Question

You and another person decide to work together on a project and split the resulting income equally. Income depends on how hard you work. Total income per hour, in dollars, will be 10 times the number of people working hard plus 5 times the number who slack off. Working hard costs the worker 4 dollars per hour (that is the money measure of the disutility to the worker of working hard), while slacking off costs only one dollar. Will you both work hard? Why or why not? Construct the game matrix for this situation, where strategies are either to work hard or slack off. Show that this is a prisoner’s dilemma. Finally, if working hard costs only $2, would the outcome be different? Why?!

Answer 1

Since the income has to be distributed among both the players equally not matter who works how much. So, both the players have advantage to let other person do hard work and loose 4 dollars and just enjoy in slack off and loose only 1 dollar.

w S

w (6,6) (3.5,6.5)

s (6.5,3.5) (4,4)

Like in prisoner's dilema if both players speak then players would meet a minor jail but same her if both players work hard they have to pay 4 dollars per but they would enjoy a certain amount and loose 4 dollars but if one of them slacks and looses only 1 dollar then definitely his pay off will be high since other person is doing hard and the total income would be distributed amonng both of them. In prisoner's dilemma also, if one of the player stays silent and another person speaks then that person may assumed criminal and may get full imprisonment. So, they both choose not work hard and slack off.

If working hard cost is only 2 dollars then the whole game moves towards working hard, both players would be motivated to work hard insted of slacking off if they both work hard together their pay off would be (8,8) wherase earlier they were getting only (6,6) had comparative advantage to slack off but now they dont have this choice.