394 INTERNATIONAL STUDIES QUARTERLY Plane Column (pursue a1) (pursue a3） 61 Row --pursue 82 1 83 3 Figure 2:Reduced Outcome Matrix Given Complete Information If complete information is assumed,each player will be able to determine those players with straightforward strategies.Since a player with a straightforward strategy cannot be hurt and may do better by choosing it,neither Plane nor Column would presumably choose either of their dominated strategies.Hence, one can eliminate these strategies from further consideration and,in Figure 1,they are crossed out.3 With these strategies eliminated,Figure I reduces to Figure 2 where one can easily see that only Row has more than one strategy choice left.Since Row clearly prefers the outcome associated with his third strategy,a3,to the outcome associated with either of his other two strategies,ai,Row's rational choice would be to "pursue a3"and thereby bring about a3 as the sophisti- cated outcome. The fact that a is the sophisticated outcome of this game is somewhat paradoxical.In the original outcome matrix,Plane can reach his first preference a in almost twice as many ways as he can reach either of the other two alternatives.Ostensibly,while Plane seems to be in the best tactical position,his worst outcome is adopted when all the players use sophisticated strategies.4 3.In this analysis,it is assumed that a player with a straightforward strategy adopts that strategy immediately.This simplification in Farquharson's(1969)reduction method is suggested by Brams(1975:67-78). 4.Farquharson(1969:50)calls a similar result with a slightly different decision rule "The Paradox of the Chairman's Vote." 物2226w rms and Conditions
394 INTERNATIONAL STUDIES QUARTERLY Plane Column (pursue a,) (pursue a3) al 1 Row - - pursue a2 1 a3 3 Figure 2: Reduced Outcome Matrix Given Complete Information If complete information is assumed, each player will be able to determine those players with straightforward strategies. Since a player with a straightforward strategy cannot be hurt and may do better by choosing it, neither Plane nor Column would presumably choose either of their dominated strategies. Hence, one can eliminate these strategies from further consideration and, in Figure 1, they are crossed out.3 With these strategies eliminated, Figure I reduces to Figure 2 where one can easily see that only Row has more than one strategy choice left. Since Row clearly prefers the outcome associated with his third strategy, a3, to the outcome associated with either of his other two strategies, a,, Row's rational choice would be to "pursue a3" and thereby bring about a3 as the sophisticated outcome. The fact that a3 is the sophisticated outcome of this game is somewhat paradoxical. In the original outcome matrix, Plane can reach his first preference a, in almost twice as many ways as he can reach either of the other two alternatives. Ostensibly, while Plane seems to be in the best tactical position, his worst outcome is adopted when all the players use sophisticated strategies.4 3. In this analysis, it is assumed that a player with a straightforward strategy adopts that strategy immediately. This simplification in Farquharson's (1969) reduction method is suggested by Brams (1975: 67-78). 4. Farquharson (1969: 50) calls a similar result with a slightly different decision rule "The Paradox of the Chairman's Vote." This content downloaded on Sun, 27 Jan 2013 21:58:56 PM All use subject to JSTOR Terms and Conditions
Zagare GENEVA CONFERENCE 1954 395 It should be pointed out that this result occurs not because the sophisticated outcome in this example is in any sense "socially preferred."In fact,the configuration of preferences of the three players actually creates a paradox of voting situation and makes no alternative socially preferred,i.e.,majorities are cyclical. If information is complete,Plane has no recourse in this strategically unfavorable position.Sophisticated strategies are optimal when information is complete.However,as Brams and Zagare (1977)have shown,if Plane could conceal his true preferences and somehow announce a false preference order which Row and Column believe,two additional strategies become available.First,after this announcement,Plane could act as if this announcement were his true preferences in his play of the game.This type of deceptive strategy is called tacit deception since the other players cannot detect the deception unless they know the user's true preference order.A second option open to Plane also entails making a false announcement but acting in the play of the game consistently with his true preferences.Since other players can easily detect an action that contradicts the deceiver's announced preference order,this strategy is called revealed deception. To illustrate how these deceptive strategies operate,assume that Plane announces his true preference order to be(a2,a1,a3) instead of(a1,az,a3).If Row and Column believe this (false) announcement,they perceive Plane's second strategy(rather than his first)to be straightforward.Since their preferences remain constant,Column continues to have a straightforward strategy (the third column)but Row does not. After eliminating the(apparent)dominated strategies of Plane and the (actual)dominated strategy of Column from considera- tion,as before,Figure I reduces to Figure 3.This figure is remarkably similar to Figure 2 except that now there is a different outcome (az)associated with Row's second strategy ("pursue a”"). Given Row's preference for az over ar and a3,his rational strategy,if he believes Plane's false announcement,is to"pursue ThPM
Zagare / GENEVA CONFERENCE 1954 395 It should be pointed out that this result occurs not because the sophisticated outcome in this example is in any sense "socially preferred." In fact, the configuration of preferences of the three players actually creates a paradox of voting situation and makes no alternative socially preferred, i.e., majorities are cyclical. If information is complete, Plane has no recourse in this strategically unfavorable position. Sophisticated strategies are optimal when information is complete. However, as Brams and Zagare (1977) have shown, if Plane could conceal his true preferences and somehow announce a false preference order which Row and Column believe, two additional strategies become available. First, after this announcement, Plane could act as if this announcement were his true preferences in his play of the game. This type of deceptive strategy is called tacit deception since the other players cannot detect the deception unless they know the users true preference order. A second option open to Plane also entails making a false announcement but acting in the play of the game consistently with his true preferences. Since other players can easily detect an action that contradicts the deceiver's announced preference order, this strategy is called revealed deception. To illustrate how these deceptive strategies operate, assume that Plane announces his true preference order to be (a2, a,, a3) instead of (a,, a2, a3). If Row and Column believe this (false) announcement, they perceive Plane's second strategy (rather than his first) to be straightforward. Since their preferences remain constant, Column continues to have a straightforward strategy (the third column) but Row does not. After eliminating the (apparent) dominated strategies of Plane and the (actual) dominated strategy of Column from consideration, as before, Figure 1 reduces to Figure 3. This figure is remarkably similar to Figure 2 except that now there is a different outcome (a2) associated with Row's second strategy ("pursue a2"). Given Row's preference for a2 over al and a3, his rational strategy, if he believes Plane's false announcement, is to "pursue This content downloaded on Sun, 27 Jan 2013 21:58:56 PM All use subject to JSTOR Terms and Conditions
396 INTERNATIONAL STUDIES QUARTERLY Plane Column (pursue a2) (pursue a3) a1 1 Row --pursue 92 2 83 3 Figure 3:Reduced Outcome Matrix Given Plane's False Announcement az."If Plane acts consistently with his announcement and also chooses to "pursue az,"the(manipulated)sophisticated outcome is az,which is a better outcome for Plane than the (unmani- pulated)sophisticated outcome as.Thus,Plane has an incentive tacitly to deceive the other players in this game. It is important to note that the (manipulated)sophisticated outcome induced by Plane's tacit deception is not stable with respect to Plane's true preference order.By choosing his strategy "pursue a,"Plan could induce al as the (manipulated)sophisti- cated outcome which he prefers to the tacit outcome.How- ever,Plane's choice of this strategy is inconsistent with his announced preference order.Since the other players can read- ily observe this inconsistency,Plane's action reveals his decep- tion to them.Depending on the value Plane associates with his most-preferred alternative,it may or may not be rational for Plane to reveal his deception and risk the loss of his future credibility. The Geneva Conference Game The structure of the game just discussed is strikingly similar to that of a game played at the Geneva Conference on Indochina in 1954.That game began to crystallize in late 1953.By the fall of that year,the Franco-Vietminh War was stalemated and pres- sures began to mount on the French government of Joseph Laniel 品2品226w
396 INTERNATIONAL STUDIES QUARTERLY Plane Column (pursue a2) (pursue a3) a, 1 / Row - - pursue _a2 2 a3 3 Figure 3: Reduced Outcome Matrix Given Plane's False Announcement a2." If Plane acts consistently with his announcement and also chooses to "pursue a2," the (manipulated) sophisticated outcome is a2, which is a better outcome for Plane than the (unmanipulated) sophisticated outcome a3. Thus, Plane has an incentive tacitly to deceive the other players in this game. It is important to note that the (manipulated) sophisticated outcome induced by Plane's tacit deception is not stable with respect to Plane's true preference order. By choosing his strategy "pursue a," Plan could induce ai as the (manipulated) sophisticated outcome which he prefers to the tacit outcome. However, Plane's choice of this strategy is inconsistent with his announced preference order. Since the other players can readily observe this inconsistency, Plane's action reveals his deception to them. Depending on the value Plane associates with his most-preferred alternative, it may or may not be rational for Plane to reveal his deception and risk the loss of his future credibility. The Geneva Conference Game The structure of the game just discussed is strikingly similar to that of a game played at the Geneva Conference on Indochina in 1954. That game began to crystallize in late 1953. By the fall of that year, the Franco-Vietminh War was stalemated and pressures began to mount on the French government of Joseph Laniel This content downloaded on Sun, 27 Jan 2013 21:58:56 PM All use subject to JSTOR Terms and Conditions