Team Formation (TF): Models & Mechanisms

• Team Formation (TF) is the process of grouping individuals into teams by optimizing criteria like skill coverage, social welfare, and stability while navigating structural and resource constraints.
• The literature spans formal models—from hedonic partitioning and pairwise-utility assignments to expert selection and distributed algorithms—each tailored to specific observability and constraint settings.
• Key challenges include balancing trade-offs (efficiency vs. fairness, stability vs. incentives) and developing adaptive, mechanism-based approaches to handle dynamic, real-world team assembly.

Team Formation (TF) denotes a family of problems in which individuals, experts, agents, or tokens must be grouped into teams under structural constraints while optimizing one or more criteria such as skill coverage, social welfare, coordination cost, stability, fairness, robustness, or downstream performance. In the literature, TF appears in several mathematically distinct forms: hedonic partitioning with private teammate preferences, expert selection in social networks under skill and communication constraints, online matching under latent synergies, educational cohort partitioning with agency constraints, domain-specific drafting under procedural rules, and even long-lived distributed token assembly in asynchronous systems (Wright et al., 2015, Addanki et al., 2020, Galbiati et al., 2024, Emek et al., 18 Aug 2025). This breadth has produced no single canonical formulation; instead, TF is best understood as a unifying optimization and mechanism-design theme whose concrete model depends on what is observable, what constraints are binding, and what notion of “good team” is operative.

1. Formal models and problem classes

A central line of work models TF as a hedonic partitioning problem with private preferences. In "Mechanism Design for Team Formation" (Wright et al., 2015), an instance is formalized as $(N, \succ, k\text{-constraints})$, where agents have additively separable, non-negative utilities over teammates, and every team size must lie in $[\underline{k}, \overline{k}]$. A partition $P$ assigns each agent $i$ to a team $P(i)$, and utility is induced by the sum of valuations over teammates. This formulation is explicitly non-transferable and excludes monetary transfers.

A second line models TF as combinatorial assignment with pairwise intra-team interactions. "On Finding Stable and Efficient Solutions for the Team Formation Problem" (Yekta et al., 2018) assumes $n = m \cdot s$ agents must be partitioned into $m$ equal-sized teams of size $s$, with pairwise utilities $u_{i,j} \ge 0$. Feasible formations are partitions, and welfare is quadratic in same-team assignment variables. This model is suited to settings where pairwise compatibility is the primitive rather than aggregate team statistics.

A third class treats TF as expert selection under explicit task requirements. In "Multi-team Formation using Community Based Approach in Real-World Networks" (Addanki et al., 2020), a social network is a weighted graph $G=(V,E)$ whose nodes are experts and whose edges encode collaboration strength. A task is a required skill set $[\underline{k}, \overline{k}]$0, and the objective is to find a team $[\underline{k}, \overline{k}]$1 satisfying

$[\underline{k}, \overline{k}]$2

while minimizing a communication cost such as diameter, leader distance, or sum distance. Related work generalizes this to densest-subgraph formulations with mandatory members, budgets, and locality constraints (Rangapuram et al., 2015).

A fourth class departs from partitioning entirely and allows overlapping teams and heterogeneous team sizes. In "Efficiency and Stability in a Process of Teams Formation" (Boncinelli et al., 2021), agents possess integer time endowments, a feasible project is a pair $[\underline{k}, \overline{k}]$3 consisting of an activity and a team-time vector, and a state is a feasible collection of projects subject to capacity and activity-exclusivity constraints. Here TF is not merely partitioning; it is the dynamics of building feasible sets of overlapping teams.

A fifth class is procedural and domain-specific. In the FIRST Robotics Competition, alliances are formed by a constrained snake draft after qualification matches, with captains, draft order reversals, and captain-replacement rules. The TF problem is therefore to infer robot-level effectiveness from alliance-level match statistics and to choose partners under draft-order and availability constraints (Galbiati et al., 2024).

A sixth class is distributed rather than centrally optimized. "Team Formation and Applications" (Emek et al., 18 Aug 2025) defines TF over an asynchronous complete communication graph with bounded-size messages and token injections. The goal is to assemble tokens into teams of size $[\underline{k}, \overline{k}]$4 while preserving safety and liveness under a strong initial-failure model. In this setting, “team” is an abstract distributed object rather than a human group.

Problem family	Core decision object	Representative source
Hedonic partitioning	Partition of agents into bounded-size teams	(Wright et al., 2015)
Pairwise-utility partitioning	Equal-sized team assignment	(Yekta et al., 2018)
Skill-coverage selection	Subset of experts covering required skills	(Addanki et al., 2020)
Overlapping project formation	Feasible set of projects with shared members	(Boncinelli et al., 2021)
Draft-constrained assembly	Sequential alliance selection under snake draft	(Galbiati et al., 2024)
Distributed token assembly	Tokens grouped into teams of size $[\underline{k}, \overline{k}]$5	(Emek et al., 18 Aug 2025)

This diversity explains why TF papers often disagree about whether the primitive object is a team, a partition, a coalition, a project, an alliance, or a matching. They are studying related but non-isomorphic optimization problems.

2. Objectives, criteria, and trade-offs

The most classical objective is social welfare. In the hedonic mechanism-design model, welfare is

$[\underline{k}, \overline{k}]$6

and is paired with Pareto efficiency, envy-freeness, and EF1 as competing desiderata (Wright et al., 2015). The same paper makes explicit that TF is not simply about maximizing welfare: incentive compatibility and equity can be in direct tension with welfare-optimality.

Stability is a distinct evaluative axis. "Efficiency and Stability in a Process of Teams Formation" (Boncinelli et al., 2021) studies myopic team-wise stability, coalitional stability, and stochastic stability. These notions are not interchangeable. Myopic team-wise stability is characterized by the absence of profitable single-project additions or deletions, whereas coalitional stability allows coordinated deviations by groups of agents. Stochastic stability instead selects absorbing states of a perturbed dynamic and is shown, under the paper’s assumptions, to coincide with feasible states maximizing the number of projects.

In pairwise-utility partitioning, stability is operationalized through blocking coalitions and “core uplift.” "On Finding Stable and Efficient Solutions for the Team Formation Problem" (Yekta et al., 2018) defines

$[\underline{k}, \overline{k}]$7

and optimizes a weighted welfare–stability trade-off

$[\underline{k}, \overline{k}]$8

This formulation is useful precisely when the core may be empty.

In expert-selection TF, the objective is often skill coverage subject to communication cost. "Multi-team Formation using Community Based Approach in Real-World Networks" (Addanki et al., 2020) defines three explicit costs: $[\underline{k}, \overline{k}]$9

$P$0

$P$1

A different unification appears in the QUBO framework, where TF is written as

$P$2

with alternative cost definitions for cardinality, linear expert costs, or pairwise coordination costs (Vombatkere et al., 29 Mar 2025).

Educational TF adds explicit agency objectives. "A Hierarchical Integer Linear Programming Approach for Optimizing Team Formation in Education" (Kessler et al., 3 Jun 2025) distinguishes maximizing realized teammate preferences, maximizing the smallest realized preference, and maximizing or minimizing the number of realized preferences of a specified value. The paper’s hierarchical objective design reflects the fact that in educational settings, no student can be excluded and teacher constraints coexist with student-expressed acceptance and veto structure.

Across these formulations, TF is characterized less by one universal objective than by a recurring set of trade-offs: efficiency versus stability, coverage versus cost, fairness versus manipulability, speed versus optimality, and agency versus centralized control.

3. Mechanisms and algorithmic paradigms

Mechanism design for TF begins from the elicitation problem. "Mechanism Design for Team Formation" (Wright et al., 2015) studies four mechanisms. Random Serial Dictatorship (RSD) is strategyproof and ex post Pareto efficient under a technical team-size condition. The Harvard Business School draft implements a snake draft but is not strategyproof and not ex post Pareto efficient. The One-Player-One-Pick draft is also not strategyproof and not ex post Pareto efficient, but performs strongly empirically. A-CEEI-TF adapts approximate competitive equilibrium from equal incomes to TF, is strategyproof-in-the-large, and yields EF1 under exact-clearing consistency conditions.

Sequential bargaining provides another paradigm. "A Rotating Proposer Mechanism for Team Formation" (Low et al., 2022) models TF as a finite extensive-form game in which proposers offer feasible coalitions and all proposed teammates must accept. RPM computes a subgame perfect Nash equilibrium via backward induction, uses Iterated Matching of Soulmates (IMS) as preprocessing, and is individually rational and Pareto optimal under truthful reports. Exact RPM is exponential in the worst case, which motivates approximate RPM and the Heuristic Rotating Proposer Mechanism (HRPM), the latter running in $P$3 under additively separable utilities.

Exact mathematical programming enters through bi-level and column-generation formulations. In "On Finding Stable and Efficient Solutions for the Team Formation Problem" (Yekta et al., 2018), the welfare–stability problem is transformed into a single-level, exponentially sized binary integer program and solved by branch-cut-and-price. The pricing problem is a cardinality-constrained binary quadratic program, and uplift constraints for blocking coalitions are separated dynamically. This is an exact approach rather than a heuristic one.

Graph-based heuristics dominate expert-network TF. Community-centric methods TFC-R and TFC-N choose high-degree leaders inside “desirable communities,” greedily cover skills from 1- and 2-hop neighborhoods, and fill uncovered skills either randomly or with nearest experts (Addanki et al., 2020). FORTE, by contrast, formulates a generalized densest-subgraph problem with skills, mandatory members, budget, and locality constraints, then solves an exact-penalty continuous relaxation using a ratio-of-difference-of-convex-functions procedure (Rangapuram et al., 2015).

Learning-based search has also become prominent. "A Reinforcement Learning-assisted Genetic Programming Algorithm for Team Formation Problem Considering Person-Job Matching" (Guo et al., 2023) combines a 0–1 formulation, intuitionistic fuzzy person–job matching, a communication-willingness term, Q-learning over four population search modes, ensemble population strategies, and KNN surrogate fitness evaluation. "A QUBO Framework for Team Formation" (Vombatkere et al., 29 Mar 2025) instead encodes several TF variants as quadratic unconstrained binary optimization problems and solves them using both a QUBO solver and a graph neural network that directly minimizes the relaxed QUBO energy.

No single algorithmic family dominates across all TF regimes. Mechanisms are natural when preferences are private; exact optimization is natural when constraints are explicit and instance sizes moderate; graph heuristics are natural when communication structure is primary; and learning-based approaches are natural when evaluation is expensive or repeated across related tasks.

4. Learning, inference, and online or adaptive TF

A major branch of TF studies repeated matching under uncertainty. "Exploration vs. Exploitation in Team Formation" (Johari et al., 2018) examines a platform repeatedly partitioning workers into pairs when each worker has an unknown binary type and team performance is determined by either the strongest or weakest member. The paper establishes regret bounds, shows that the two aggregation rules induce different exploration–exploitation trade-offs, and develops near-optimal policies such as Exponential Cliques and chain-based strategies.

A broader characterization appears in "Online Team Formation under Different Synergies" (Eichhorn et al., 2022), where the team score is any symmetric function of two binary latent types: $P$4 The full-information optimum depends on the sign of $P$5: heterophily-type regimes maximize mixed pairs, homophily-type regimes minimize them, and Boolean functions such as AND, OR, XOR, and XNOR become special cases. The paper’s policies are notable for being agnostic to model parameters while remaining optimal or near-optimal against an adaptive adversary.

Team-level inference can also proceed when only aggregate statistics are observed. In the FRC framework, robot-level performance in seven standardized indicators is estimated from alliance-level qualification data by

$P$6

followed by normalization and alliance aggregation

$P$7

Alliance quality is then approximated by radar-polygon area, and a four-hidden-layer MLP predicts match winners from 14 alliance features, reaching 84.08% test accuracy on 63,945 processed matches (Galbiati et al., 2024). The importance of this result is methodological: TF is solved without individual action logs, only alliance-level statistics.

Transformer-based methods extend this logic to adversarial multiagent settings. "Transformer Guided Coevolution: Improved Team Selection in Multiagent Adversarial Team Games" (Rajbhandari et al., 2024) formulates post-training team selection as

$P$8

and trains BERTeam, a BERT-style masked-LLM over agent tokens. Because weighted training makes team frequency proportional to empirical win probability, sequence likelihood acts as a surrogate for team strength. The model is integrated with coevolutionary reinforcement learning and outperforms MCAA in Marine Capture-The-Flag.

Preference-aware adaptive TF also appears in human-centered AI systems. "Teaming in the AI Era: AI-Augmented Frameworks for Forming, Simulating, and Optimizing Human Teams" (Almutairi, 5 Jun 2025) treats each feasible team composition as a bandit arm and scores it using UCB: $P$9 The framework iteratively updates team recommendations from user feedback, balancing consensus, preference alignment, and task objectives.

These works collectively shift TF from one-shot assignment to adaptive inference. The central technical issue is no longer just selecting a good team, but learning enough about latent types, compatibility, or outcome structure to know what “good” means.

5. Empirical determinants and domain-specific instantiations

Domain constraints materially reshape TF. In the FIRST Robotics Competition, skills and rules change year to year, only alliance-level match statistics are available, alliance drafting follows a snake draft, and partner selection occurs under strong time pressure (Galbiati et al., 2024). The resulting TF problem is inseparable from competition format.

MOOC TF emphasizes social connectivity and evolving interaction structure rather than fixed skill vectors. "Together we stand, Together we fall, Together we win: Dynamic Team Formation in Massive Open Online Courses" (Sinha, 2014) proposes a framework grounded in organizational team theory, social network analysis, and machine learning. Students are vertices in an interaction graph; centrality, clustering, structural holes, brokerage roles, inferred skills, and dynamic network updates all contribute to a team assignment objective that balances intra-team cohesion and inter-team exposure.

Observed human teaming behavior provides additional empirical structure. In Battlefield 4, familiarity is found to be the strongest determinant of repeated same-squad formation, homophily is weak at squad level, and competence matters through similarity rather than raw level: similarly high-competence players repeatedly form squads, while large competence disparities discourage repeated interaction (Alhazmi et al., 2017). This is an empirical correction to TF models that overemphasize demographic similarity.

Scientific collaboration data show that higher-order interactions matter. "Higher-order interactions at scientific conferences influence team formation" (Zajdela et al., 3 Mar 2026) studies Scialog workshops using a triplet-level taxonomy of synchronous and asynchronous interactions. For a final logistic model,

$i$0

all four interaction types are retained by AIC-based selection, and synchronous triad co-presence has the largest coefficient. This suggests that pairwise exposure alone is an incomplete explanation for team emergence.

Education is another domain where TF departs from standard expert selection. EDU-TF requires exhaustive partitioning, explicit student agency, and teacher-defined pedagogical constraints, making “leave some agents unmatched” formulations unsuitable (Kessler et al., 3 Jun 2025). In this context, TF is closer to constrained cohort design than to classical team recommendation.

The lesson across domains is that TF is rarely just a generic optimizer over individuals. It is usually a constrained institutional process with observability limits, procedural rules, and endogenous behavior.

6. Impossibility results, limitations, and open directions

A recurring finding in TF is that desirable properties do not generally coexist. In mechanism design, EF1 may fail to exist, exact market clearing may fail under team-size constraints and reciprocity, and mechanisms with strong finite-market incentive properties need not be the ones with the strongest fairness or welfare outcomes (Wright et al., 2015). HBS and OPOP lack strategyproofness and ex post Pareto efficiency, while A-CEEI-TF’s large-market guarantees do not automatically translate into superior empirical incentives in finite markets.

Sequential-offer mechanisms do not eliminate strategic behavior either. RPM is not strategy-proof in general hedonic domains, even though it implements an SPNE, is individually rational, and is Pareto optimal under truthful reports (Low et al., 2022). This reflects a broader impossibility: truthful elicitation, efficiency, and strong fairness guarantees are hard to align once agents choose teammates rather than objects.

Stability notions are also non-hierarchical. In the overlapping-project model, coalitional stability does not refine myopic team-wise stability in general, while stochastic stability selects states maximizing the overall number of activities performed by teams (Boncinelli et al., 2021). Thus long-run dynamic predictions can differ sharply from coalition-based normative criteria.

Algorithmic limitations are equally persistent. The FRC framework requires manual alignment of year-specific scoring rules to a common seven-indicator schema, does not report calibration or uncertainty estimates, and provides no approximation guarantees for its area-maximization heuristic (Galbiati et al., 2024). Community-based TF relies on exogenously chosen communities and likewise provides no approximation guarantees (Addanki et al., 2020). FORTE is a local optimization method for a nonconvex generalized densest-subgraph problem, and its global optimality is not guaranteed (Rangapuram et al., 2015).

Expressiveness remains constrained in many models. Additively separable, non-negative utilities are analytically convenient but do not capture complementarities or negative externalities across teammates (Wright et al., 2015). Binary latent-type models yield sharp regret characterizations, but they abstract away richer role structures, contextual tasks, and noisy outcomes (Johari et al., 2018, Eichhorn et al., 2022).

At the systems level, TF is subject to lower bounds. In the asynchronous distributed abstraction, any one-shot TF algorithm that forms a team of size $i$1 with high probability requires

$i$2

messages in expectation, even with unbounded message size (Emek et al., 18 Aug 2025). This establishes that communication-efficient TF is possible, but not arbitrarily cheap.

Open directions follow directly from these limitations: faster price-based mechanisms for finite markets, richer valuations beyond additive separability, larger-team online learning with noisy feedback, TF on general communication graphs, tighter regret bounds for non-Boolean synergies, dynamic or Bayesian variants of proposer mechanisms, and better integration of fairness, agency, and uncertainty quantification. The literature does not converge on a single grand theory of TF; instead, it points toward a modular research program in which the right formulation depends on what kind of team, what kind of data, and what kind of failure mode must be handled.