campaign effectiveness of and (that is, they are independent of the size of rent from A B office). Both and are assumed to be positive. VAS VBS Comparing power-sharing to violent conflict we have (14.A) ASC VAS VAC – (14.B) BSC VBS VBC – For parameter values such that both and are positive simultaneously, both ASC BSC A and choose a peaceful settlement. After the relevant manipulations and denoting and B < 0, we derive the following critical values when < (15.A) ASC  A > 0 when > where >0 . (15.B) BSC  B > 0 The positive signs of and follow from the positive signs of (13.A) and (13.B); I also A assume that A<1and B>0. Thus, power-sharing is adopted for values of that satisfy (15.A) and (15.B) simultaneously. This requires that < which in turn requires that B A, the following inequality is satisfied: 3(lnR)2–2[E+–ln(1–)]lnR–[E++ln(1–)]2+4E > which depends on the parameter values and cannot be solved analytically at this level 0, of generality. Contrary to risk neutrality, in the present setting there is no power-sharing variable to solve for; we can only find the range of values B <  < A over which a power-sharing settlement may be adopted. is the upper limit of war effectiveness A A’s at which compromises and shares power; analogously, is the lower limit of war B A A’s effectiveness at which settles for power-sharing see figure 2. To put it another way, if B – exceeds expects a higher payoff from not compromising and pursuing the rewards  A, A of office through fighting, while, if is below fighting effectiveness is so high  B, B’s that he expects a higher payoff from fighting. If for some reason rises or falls, A B power-sharing becomes more likely. Table 2: Comparative static properties of the boundaries of power-sharing, A and B > (<) 0 > (<) 0 as > (<) 0 as < (>) 0
campaign effectiveness of A and B (that is, they are independent of the size of rent from office). Both VAS and VBS are assumed to be positive. Comparing power-sharing to violent conflict we have ASC VAS – VAC (14.A) BSC VBS – VBC (14.B) For parameter values such that both ASC and BSC are positive simultaneously, both A and B choose a peaceful settlement. After the relevant manipulations and denoting and < 0, we derive the following critical values ASC > 0 when  < A (15.A) BSC > 0 when  > B where >0 . (15.B) The positive signs of A and follow from the positive signs of (13.A) and (13.B); I also assume that A<1and B>0. Thus, power-sharing is adopted for values of that satisfy (15.A) and (15.B) simultaneously. This requires that B < A, which in turn requires that the following inequality is satisfied: 3(lnR)2–2[E+–ln(1–)]lnR–[E++ln(1–)]2+4E > 0, which depends on the parameter values and cannot be solved analytically at this level of generality. Contrary to risk neutrality, in the present setting there is no power-sharing variable to solve for; we can only find the range of values B <  < A over which a power-sharing settlement may be adopted. A is the upper limit of A’s war effectiveness at which A compromises and shares power; analogously, B is the lower limit of A’s war effectiveness at which B settles for power-sharing – see figure 2. To put it another way, if  exceeds A, A expects a higher payoff from not compromising and pursuing the rewards of office through fighting, while, if  is below B, B’s fighting effectiveness is so high that he expects a higher payoff from fighting. If for some reason A rises or B falls, power-sharing becomes more likely. Table 2: Comparative static properties of the boundaries of power-sharing, A and B > (<) 0 as > (<) 0 > (<) 0 as < (>) 0
GT-PEPowerSharing.docx