Computational Foundations for Strategic Coopetition: Formalizing Sequential Interaction and Reciprocity
For researchers studying cooperation in multi-stakeholder systems (human or multi-agent), this provides a formal framework for sequential reciprocity, but it is incremental as it extends prior work in the same series.
This work extends computational foundations for strategic coopetition to sequential interactions, developing four reciprocity mechanisms (bounded, memory-windowed, structural, trust-gated) validated across 15,625 parameter configurations with high behavioral target achievement (e.g., cooperation emergence 97.5%, defection punishment 100%) and empirical validation on Apple iOS App Store ecosystem (84.3% applicable points, p < 0.001, Cohen's d = 1.57).
Strategic coopetition in multi-stakeholder systems requires understanding how cooperation persists through time without binding contracts. This technical report extends computational foundations for strategic coopetition to sequential interaction dynamics, bridging conceptual modeling (i* framework) with game-theoretic reciprocity analysis. We develop: (1) bounded reciprocity response functions mapping partner deviations to finite conditional responses, (2) memory-windowed history tracking capturing cognitive limitations over k recent periods, (3) structural reciprocity sensitivity derived from interdependence matrices where behavioral responses are amplified by structural dependencies, and (4) trust-gated reciprocity where trust modulates reciprocity responses. The framework applies to both human stakeholder interactions and multi-agent computational systems. Comprehensive validation across 15,625 parameter configurations demonstrates robust reciprocity effects, with all six behavioral targets exceeding thresholds: cooperation emergence (97.5%), defection punishment (100%), forgiveness dynamics (87.9%), asymmetric differentiation (100%), trust-reciprocity interaction (100%), and bounded responses (100%). Empirical validation using the Apple iOS App Store ecosystem (2008-2024) achieves 43/51 applicable points (84.3%), reproducing documented cooperation patterns across five ecosystem phases. Statistical significance confirmed at p < 0.001 with Cohen's d = 1.57. This report concludes the Foundations Series (TR-1 through TR-4) adopting uniaxial treatment where agents choose cooperation levels along a single continuum. Companion work on interdependence (arXiv:2510.18802), trust (arXiv:2510.24909), and collective action (arXiv:2601.16237) has been prepublished. Extensions Series (TR-5 through TR-8) introduces biaxial treatment where cooperation and competition are independent dimensions.