Decision Making using Game Theory: An introduction for managers

83Games with saddle pointsSurgeonStrategyAcceptincompetencyassessmentRejectincompetencyassessmentHospital boardDismiss withretirementpackageRetain&retrain£20 000 £10 000£50000 0Figure 5.7Pay-off matrix for professional incompetence: retain and retrain.declared competent, it will cost the hospital an estimated £50 000 incompensation.Figure 5.7 shows the pay-oV matrix for the game. Clearly, thesurgeon’s maximin strategy (£10 000) is to accept the committee’sassessment. The hospital board’s minimax strategy (also £10 000) is toretain and retrain the surgeon. This is therefore a unique saddle pointfor the game. Neither the surgeon nor the hospital board can do betterby choosing any other strategy.Example 5.2 Reforming a travel timetablePaciWc Western, one of the bus operating companies for Pearson Airport,Toronto, operates a 21-hour week for its drivers. The operations manager isrestructuring the travel timetable to the airport, oVering new routes and fewerstops, and he has three models in mind. One is based on twenty 63-minutejourneys; another on twenty-one 60-minute journeys; and a third model basedon twenty-eight 45-minute journeys (dubbed the ‘Airport Rocket’). At the sametime, the personnel manager is considering whether to employ four, Wve or sixbus drivers on the airport run.To meet the terms of a binding legal agreement with unions and the GeneralToronto Airport Authority, all bus drivers must receive the same weekly employmentat a Wxed rate, so some arrangements provide drivers with oV-theroadtime – which can be Wlled with clerical and maintenance duties - whileothers do not. Table 5.1 shows the balance of driving and oV-road periods foreach of the nine strategies.The personnel manager, choosing the number of drivers, wishes to maximisedriving time. The operations manager, choosing the travel schedule, wishes tominimise it to keep more Xexibility for other (shorter) routes and indirectlykeep maintenance and secretarial staYng to a minimum.