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Bargaining and Rationalist Explanations for War
Unformatted Document Text:  28 ii) Usually if the condition for “accept” is not satisfied, the state would reject the offer. However, in scenario III, and IV, when state 2’s acceptance conditions do meet, war ensues. iii) denotes state 2’s offer when it is his turn to make offer in the next round. However, when state 1, for any reason, deviate from , the game may not definitely enter the next round, for example, scenario III and IV. War may ensue when state 1 makes some mistakes. The SPEs also suggest a way to compare the effect of each individual advantage. The method is straightforward: if we keep the other two dimensions unchanged, the effect of the third dimension is manifested by comparing the same state’s utility in the presence and absence of this dimension. The effect of all three dimensions is illustrated in Figure 4. For instance, to investigate the effect of military advantage, I display all the four possible combinations of the bargaining and first-move advantage in Figure 4(a): (A) a state enjoys both bargaining and first- move advantages; (B) a state enjoys only bargaining advantage; (C) a state enjoys only first- move advantage; and (D) a state has no advantage at all. In each combination, I compare a state’s utility in SPEs when she enjoys military advantage, denoted by , with the utility when not, denoted by . To repeat, and are not the utility of two adversaries in the same games, but the same state’s utility in two games differing only in the concerned dimension. In this figure, the vertical axis represents the utility, which is between 0 and 1; and the horizontal axis stands for the four combinations of the other two advantages. The four round points (A, B, C, and D) connected by a dashed-line represent under each of the four combinations. Similarly, the four square points ( ′, ′, ′, and ′) tied by a solid-line stand for the corresponding utility . Each utility corresponds to one outcome in Table 3. The subscripts of and mark the related state and scenario in Table 3. For instance, at point A, ’s utility is denoted by , meaning ’s utility is equal to state 1’s utility in scenario I of Table 3, which is equal to 1. Similarly, I single out first-move advantage in Figure 4(b), in which represents the state that initiates the crisis bargaining, or state 1, and the state who responds in round 0, or state 2. In Figure 4(c), the

Authors: Ye, Min.
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28
ii) Usually if the condition for “accept” is not satisfied, the state would reject the offer. However, in scenario
III, and IV, when state 2’s acceptance conditions do meet, war ensues.
iii)
denotes state 2’s offer when it is his turn to make offer in the next round. However, when state 1, for any
reason, deviate from
, the game may not definitely enter the next round, for example, scenario III and IV.
War may ensue when state 1 makes some mistakes.
The SPEs also suggest a way to compare the effect of each individual advantage. The
method is straightforward: if we keep the other two dimensions unchanged, the effect of the third
dimension is manifested by comparing the same state’s utility in the presence and absence of this
dimension. The effect of all three dimensions is illustrated in Figure 4. For instance, to
investigate the effect of military advantage, I display all the four possible combinations of the
bargaining and first-move advantage in Figure 4(a): (A) a state enjoys both bargaining and first-
move advantages; (B) a state enjoys only bargaining advantage; (C) a state enjoys only first-
move advantage; and (D) a state has no advantage at all. In each combination, I compare a state’s
utility in SPEs when she enjoys military advantage, denoted by
, with the utility when not,
denoted by
. To repeat,
and
are not the utility of two adversaries in the same games, but
the same state’s utility in two games differing only in the concerned dimension. In this figure, the
vertical axis represents the utility, which is between 0 and 1; and the horizontal axis stands for
the four combinations of the other two advantages. The four round points (A, B, C, and D)
connected by a dashed-line represent
under each of the four combinations. Similarly, the four
square points ( ′, ′, ′, and ′) tied by a solid-line stand for the corresponding utility
. Each
utility corresponds to one outcome in Table 3. The subscripts of
and
mark the related state
and scenario in Table 3. For instance, at point A, ’s utility is denoted by
, meaning ’s utility
is equal to state 1’s utility in scenario I of Table 3, which is equal to 1. Similarly, I single out
first-move advantage in Figure 4(b), in which represents the state that initiates the crisis
bargaining, or state 1, and the state who responds in round 0, or state 2. In Figure 4(c), the


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