Fig. 1: The evolution of democratic peace.
The equilibrium individual strategy of Hawk-playing for leaders (PL, purple solid line) and followers (PF, yellow solid line) and the resulting collective probability of a group playing Hawk (P, green solid line) are shown against shared decision parameter (Ω). Leader Control. When leaders wield full control over the group’s decision-making (Ω = 0) the group’s probability of playing Hawk (P) is equal to ṼL = VL/CL (dashed purple line). As Ω increases above 0, the follower’s strategy (PF) begins to have increased influence on the group’s probability of playing Hawk (P). Leader strategies respond to compensate for this increased follower influence by increasing their hawkishness (PL), which acts as an anchor and ensure that the group’s strategy (P) does not deviate from the outcome under leader control. This trend continues with increasing values of Ω until the leaders become obligate Hawk players (PL = 1), at which point they cannot increase their strategy to become any more aggressive. Compromise. Once leaders have become obligate Hawk players the group’s probability of Hawk-playing (P) begins to decrease. The followers’ increasing influence works to sway the group’s strategy (P) away from the leaders’ preference (ṼL) and towards the followers’ preference (ṼF, dashed yellow line). In compromise states, both classes are observed playing strategies of either obligate Hawk or obligate Dove, for leaders or followers respectively. Follower control. At higher values of shared decision-making parameter Ω, followers will have sufficient influence over the decision-making process to ensure that the group’s played strategy (P) matches the outcome that they favour (ṼF). For the highest values of Ω the followers respond by increasing their likelihood of playing Hawk (PF). This adjustment is required to account for the diminishing relative influence of the leader’s strategy (PL) on the group’s played strategy (P), and to keep the group-level outcome in line with the follower-control outcome (ṼF). Parameter values: ε = 0.3, C = 2 V, dc = 0.55, dv = 0.55, N = 100.
