41. Every zero-sum game may be written using ordinal payoffs as used for the partial-conflict games analyzed in this chapter. Return to Example 1 (page 623) and change the payoffs to ordinal payoffs—remember to include payoffs for both Mark and Lisa. Do Mark’s and Lisa’s decisions to choose the Suburban hospital and the 8 A.M. to 4 P.M. shift remain an equilibrium? Explain, using ordinal payoffs.
41.
The zero-sum payoff matrix from Example 1 has been transformed below by using ordinal payoffs.
| (2, 7) | (3, 6) | (1, 8) |
| (6, 3) | (5, 4) | (7, 2) |
| (8, 1) | (2, 7) | (4, 5) |
The (Suburban, 8 A.M.–4 P.M. shift) outcome is still an equilibrium. Mark has no incentive to change the hospital location (the row) because payoffs of 2 and 3 are the other two payoffs in column 2. Lisa has no incentive to switch the shift schedule because she would receive payoffs of 2 or 3, instead of the 4 for the 8 A.M. to 4 P.M. shift.