Trust Dynamics in Strategic Coopetition: Computational Foundations for Requirements Engineering in Multi-Agent Systems

TL;DR

This work addresses how trust evolves in strategic coopetition and its impact on requirements engineering. It introduces a two-layer trust model that couples immediate trust $T_{ij}^t$ with reputation damage $R_{ij}^t$, implementing asymmetric updating (builds slowly with rate $\lambda_+$ and erodes rapidly with rate $\lambda_-$) and a trust ceiling governed by reputation, capturing hysteresis. The framework integrates i* structural dependencies through an interdependence amplification factor and extends the Coopetitive Equilibrium to a Perfect Bayesian Equilibrium with evolving trust, enabling dynamic analysis of cooperation under evidence-based trust signals. Extensive validation includes a 78{,}125-configuration experimental study showing robust negativity bias and hysteresis, and a qualitative-to-quantitative empirical validation of Renault-Nissan (1999–2025) achieving 81.7% validation score, reproducing five phases of trust evolution from formation to crisis and partial recovery. The results offer practical guidance for requirements engineers to quantify trust trajectories, design trust-building protocols, and integrate trust considerations into multi-agent system design, thereby bridging conceptual modeling and computational analysis in coopetitive contexts.

Abstract

Requirements engineering increasingly occurs in multi-stakeholder environments where organizations simultaneously cooperate and compete, creating coopetitive relationships in which trust evolves dynamically based on observed behavior over repeated interactions. While conceptual modeling languages like i* represent trust relationships qualitatively, they lack computational mechanisms for analyzing how trust changes with behavioral evidence. Conversely, computational trust models from multi-agent systems provide algorithmic updating but lack grounding in requirements engineering contexts and conceptual models. This technical report bridges this gap by developing a computational trust model that extends game-theoretic foundations for strategic coopetition with dynamic trust evolution. We introduce trust as a two-layer system with immediate trust responding to current behavior and reputation tracking violation history. Trust evolves through asymmetric updating where cooperation builds trust gradually while violations erode it sharply, creating hysteresis effects and trust ceilings that constrain relationship recovery. We develop a structured translation framework enabling requirements engineers to instantiate computational trust models from i* dependency networks and organizational contexts. Comprehensive experimental validation across 78,125 parameter configurations establishes robust emergence of negativity bias, hysteresis effects, and cumulative damage amplification. Empirical validation using the Renault-Nissan Alliance case study (1999-2025) achieves 49 out of 60 validation points (81.7%), successfully reproducing documented trust evolution across five distinct relationship phases including crisis and recovery periods. This technical report builds upon its foundational companion work in arXiv:2510.18802.

Figures (20)

• Figure 1: Parameter correlation matrix for the seven-parameter factorial design across 78,125 configurations. The heatmap reveals near-zero correlations (all $|r| < 0.05$) between core parameters ($\lambda_+$, $\lambda_-$, $\mu_R$, $\delta_R$, $\xi$, $\rho$, $\kappa$), confirming orthogonal parameter space exploration by design. Diagonal elements show perfect self-correlation (1.0) as expected. Off-diagonal near-zero values validate that the factorial sweep independently varies each dimension without confounding, enabling clean attribution of outcome variations to specific parameters. This independence ensures that parameter sensitivity analysis (Figure \ref{['fig:param_sensitivity']}) identifies true causal influences rather than correlation artifacts.
• Figure 2: Distribution of trust building rates across 78,125 configurations, organized by trust building parameter $\lambda_+$. The violin plot shows five distinct distributions corresponding to the five tested levels of $\lambda_+$$\in$ {0.05, 0.075, 0.10, 0.125, 0.15}, with width indicating frequency density at each rate value. Building rates range from 0.020 (slowest trust accumulation) to 0.040 (fastest accumulation), with median 0.032 and mean 0.031 $\pm$ 0.007. The strong clustering within each $\lambda_+$ level and clear separation between levels demonstrates that $\lambda_+$ dominates building rate outcomes with minimal influence from other parameters, consistent with correlation analysis showing $r = 0.988$ between $\lambda_+$ and building rate. The narrow within-group distributions (coefficient of variation < 10%) validate that trust accumulation speed is robustly determined by the positive learning rate parameter across diverse settings of other parameters. This confirms that practitioners can reliably control relationship development pace through $\lambda_+$ specification.
• Figure 3: Three-dimensional visualization of parameter space exploration across 78,125 configurations. The scatter plot projects the seven-dimensional parameter space onto three principal dimensions, with points colored by reputation decay rate $\delta_R$ ranging from low (blue) to high (red). The dense, uniform distribution of points throughout the visible volume demonstrates comprehensive exploration of the parameter space with no sparse regions or clustering artifacts. All combinations of trust building rate $\lambda_+$, erosion rate $\lambda_-$, and reputation parameters are well-represented, validating the factorial design's thoroughness. The color gradient shows that $\delta_R$ variation spans the entire parameter space uniformly, confirming independence from other dimensions as shown in Figure \ref{['fig:param_correlation']}. This visualization provides confidence that observed phenomena emerge across diverse parameter regimes rather than narrow regions.
• Figure 4: Distribution of negativity ratios ($\lambda_- / \lambda_+$) across 78,125 parameter configurations. The histogram shows frequency distribution with median (green vertical line) at 3.00 precisely matching the empirical target from behavioral trust literature slovic1993trustrozin2001negativity. The distribution ranges from 1.00 (symmetric updating) to 9.00 (extreme asymmetry), with mean 3.47 $\pm$ 1.93 (red dashed line). Approximately 68% of configurations fall within $\pm$1 ratio unit of the median, demonstrating concentration around the validated 3:1 erosion-to-building asymmetry. The positive skew (mean > median) indicates that stronger negativity biases are more common than weaker ones across parameter space, consistent with extensive empirical evidence for negativity dominance in social judgment. This robust emergence validates that asymmetric trust updating is an inherent architectural property of the two-layer trust-reputation system rather than an artifact of specific parameter choices.
• Figure 5: Hysteresis recovery ratio versus trust erosion rate $\lambda_-$ across 78,125 configurations, with points colored by trust building rate $\lambda_+$. The scatter plot reveals that recovery ratios (measured after 35 periods of sustained cooperative effort following severe violation) range from 0.788 to 1.171, with median 1.112 indicating typical recovery to approximately 111% of pre-violation baseline. The color gradient demonstrates strong influence of building rate $\lambda_+$ on recovery potential: configurations with high $\lambda_+$ (warm colors, upper regions) achieve higher recovery ratios, while low $\lambda_+$ (cool colors, lower regions) experience more constrained recovery. The negative correlation between erosion rate and recovery ($r = -0.817$) confirms that faster trust erosion creates more persistent damage constraining subsequent restoration. Notably, all data points remain below 1.2, validating that trust ceiling mechanisms from reputation damage prevent complete erasure of violation history even after extended cooperative recovery periods. The tight vertical clustering at each erosion level demonstrates that recovery patterns are remarkably consistent across diverse settings of other parameters.

Theorems & Definitions (19)

• Definition 3.1: Trust in Strategic Coopetition
• Definition 3.2: Dynamic Trust Evolution
• Definition 3.3: Reputation and Trust Memory
• Definition 3.4: Trust-Dependent Cooperation
• Definition 3.5: Interdependence Amplification of Trust Sensitivity
• Definition 5.1: Immediate Trust
• Definition 5.2: Reputation Damage
• Definition 7.1: Markov Strategy
• Definition 7.2: Perfect Bayesian Equilibrium with Trust
• Proposition 7.3: Trust-Contingent Cooperation