Adversarial decision strategies in multiple network phased oscillators: The Blue-Green-Red Kuramoto-Sakaguchi model

Abstract

We consider a model of three interacting sets of decision-making agents, labeled Blue, Green and Red, represented as coupled phased oscillators subject to frustrated synchronisation dynamics. The agents are coupled on three networks of differing topologies, with interactions modulated by different cross-population frustrations, internal and crossnetwork couplings. The intent of the dynamic model is to examine the degree to which two of the groups of decision-makers, Blue and Red, are able to realise a strategy of being ahead of each others' decision-making cycle while internally seeking synchronisation of this process-all in the context of further interactions with the third population, Green. To enable this analysis, we perform a significant dimensional reduction approximation and stability analysis. We compare this to a numerical solution for a range of internal and cross-network coupling parameters to investigate various synchronisation regimes and critical thresholds. The comparison reveals good agreement for appropriate parameter ranges. Performing parameter sweeps, we reveal that Blue's pursuit of a strategy of staying too-far ahead of Red's decision cycles triggers a second-order effect of the Green population being ahead of Blue's cycles. This behaviour has implications for the dynamics of multiple interacting social groups with both cooperative and competitive processes.

`Friend or foe’ and decision making initiative in complex conflict environments

“…To reduce the dimensions of the decision-making component of Eq (1) , we assume that the phases of each of the three networks have approximately phase synchronised, each network centred on a global phase given by Eq (13) . The procedure, which relies on the eigenspectrum of matrices and , is a generalisation of Section 2.3 and Appendix B of [ 42 ]—we omit the details from here for brevity. Ultimately, the average phase differences Δ BG and Δ GR are given by with the ‘renormalised’ couplings given by and the mean of each network’s natural frequencies defined by …”

“…The Kuramoto-Sakaguchi model under the parameter and initial condition values given in Table 4 , and the topology offered in Fig 2 , has been studied in our previous work [ 42 ], leading to an understanding of expected behaviours which shall inform the current work. Specifically, careful attention was given to the changes in parameter values which resulted in oscillator equilibrium, or limit cycle behaviour.…”

“…Notably, the dynamics of the conflict and population model components-defined shortly-are equivalently determined by feedback from agent decision-making. The specific network topologies and natural frequencies used for illustrative purposes throughout this work are given in Fig 2, which were the topologies considered in [42], and are provided as supplementary comma separated variable files. Frustration parameters � 2 S 1 are key considerations in this work, representing an intended lag in the oscillator states between networks.…”

“…Various components of the model in Fig 1 have been considered in conflict modelling. Adversarial decision-making was explored in [ 41 ] for two networks, and in [ 42 ] for three where the tension between each force’s strategy was highlighted. Distributed decision-making coupled with engagement was explored in [ 43 ].…”

Unifying warfighting functions in mathematical modelling: combat, manoeuvre, and C2

“…The same framework of Eq. ( 2) can be extended to two (or more (Zuparic et al, 2021)) forces or populations in competition with each other. Two elements quantified here mathematically are well documented as qualitative properties of decision-making and organisations: the cyclicity of individual decision-making, in the Perception-Action cycle of cognitive psychology (Neisser, 1976) or the Observe-Orient-Decide-Act (OODA) loop of military and business strategy (Osinga, 2006); and the role of loose and tight coupling in organisations as articulated by (Weick, 1976), (Perrow, 2011) and (Hollenbeck & Spitzmueller, 2012).…”