Zagare GENEVA CONFERENCE 1954 393 Column players results in the outcome al at the intersection of the first plane,first row,and first column. To illustrate the subsequent analysis,assume that the players prefer the outcomes in the order listed: Plane: (a1,a2,a3) Row: (a2,a3,a） Column: (a3,a1,az) How,then,should the players select a strategy that ensures the best possible outcome for themselves?If information is complete, that is,if the players are informed about both the preferences of the other players and the decision rule,a sophisticated strategy is optimal for each player,provided that the other players are also sophisticated (Farquharson,1969). A sophisticated strategy requires each player to eliminate successively his dominated strategies.A strategy is dominated when another strategy available to a player produces at least as good a result for him in every contingency and a better result in one or more contingencies.A strategy which dominates all a player's other strategies is called straightforward.A straight- forward strategy is a player's unconditionally best strategy. In the game outlined above,a emerges as the"sophisticated" outcome,as may easily be demonstrated.From Figure I it can be seen that both Plane and Column have straightforward strategies. For Plane,the choice of his strategy "pursue ar"(the first plane) is unconditionally best since it dominates both of his other two strategies,that is,no matter what choices are made by the other players,the outcomes resulting are either the same as or better than the outcomes resulting from the choice of either of his other two strategies,given his preference scale postulated earlier. Similarly,Column's choice of "pursue a"(the third column)is straightforward-it dominates both his first and second strate- gies. In contrast,Row has no unconditionally best strategy.His second strategy dominates his first but not his third.Therefore, Row's choice of a best strategy depends upon the other two players'choices. ThPMZagare / GENEVA CONFERENCE 1954 393 Column players results in the outcome ai at the intersection of the first plane, first row, and first column. To illustrate the subsequent analysis, assume that the players prefer the outcomes in the order listed: Plane: (a,, a2, a3) Row: (a2, a3, al) Column: (a3, a,, a2) How, then, should the players select a strategy that ensures the best possible outcome for themselves? If information iscomplete, that is, if the players are informed about both the preferences of the other players and the decision rule, a sophisticated strategy is optimal for each player, provided that the other players are also sophisticated (Farquharson, 1969). A sophisticated strategy requires each player to eliminate successively his dominated strategies. A strategy is dominated when another strategy available to a player produces at least as good a result for him in every contingency and a better result in one or more contingencies. A strategy which dominates all a player's other strategies is called straightforward. A straight￾forward strategy is a player's unconditionally best strategy. In the game outlined above, a3 emerges as the "sophisticated" outcome, as may easily be demonstrated. From Figure l it can be seen that both Plane and Column have straightforward strategies. For Plane, the choice of his strategy "pursue ai" (the first plane) is unconditionally best since it dominates both of his other two strategies, that is, no matter what choices are made by the other players, the outcomes resulting are either the same as or better than the outcomes resulting from the choice of either of his other two strategies, given his preference scale postulated earlier. Similarly, Column's choice of "pursue a3" (the third column) is straightforward-it dominates both his first and second strate￾gies. In contrast, Row has no unconditionally best strategy. His second strategy dominates his first but not his third. Therefore, Row's choice of a best strategy depends upon the other two players' choices. This content downloaded on Sun, 27 Jan 2013 21:58:56 PM All use subject to JSTOR Terms and Conditions