Decision Making using Game Theory: An introduction for managers

62Sequential decision making and cooperative games of strategyExample 4.5 A university research partnershipAstraZeneca, the pharmaceutical company whose R&D division is headquarteredat Sodertajle, Sweden, was involved in a research partnership with aleading Swedish university. Unfortunately, the partnership was not successfuland the agreement to collaborate lapsed. A newly appointed professor at theuniversity wishes to revive the consortium and the company is considering howmuch to commit to it.The company has decided on some involvement at least. If the companyundertakes a small commitment (i.e. another company carries out the clinicaltrials) and it fails to produce any beneWt, it will lose 150 hours of staV time. If thecompany undertakes a large commitment (i.e. AstraZeneca itself carries out theclinical trials) and it fails to produce any beneWt, it will lose 2250 hours of staVtime.It has been estimated that success will bring 8000 or 9000 hours of freeuniversity laboratory time and professional training to the staV, depending onwhether the company commits on a small or large scale, respectively.Figure 4.9 shows the decision tree for the game. Naturally, the companywishes to maximise its beneWts, although they will only accrue to the company ifit continues its involvement beyond the Wrst year, because of the longitudinalnature of the clinical trials.The nodes marked ‘chance’ represent the uncertainties associated withthe company’s involvement; in other words, what nature does inresponse to the company’s selected strategy. The nodes marked ‘company’represent the selection of a strategy by the company.The method of backward induction, α stage, reveals that the companyshould never discontinue its involvement, irrespective of its levelof commitment. So the nodes marked ‘company’ have the valuesshown in brackets and the nodes marked ‘chance’ have the values:9000p 2250(1 p) (upper chance node)and8000q 150(1 q) (lower chance node)Clearly, the company will opt for large-scale involvement only when:9000p 2250(1 p) 8000q 150(1 q)