Decision Making using Game Theory: An introduction for managers

70Sequential decision making and cooperative games of strategy(2, 1)Accept proposalsP 2Propose changeReject proposals( 2, 0)P 1Propose no change(0, 0)Figure 4.13Proposing change: a game of perfect information.one of perfect information if every information set has only oneelement. Otherwise, the game will be one of imperfect information, asthe following example shows.Example 4.8 Proposing change under uncertaintySuppose in the situation outlined in the previous example (Example 4.7), theboard of directors had already been approached by the Sam’s Super Centres’regional manager who wished to take early retirement on health grounds. Theboard then made its decision in relation to the regional manager but, uponrequest, did not make the new operations manager aware of it before the latterhad made her recommendations for change.This game can be represented as a three-player game – the third playerbeing nature, which has decided whether or not the grounds forill-health retirement are suYciently strong (see Figure 4.14).The ordinal pay-oVs shown on Figure 4.14 are explained as follows.If the board has not accepted the regional manager’s retirement, thepay-oVs revert to those of Example 4.7 (bottom half of Figure 4.14). If