Computational Foundations for Strategic Coopetition: Formalizing Interdependence and Complementarity

TL;DR

The paper addresses the quantitative analysis of strategic coopetition by merging i* structural dependencies with game-theoretic equilibrium concepts. It introduces interdependence and complementarity as core dimensions, and provides a structured translation framework to convert qualitative i* models into a quantitative utility-based game framework, culminating in a Coopetitive Equilibrium. Through both experimental validation of functional-form robustness (power vs. logarithmic value functions) and empirical validation on the Samsung-Sony S-LCD joint venture, it demonstrates that the approach captures real-world coopetitive dynamics and supports scenario-based decision making. The work lays a foundation for a broader research program in requirements engineering and multi-agent systems, with companion studies on trust, team production, and reciprocity mechanisms.

Abstract

Modern socio-technical systems are characterized by strategic coopetition where actors simultaneously cooperate to create value and compete to capture it. While conceptual modeling languages like i* provide rich qualitative representations of strategic dependencies, they lack mechanisms for quantitative analysis of dynamic trade-offs. Conversely, classical game theory offers mathematical rigor but strips away contextual richness. This technical report bridges this gap by developing computational foundations that formalize two critical dimensions of coopetition: interdependence and complementarity. We ground interdependence in i* structural dependency analysis, translating depender-dependee-dependum relationships into quantitative interdependence coefficients through a structured translation framework. We formalize complementarity following Brandenburger and Nalebuff's Added Value concept, modeling synergistic value creation with validated parameterization. We integrate structural dependencies with bargaining power in value appropriation and introduce a game-theoretic formulation where Nash Equilibrium incorporates structural interdependence. Validation combines comprehensive experimental testing across power and logarithmic value function specifications, demonstrating functional form robustness, with empirical application to the Samsung-Sony S-LCD joint venture (2004-2011), where logarithmic specifications achieve validation score 59/60 compared to power functions (55/60), with both demonstrating strong empirical fit to S-LCD historical patterns. This technical report serves as the foundational reference for a coordinated research program examining strategic coopetition in requirements engineering and multi-agent systems, with companion work addressing trust dynamics, team production, and reciprocity mechanisms.

Figures (9)

• Figure 1: i* Strategic Dependency model for Platform-Developer coopetition. The App Developer (D) depends on the Platform Provider (P) for Platform Access (resource, criticality 1.0, weight 0.6) and User Discovery (resource, criticality 0.6, weight 0.4). The Platform Provider depends on the Developer for App Ecosystem Quality (softgoal, criticality 0.1, weight 0.5). This asymmetric dependency structure yields interdependence coefficients: $D_{DP} = 0.84$ (Developer's high dependence on Platform), $D_{PD} = 0.1$ (Platform's low dependence on any single Developer).
• Figure 2: Interdependence effects across functional forms. Both specifications show monotonically increasing cooperation with interdependence. Power functions exhibit 57% increase from $D=0$ to $D=0.9$, logarithmic functions show 52% increase---remarkably consistent response magnitudes validating functional form robustness.
• Figure 3: Complementarity effects across functional forms. Both specifications show superlinear value growth with $\gamma$. Power functions exhibit 120% value increase from $\gamma=0$ to $\gamma=2$, logarithmic functions show 115% increase---highly consistent response confirming complementarity mechanisms are robust to functional form choice.
• Figure 4: Framework robustness across functional forms. Left panel compares effect sizes for interdependence, complementarity, and synergistic interactions---both specifications show consistent positive effects despite magnitude differences. Right panel confirms both specifications pass all three core theoretical tests, validating framework generality.
• Figure 5: i* Strategic Dependency model for Samsung-Sony S-LCD joint venture. Sony depends on Samsung for LCD Panel Manufacturing Capacity (resource, criticality 1.0, high importance) and Gen 7 Production Expertise (resource, criticality 0.9, high importance). Samsung depends on Sony for Capital Investment (resource, $2B, criticality 0.8, high importance), Guaranteed Panel Offtake (goal, criticality 0.7, high importance), and Premium Brand Association (softgoal, criticality 0.5, medium importance). This dependency structure yields interdependence coefficients: $D_{\text{Sony},\text{Samsung}} = 0.8$ (Sony's high dependence on Samsung's manufacturing), $D_{\text{Samsung},\text{Sony}} = 0.6$ (Samsung's moderate dependence on Sony's capital and market access).

Theorems & Definitions (3)

• Definition 1: Interdependence
• Definition 2: Complementarity
• Definition 3: Coopetitive Equilibrium