Computational Foundations for Strategic Coopetition: Formalizing Collective Action and Loyalty

TL;DR

This paper develops a formal framework for understanding strategic coopetition and collective action in multi-agent teams, incorporating loyalty dynamics and validating through extensive experiments and a real-world case study.

Contribution

It introduces loyalty-moderated utility functions and team cohesion mechanisms, extending computational models to analyze collective action and loyalty effects in multi-agent systems and human teams.

Findings

Loyalty effects increase median effort by 15.04x

Achieved 96.5% baseline free-riding detection

Validated framework with Apache HTTP Server case study

Abstract

Mixed-motive multi-agent settings are rife with persistent free-riding because individual effort benefits all members equally, yet each member bears the full cost of their own contribution. Classical work by Holmstr\"om established that under pure self-interest, Nash equilibrium is universal shirking. While i* represents teams as composite actors, it lacks scalable computational mechanisms for analyzing how collective action problems emerge and resolve in coopetitive settings. This technical report extends computational foundations for strategic coopetition to team-level dynamics, building on companion work formalizing interdependence/complementarity (arXiv:2510.18802) and trust dynamics (arXiv:2510.24909). We develop loyalty-moderated utility functions with two mechanisms: loyalty benefit (welfare internalization plus intrinsic contribution satisfaction) and cost tolerance (reduced effort burden for loyal members). We integrate i* structural dependencies through dependency-weighted team cohesion, connecting member incentives to team-level positioning. The framework applies to both human teams (loyalty as psychological identification) and multi-agent systems (alignment coefficients and adjusted cost functions). Experimental validation across 3,125 configurations demonstrates robust loyalty effects (15.04x median effort differentiation). All six behavioral targets achieve thresholds: free-riding baseline (96.5%), loyalty monotonicity (100%), effort differentiation (100%), team size effect (100%), mechanism synergy (99.5%), and bounded outcomes (100%). Empirical validation using published Apache HTTP Server (1995-2023) case study achieves 60/60 points, reproducing contribution patterns across formation, growth, maturation, and governance phases. Statistical significance confirmed at p<0.001, Cohen's d=0.71.