Creator Incentives in Recommender Systems: A Cooperative Game-Theoretic Approach for Stable and Fair Collaboration in Multi-Agent Bandits

Ramakrishnan Krishnamurthy; Arpit Agarwal; Lakshminarayanan Subramanian; Maximilian Nickel

cs.LGApr 9, 2026

Creator Incentives in Recommender Systems: A Cooperative Game-Theoretic Approach for Stable and Fair Collaboration in Multi-Agent Bandits

Authors: Ramakrishnan Krishnamurthy, Arpit Agarwal, Lakshminarayanan Subramanian, Maximilian Nickel

Organizations: Courant Institute, New York University · Indian Institute of Technology Bombay · FAIR, Meta AI

Abstract

User interactions in online recommendation platforms create interdependencies among content creators: feedback on one creator's content influences the system's learning and, in turn, the exposure of other creators' contents. To analyze incentives in such settings, we model collaboration as a multi-agent stochastic linear bandit problem with a transferable utility (TU) cooperative game formulation, where a coalition's value equals the negative sum of its members' cumulative regrets. We show that, for identical (homogenous) agents with fixed action sets, the induced TU game is convex under mild algorithmic conditions, implying a non-empty core that contains the Shapley value and ensures both stability and fairness. For heterogeneous agents, the game still admits a non-empty core, though convexity and Shapley value core-membership are no longer guaranteed. To address this, we propose a simple regret-based payout rule that satisfies three out of the four Shapley axioms and also lies in the core. Experiments on MovieLens-100k dataset illustrate when the empirical payout aligns with -- and diverges from -- the Shapley fairness across different settings and algorithms.

Figures & tables

Panel of Figure 1 — Figure 1: Movielens experiments

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 2 — Figure 2: Synthetic experiments

Panel of Figure 3 — Figure 3: MovieLens experiments - Instances based on classification by age and gender.

Coalition $Q$	Agent $a\in Q$	Regret $R^{Q}_{a}$	Sub-coalition $S$	Reg. $R^{S}_{a}$	$\nicefrac{{R^{Q}_{a}}}{{R^{S}_{a}}}\geq 1$
\csvreader [ separator=pipe, late after line=
]coop-content/mtm-table/occ-full-1-occupation.txt \csvcoli \csvcolii \csvcoliii $\pm$ \csvcoliv \csvcolv \csvcolvi $\pm$ \csvcolvii \csvcolviii

Appendix

Table 1:

(I_{\text{occ}},\textsc{LinUcb-M})

Coalition $Q$	Agent $a\in Q$	Regret $R^{Q}_{a}$	Sub-coalition $S$	Reg. $R^{S}_{a}$	$\nicefrac{{R^{Q}_{a}}}{{R^{S}_{a}}}\geq 1$
\csvreader [ separator=pipe, late after line=
]coop-content/mtm-table/occ-greedy-full-1-occupation.txt \csvcoli \csvcolii \csvcoliii $\pm$ \csvcoliv \csvcolv \csvcolvi $\pm$ \csvcolvii \csvcolviii

Appendix

Table 2:

(I_{\text{occ}},\textsc{Greedy})

Coalition $Q$	Agent $a\in Q$	Regret $R^{Q}_{a}$	Sub-coalition $S$	Reg. $R^{S}_{a}$	$\nicefrac{{R^{Q}_{a}}}{{R^{S}_{a}}}$
\csvreader [ separator=pipe, late after line=
]coop-content/mtm-table/gender-full-1-gender.txt \csvcoli \csvcolii \csvcoliii $\pm$ \csvcoliv \csvcolv \csvcolvi $\pm$ \csvcolvii \csvcolviii

Appendix

Table 3:

(I_{\text{gen}},\textsc{LinUcb-M})

Coalition $Q$	Agent $a\in Q$	Regret $R^{Q}_{a}$	Sub-coalition $S$	Reg. $R^{S}_{a}$	$\nicefrac{{R^{Q}_{a}}}{{R^{S}_{a}}}$
\csvreader [ separator=pipe, late after line=
]coop-content/mtm-table/gender-greedy-full-1-gender.txt \csvcoli \csvcolii \csvcoliii $\pm$ \csvcoliv \csvcolv \csvcolvi $\pm$ \csvcolvii \csvcolviii

Appendix

Table 4:

(I_{\text{gen}},\textsc{Greedy})

Multi-Agent Bandits

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May 1, 2026Shradha Sharma, Swapnil Dhamal, Shweta JainMulti-Armed Bandits Cooperative Game Theory
Indian Institute of Technology Ropar
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May 1, 2026J/K move · Enter open · S save

Meritocratic Fairness in Budgeted Combinatorial Multi-armed Bandits via Shapley Values

Shradha Sharma, Swapnil Dhamal, Shweta Jain

Indian Institute of Technology Ropar

Multi-Armed Bandits Cooperative Game Theory Game Theory Algorithmic Fairness Shapley Value Attribution Combinatorial Multi-Armed Bandits

Open paper AskPDF arXiv

We propose a new framework for meritocratic fairness in budgeted combinatorial multi-armed bandits with full-bandit feedback (BCMAB-FBF). Unlike semi-bandit feedback, the contribution of individual arms is not received in full-bandit feedback, making the setting significantly more challenging. To compute arm contributions in BCMAB-FBF, we first extend the Shapley value, a classical solution concept from cooperative game theory, to the

K

-Shapley value, which captures the marginal contribution of an agent restricted to a set of size at most

K

. We show that

K

-Shapley value is a unique solution concept that satisfies Symmetry, Linearity, Null player, and efficiency properties. We next propose K-SVFair-FBF, a fairness-aware bandit algorithm that adaptively estimates

K

-Shapley value with unknown valuation function. Unlike standard bandit literature on full bandit feedback, K-SVFair-FBF not only learns the valuation function under full feedback setting but also mitigates the noise arising from Monte Carlo approximations. Theoretically, we prove that K-SVFair-FBF achieves

O(T^{3/4})

regret bound on fairness regret. Through experiments on federated learning and social influence maximization datasets, we demonstrate that our approach achieves fairness and performs more effectively than existing baselines.

Abstract

Multi-Agent Bandits

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