What is the probability that the employee will shirk?.
lega Show more Scenario 1 (length: as needed) Suppose two entities are considering collusion to make things legal consider a situation similar to OPEC except with only two countries: Saudi Arabia and Indonesia. The two countries have negotiated an agreement to restrict their production of petroleum. If both countries follow the agreement the market price of petroleum will be high and both countries will make $100 million per year. If one country reneges and produces more petroleum than dictated in the agreement then the market price will decrease. However the increased production will offset the lower price for the country that reneges so that country will make $120 million per year while the country who adhered to the agreement will make $75 million. If both countries renege on the agreement then the market price will drop further and both countries will make $80 million per year. The game is illustrated in the table below with Indonesias payoff listed first and Saudi Arabias payoff listed second in every pair: Saudi Arabia Saudi Arabia Adhere Renege Indonesia A 100 100 75 120 Indonesia R 120 75 80 80 Find the Nash Equilibria of this game. Suppose the game was repeated indefinitely. Explain how if both countries follow a trigger strategy (page 177 of your text) in which they adhere in the first period and continue to adhere to the agreement as long as the other country has always adhered but will renege otherwise leads to a long-term collusive arrangement. Hint: consider one country following the trigger strategy and determine what happens to the other countrys payoff if it decides to deviate from the strategy to play renege. What are the payoffs in that period and in all future periods? Scenario 2 (length: as needed) Consider the employee-employer relationship an employee would like to be paid but also gets some benefit by shirking his duties. An employer would like the employee to work diligently but monitoring the employee is costly. This dynamic can be modeled using a game. The payoffs of the monitoring game are given below: Business Business Monitor Dont Monitor Shirk Employee Work 0 -20 150 -100 Shirk Employee Work 100 80 100 100 For the employer this assumes that the worker receives 100 in wages produces 200 worth of goods if the employee works and monitoring costs 20. From the employees point of view the net benefit to the employee from working and getting paid is 100. If the worker can shirk and get paid the worker is better off however the employee is fired if the worker shirks and the employer monitors and thus is worse off. Show that there are no pure strategy Nash equilibria in this game. What is the mixed strategy Nash equilibria? In other words what is the probability that the employer will monitor? What is the probability that the employee will shirk? See the lecture for details on how to calculate the probabilities. Briefly interpret the Nash equilibria in words. Scenario 3 (length: as needed) Suppose the hotel in the lecture example raised its price from $30 to $30.50. With the new price the hotel expects 96 guests to arrive 5% of the time 97 guests 10% of the time 98 guests 20% of the time 99 guests 30% of the time 100 guests 25% of the time and 101 guests 10% of the time. The variable costs per occupied room and overbooking costs are the same as in the lecture. Calculate the expected revenue expected variable costs and expected costs from overbooking. Using marginal analysis should the hotel raise its price? Explain your answer. Show less