Decision Making using Game Theory: An introduction for managers

136Repeated gamesStrategyBUPALargesubsidyfor NHSSmallsubsidyfor NHSGHGLargesubsidyfor NHSSmallsubsidyfor NHS20, 20 40, 1010, 40 30, 30Figures represent profits in millions of pounds sterling.Figure 7.1Pay-off matrix for two private healthcare firms.Example 7.1 Funding publicityTwo Wrms dominate the UK private healthcare industry: the General HealthcareGroup (GHG) and British United Provident Association (BUPA) (Source: Laing& Buisson). The more the state-run National Health Service (NHS) uses privatehealthcare facilities to make up the shortfall in public health provision, thegreater the proWts made by the two Wrms. However, the relationship is far fromsimple. The private healthcare Wrms actually subsidise the cost of healthcare tothe state by ‘selling’ at a discount, but their involvement and the good publicitysurrounding it enhances their proWts by attracting more subscribing customers.Generally, each Wrm’s proWt depends negatively on how much the othercompany subsidises NHS provision. The more GHG subsidises it, the fewerrecruits BUPA gets, and vice versa. If matters are simpliWed by categorisingsubsidies to the NHS as either ‘large’ or ‘small’, then the pay-oVs will be asshown on Figure 7.1 (Wgures represent proWt in millions of pounds sterling).A comparison between Example 7.1 and Example 6.4 in the previouschapter reveals the similarity. In both cases, higher pay-oVs are moredesirable than lower ones (though some models of the prisoner’sdilemma game focus on the penalties inXicted in each eventuality, inwhich case lower values indicate more preferred outcomes).It can be seen that both Wrms are better oV if they oVer smallsubsidies to the NHS, (30, 30), as opposed to big subsidies, (20, 20),because if both Wrms oVer large subsidies simultaneously, market sharewill be unaVected and proWts will fall. Nevertheless, each Wrm has an