1. Suppose that a married couple, both of whom have just finished medical school
ID: 3196405 • Letter: 1
Question
1. Suppose that a married couple, both of whom have just finished medical school, now have choices regarding their residencies. One of the new doctors has three choices of programs, while the other has two choices. They value their prospects numerically on the basis of the program itself, the citv, staying together, and other factors, and arrive at the bimatrix (5.2,5.0) (4.4,4.4) (4.4,4.1) (4.2,4.2) (4.6,4.9) (3.9,4.3) a) Find all the pure Nash equilibria (using definition) b) Which equilibria should be played? c) Find the safety levels for each player.Explanation / Answer
A,B
Let the doctors be A and B. A hs three programs A1, A2, A3 and B has got 2 programs B1 and B2. The above table shows the value the doctors prospects for each of those programs.
Let us now consider each combination:
A1:B1: 5.2:5.0
A1:B2 : 4.2, 4.2
A2: B1 : 4.4: 4.4
A2,B2 : 4.6:4.9
A3: B1 : 4.4:4.1
A3: B2 : 3.9,4.3
A gets the highest benefit by choosing A1 which is 5.2and B by choosing B1 which is 5.0 and least benifited by A3 an B2 respectively.
Lets consider if B chose B1, then if A choses A1 then both gets high value, if A2 then then both have equal and moderate gain of 4.4, if A3 then B can get low value but A has still the moderate value. This can be given by the below table
if B chooses B2
1) Nash equilibrium by definition states a stable state of a system involving the interaction of different participants, in which no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged. Thus from the above definition wehad to find out a state where no one can gain by changing their decision if the other's decision is unchanged.
From the above two tables, A chooses A2 which gives A a moderate gain no mater what B chooses. Similarly, for B if B chooses B1, except for A3 other choices have good gain, if B chooses B2, except for A2 for all the other choices the gains are low. So by choosing B1 thus B is better off most of the times.Thus the pure nash equilibrium is A2 and B1.
2) Since Both A and B has the highest gains for A1 and A2 they should play A1: B1.
3) For A the safety level is A2 where the loss is least and for B the safety level is B1 where the probabilty of loss id low.
A,B
A1 A2 A3 B1 5.2 , 5.0 4.4, 4.4 4.4, 4.1 B2 4.2, 4.2 4.6, 4,9 3.9, 4.3Related Questions
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