Decision Making using Game Theory: An introduction for managers

201Indexmaximin principle, in chance games 46maximiser/optimiser in games of skill 18maximising funding at New York OMB,multi-person game example 152–3McDonald’s sanction and reward system,sequential decision making example 52,54medical incompetence ethics, saddle point gameexample 82–3metagame theory 110–12minimal winning coalition theory 154minimax mixed strategies, no saddle pointgames 89minimax theorem/principle 8in chance games 47and games with no saddle points 89graphic model for 184–6proof 182–9Waldegrave fails to prove 9minimum resource theory 154–5mixed strategies, games with no saddle-points89mixed-motive two-person games of strategyabout 2, 7, 98–9Bertrand model of duopoly 116, 125–9supermarket sector example 125–7Bertrand paradox 126Bertrand–Nash equilibrium 128contract lines 121–2Cournot model of duopoly 115–16paper and packaging sector example116–20, 122–5demand functions 126dominance 99–100duopoly 115exploitation games 105–7example 106–7summary of features 114heroic games 104–5example 104–5summary of features 113–14inadmissibility 99–100iso-proWt curves 120iterated elimination of dominated strategies100–2leadership games 102–4example 102–4summary of features 113martyrdom games 107–13metagame theory 110–12stockbroker/lawyer prisoner’s dilemmagame example 108–9summary of features 114–15Nash equilibrium 98–9, 99–102, 118–20oligopoly 115pareto-ineYciency 129reaction functions 117–18solutions without Nash equilibrium points129–34mutual society/life companies changingstatus example 132–4von Stackelberg model of duopoly 115–16,122–5paper and packaging sector example116–20, 122–5see also multi-person games, mixed motivemoral imperative, Kant’s notion of 176Morgenstern, Oskar 10multi-person gamesabout 149–50mixed motive 151–3maximising funding example 152–3Nash equilibrium 151non-cooperative 150–1Nash equilibrium points 150–1partially cooperative 153–5characteristic functions 153–5imputation payments 155minimal winning coalition theory 154minimum resource theory 154–5whole pot payments 155see also power analysis/indicesmutual society/life companies changing statusexample 132–4Nash, Johnand the minimax theorem 11Nash equilibrium 98–9, 99–102, 118–21,137–8, 140, 150–1multiple Nash equilibria 142–3solving mixed strategy games without Nashequilibrium points 129–34mutual society/life companies changingstatus example 132–4natural selection 3nature as a player 3–4New York city OMB funding maximising,multi-person game example 152–3Nokia/Ericsson share issue, exploitation gamesexample 106–7non-cooperative gamesmulti-person 150–1zero-sum 2oligopoly situations 115optimisation with games of skillbasics 18–19examples 20–7optimiser/maximiser in games of skill 18ordered pairs 49ordinal pay-oVs 94–7outcome of a game 4paper and packaging sector, mixed-motivegame example 116–20, 122–5parents/predecessors, of decision edges 49pareto-eYciency 77pareto-ineYciency 129