arXiv subjects

Eric Yu

Publications and source records attributed to Eric Yu.

9 recordsLinked to original sources

arXiv2026

On pushouts of strict symmetric monoidal categories

Toward modeling computational concurrency using the language of central idempotents in monoidal categories, we give an explicit construction of the pushout of strict symmetric monoidal categories with strong monoidal functors between them. We show that any braided strong monoidal functor strongly preserves central idempotents, and as a corollary, that the lattice of central idempotents of a symmetric monoidal category is isomorphic as a meet-semilattice to that of its strictification.

math.CT↗

arXiv2026

On extending results of Gluck and Warner on fibrations of spheres by great subspheres

In this paper, we build upon the work of Gluck and Warner who showed in 1983 that the set of positively oriented fibrations of a 3-sphere by oriented great circles is in bijection with the set of distance-decreasing maps from the 2-sphere to itself. One approach to generalizing their result to higher-dimensional spheres involves understanding when exactly two Hopf fibrations of $S^{2n-1}$ are guaranteed to agree on a fiber. We give a complete characterization of this phenomenon, and we discuss the barriers which prevent us from obtaining a fully general version of Gluck and Warner's result.

math.GT↗

arXiv2026

Coopetition-Gym v1: A Formally Grounded Platform for Mixed-Motive Multi-Agent Reinforcement Learning under Strategic Coopetition

We present Coopetition-Gym v1, a benchmark platform for mixed-motive multi-agent reinforcement learning under strategic coopetition. The platform comprises twenty environments organized into four mechanism classes that correspond to four foundational technical reports: interdependence and complementarity (arXiv:2510.18802), trust and reputation dynamics (arXiv:2510.24909), collective action and loyalty (arXiv:2601.16237), and sequential interaction and reciprocity (arXiv:2604.01240). Each environment carries a closed-form payoff structure and a calibrated interdependence matrix derived from the corresponding report. Every environment exposes a parameterized reward layer configurable across three structurally distinct modes (private, integrated, cooperative). This separation of payoff from reward enables reward-type ablation, the platform's principal methodological apparatus. Four of the twenty environments are calibrated against historically documented coopetitive relationships and reproduce their outcomes at 98.3, 81.7, 86.7, and 87.3 percent on the validation rubric (Samsung-Sony LCD, Renault-Nissan Alliance, Apache HTTP Server, Apple iOS App Store). The platform exposes Gymnasium, PettingZoo Parallel, and PettingZoo AEC interfaces and ships 126 reference algorithms: 16 learning algorithms, 7 game-theoretic oracles, 2 heuristic baselines, and 101 constant-action policies. A reference experimental study trained the 16 learning algorithms on every environment under every reward configuration with seven random seeds, producing a 25,708-run training corpus and a 1,116-run behavioral audit corpus, both released under CC-BY-4.0 with Croissant 1.0 metadata. Coopetition-Gym v1 is the first platform to combine continuous-action mixed-motive environments, parameterized reward mutuality, calibrated interdependence coefficients, game-theoretic oracle baselines, and validated case studies.

cs.MA↗

arXiv2026

Computational Foundations for Strategic Coopetition: Formalizing Sequential Interaction and Reciprocity

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.

cs.MA↗

arXiv2026

Computational Foundations for Strategic Coopetition: Formalizing Collective Action and Loyalty

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.

cs.MA↗

arXiv2025

Computational Foundations for Strategic Coopetition: Formalizing Trust and Reputation Dynamics

Modern socio-technical systems increasingly involve multi-stakeholder environments where actors simultaneously cooperate and compete. These coopetitive relationships exhibit dynamic trust evolution 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 conceptual models that capture strategic dependencies covering mixed motives of actors. This technical report bridges this gap by developing a computational trust model that extends game-theoretic foundations for strategic coopetition with dynamic trust evolution. Building on companion work that achieved 58/60 validation (96.7%) for logarithmic specifications, 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 practitioners to instantiate computational trust models from i* dependency networks encompassing mixed motives of actors. 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 49/60 validation points (81.7%), successfully reproducing documented trust evolution across five distinct relationship phases including crisis and recovery periods.

cs.MA↗

arXiv2025

Criteria for Classifying Prime Graphs of PSL(2, q)-Solvable Groups

For a finite group $G$, the prime graph $\Gamma(G)$ (also known as Gruenberg-Kegel graph) is defined to be the graph where the vertices are the primes that divide $|G|$ such that two vertices $p$ and $q$ share an edge if and only if there is an element of order $pq$ in $G$. The prime graphs of solvable groups have been classified. The prime graphs of groups whose noncyclic composition factors are isomorphic to a single nonabelian simple group $T$ where $|T|$ is divisible by three or four distinct primes have been classified except for the cases where $T = \operatorname{PSL}(2,q)$ for $q\neq 2^5$ and $|\operatorname{PSL}(2,q)|$ is divisible by exactly four primes. In this paper, we provide criteria for general classification results for certain classes of $T$, and then use them to classify the prime graphs of some $T$-solvable groups for $T$ a suitably small $\operatorname{PSL}(2, q)$-group. We also provide general results on the prime graphs of $T$-solvable groups where $T$ is a member of the possibly infinite family of groups $\operatorname{PSL}(2, 2^f)$ such that $f\geq 5, f$ is prime, and $|\operatorname{PSL}(2, 2^f)|$ is divisible by exactly four primes. This is the first paper to prove general results about the prime graphs of $T$-solvable groups where $T$ belongs to a large (probably infinite) family of groups.

math.GR↗

arXiv2025

Computational Foundations for Strategic Coopetition: Formalizing Interdependence and Complementarity

Coopetition refers to simultaneous cooperation and competition among actors who "cooperate to grow the pie and compete to split it up." Modern socio-technical systems are characterized by strategic coopetition in which actors concomitantly cooperate to create value and compete to capture it. While conceptual modeling languages such as 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 comprising over 22,000 trials across power and logarithmic value function specifications, demonstrating functional form robustness, with empirical application to the Samsung-Sony S-LCD joint venture (2004-2011). This technical report serves as the foundational reference for a coordinated research program examining strategic coopetition in multi-agent systems, with companion work addressing trust dynamics, collective action, and reciprocity mechanisms.

cs.MA↗

arXiv2024

Classification of the Prime Graphs of $\operatorname{Sz}(8)$-, $\operatorname{Sz}(32)$-, and $\operatorname{PSL}(2, 2^5)$-Solvable Groups

For a finite group $G$, the vertices of the prime graph $\Gamma(G)$ are the primes that divide $|G|$, and two vertices $p$ and $q$ are connected by an edge if there is an element of order $pq$ in $G$. Prime graphs of solvable groups have been classified, and prime graphs of groups whose noncyclic composition factors are isomorphic to a single nonabelian simple group $T$ have been classified in the case where $T$ has order divisible by exactly three or four distinct primes, except for the cases $T = \operatorname{Sz}(8)$, $T = \operatorname{Sz}(32)$, and $T = \operatorname{PSL}(2,q)$, which in some sense are the hardest cases. In this paper, we complete the classification for $T = \operatorname{Sz}(32)$, $T = \operatorname{Sz}(8)$, and $T = \operatorname{PSL}(2,2^5)$, with the latter two being the first cases ever studied where $|\text{Out}(T)|$ has prime factors which do not divide $|T|$. The groups studied in this paper are also the first ones requiring knowledge of their Brauer character tables to complete the classification task.

math.GR↗