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Sourcing from competitors triggers innovation spillovers that challenge cooperative stability and strategic decisions. This study employs a nonlinear dynamic game-theoretic model to analyze supply chain behavior under two innovation modes: non-cooperative (firms independently set prices and innovation levels) and cartel cooperative (joint innovation optimization followed by independent pricing). Incorporating behavioral economics (perceived unfairness) and market heterogeneity (brand differentiation), the model reveals how strategic interactions drive system evolution. Key findings demonstrate that while high innovation spillovers enhance knowledge sharing and increase cartel profits within stable regimes, they simultaneously amplify system fragility—exceeding critical spillover thresholds induces bifurcation and chaotic dynamics, disrupting pricing mechanisms and causing severe profit volatility. Furthermore, perceived unfairness reduces cooperation willingness through negative feedback loops, destabilizing alliances, while brand differentiation exhibits dual effects: moderate levels bolster market stability whereas excessive differentiation erodes resilience. Attraction basin analysis confirms the coexistence of multi-stability states (periodic, quasi-periodic, chaotic), highlighting strategic uncertainty. • A chaos-game for predicting destabilization in innovation alliances; • Quantified robustness thresholds enabling bifurcation risk alerts; • Fairness-sensitive agents modeling behavioral feedback loops; • Basin-attraction proven multi-stability in collaborative systems.
Zhang et al. (Mon,) studied this question.