In a zero-sum game a worker and a manager play, the worker can actually work or

Question

In a zero-sum game a worker and a manager play, the worker can actually work or can shirk (not work). The manager can monitor the worker or not monitor the worker. If the manager (the row player) monitors and the worker works, then the manager loses a value of one because the manager could have done something else. Also if the manager doesn’t monitor and the worker shirks the manager loses one because the worker isn’t being productive. Otherwise the manager gains a value of one. The value of the game is

Explanation / Answer

There are these possibilities

A Manager monitoring has prob p say and a worker working has a prob p'

then value of the game would be

pp'(-1)+p(1-p')1+(1-p)p' -(1-p)(1-p')

= -pp'+p-pp'+p'-pp'-(1-p-p'+pp')

= -3pp'+2p+2p'-1-p2p'2

----------------------------------

If say both p and p' = 0.5

then value of the game is

-2(0.25)

=-0.5

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