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Homework answers / question archive / Suppose the Super Wine Co
Suppose the Super Wine Co. and Great Wine Co., two rival wine retailers, are both considering to advertise its brand on TV. The payoffs, in terms of quarterly profits in Smillion, are shown in the table below: Super Wine Co. Don't Advertise Advertise Advertise 5,5 15,3 Great Wine Co. Don't Advertise 3,15 11, 11 (a) Is there a dominant strategy for Super Wine Co. and Great Wine Co.? Explain. (b) What is (are) the Nash equilibrium(s) in the above game? Explain. (c) What is the name of this game? What does this game imply about human cooperation? (d) If both companies expect that they will be in business for an indefinite period, would your prediction in (a) and (b) be different? Explain. Q2. Suppose a manager is considering whether or not to monitor employees, and the workers are considering whether to work or shirk in their workplace. (a) Draw the payoff matrix for this game. Explain whether there is a dominant strategy for manager and worker. (b) What is the name of this game? Does it have any Nash equilibrium? Q3. Explain to the class how the following factors affecting effectiveness of cartels and state the direction of the effect: (a) Number of sellers in the market (b) Extent of sunk costs during initial investment (c) Extent of entry and exit barrier
The payoff matrix for the game is given below
Worker
Manager
| Work | shirk | |
| Monitor | (-1,1) | (1,-1) |
| Not monitor | (1,-1) | (-1,1) |
In this game no player has a dominant strategy because given manager is monitoring the worker would work and given manager is not monitoring the worker would shirk. Similarly if the worker is shirking the manager would monitor and if he is working, the manager chooses not to monitor.
Hence no player has dominant strategy.
ii) There is no pure nash equilibrium because each player works according to what other player does and hence there is no pure strategy nash nash equilibrium.
There would exist mixed strategy nash equilibrium which is explained below.
Given the worker works or shirks is given by probabilities p and (1-p). While given the manager monitors or not is represented by q and (1-q)
The worker would be indifferent between choosing work or shirk is given as
1q+(-1)(1-q)= -1q+(1-q)
q-1+q= -q+1-q
4q= 2
q= 1/2
So 1-q= 1/2
The same would be shown for manager, which is
(-)1p+1(1-p)= p+(-1)(1-p)
-p+ 1-p= p-1+p
2= 4p
p=1/2=1-p
Hence the worker chooses shirk or work with probability (1/2,1/2) and manager chooses to monitor or not with probability (1/2,1/2)
This type of game is called principal agent problem wherein the worker after being appointed shirks from his work ( moral hazard) in absence of efforts linked incentive. Since the worker would get the fixed salary, he would put in not much efforts at the workplace.
Also the manager would want to get higher payoff by not monitoring and hence when workers are working, the manager prefers not to monitor.
(You can comment for doubts)
