between relaxing the privacy laws so that monitoring is made easier (i.e., reduce c), or forcing the social media firms to make their sites more difficult to access during work time (i.e., reduce s).

4) What should the government do? Explain.

Answer 1

ANS 2: Here w= Wage paid to the workers, w>0

c=monitoring a worker costs, c>0

s=The use of social media , s>0

Given assumptions: w>c and w>s

From the above assumptions, we can say that there must be a limitation in the use of social media among the work force during working hours. During the leisure time a labor can give time to social media. The employer must make some policies before employing labor force so that they are abide by the rules and regulations.This will give an optimal result in monitoring by the employer.

ANS 3: If an experiment can result in "n" mutually exclusive and equally likely outcomes, and if "m" of these outcomes are optimal to event 'A', then P(A), the probability that A occurs , is the ratio m/n.

Thus, P(A)=m/n

=the number of outcomes favorable to A/ the total number of outcomes.

where, P(A) is the probability that a worker be monitored to be indifferent between using social media or not.

The outcomes must be mutually exclusive, i.e, they cannot occur at the same time and each outcome must have an equal chance of occurring. Example- The use of social media or not must result in equal outcome.

ANS 4: In order to decrease the use of social media among the work force during working hours , the government must take some strict steps in order to balance the use of social media so that the working force can give full dedication towards their work. The government should implement a detailed and effective social media policy.