Social World Model-Augmented Mechanism Design Policy Learning
Authors: Xiaoyuan Zhang
Yizhe Huang
Chengdong Ma
Zhixun Chen
Long Ma
Yali Du
Song-Chun Zhu
Yaodong Yang
Xue Feng
Venue: NeurIPS 2025 poster ()
Keywords: Model-based Reinforcement Learning
Primary area: reinforcement_learning

Abstract: Designing adaptive mechanisms to align individual and collective interests remains a central challenge in artificial social intelligence. Existing methods often struggle with modeling heterogeneous agents possessing persistent latent traits (e.g., skills, preferences) and dealing with complex multi-agent system dynamics. These challenges are compounded by the critical need for high sample efficiency due to costly real-world interactions. World Models, by learning to predict environmental dynamics, offer a promising pathway to enhance mechanism design in heterogeneous and complex systems. In this paper, we introduce a novel method named SWM-AP (Social World Model-Augmented Mechanism Design Policy Learning), which learns a social world model hierarchically modeling agents' behavior to enhance mechanism design. Specifically, the social world model infers agents' traits from their interaction trajectories and learns a trait-based model to predict agents' responses to the deployed mechanisms. The mechanism design policy collects extensive training trajectories by interacting with the social world model, while concurrently inferring agents' traits online during real-world interactions to further boost policy learning efficiency. Experiments in diverse settings (tax policy design, team coordination, and facility location) demonstrate that SWM-AP outperforms established model-based and model-free RL baselines in cumulative rewards and sample efficiency.

Social World Model-Augmented Mechanism Design
Policy Learning
Xiaoyuan Zhangl23. Yizhe Huang Chengdong Ma Zhixun Chen
Long Ma²
Yali Du Song-Chun Zhu Yaodong Yang 1 Xue Feng"t
Institute for Artificial Intelligence, Peking University
State Key Laboratory of General Artificial Intelligence, BIGAI, Beijing, China
State Key Laboratory General Artificial Intelligence, Peking University, Beijing, China "The Hong Kong University of Science and Technology (Guangzhou)
CCenter for Data Science, Academy for Advanced Interdisciplinary Studies, Peking University Kiig's 's College London
Abstract
Designing adaptive mechanisms align individual and collective interests remains a central challenge in artificial social intelligence. Existing methods often strug- gle with modeling heterogeneous agents possessing persistent latent traits (e.g.. skills, preferences) and dealing with complex multi-agent system dynamics. These challenges are compounded by the critical need for high sample efficiency due costly real-world interactions. World Models, by learning to predict environmental dynamics, offer a promising pathway to enhance mechanism design in heteroge- neous and complex systems. In this paper, we introduce novel method named SWM-AP (Social World Model- Podel-Augmented Mechanism Design Policy Learning), which learns social world model hierarchically modeling agents' behavior enhance mechanism design. Specifically, the social world model infers agents' traits from their interaction trajectories and learns trait-based model predict agents' responses to the deployed mechanisms. The mechanism design policy collects extensive training trajectories by interacting with the social world model, while concurrently inferring agents' traits online during real-world interactions further boost policy learning efficiency. Experiments in diverse settings (tax policy design, team coordination, and facility location) demonstrate that SWM-AP outperforms established model-based and model-free RL baselines cumulative rewards and sample efficiency.
Introduction
Mechanism design, the art of engineering incentive structures to guide self-interested agents towards desirable collective outcomes, underpins a vast array of societal functions, from resource allocation in digital economies and smart cities to the formulation of public policies [23]. Its profound significance
lies in its potential maximize social welfare, foster efficient cooperation, and resolve complex coor- dination problems in multi-agent systems (25). However, traditional mechanism design paradigms often grapple with fundamental challenges inherent in real-world social systems. Chief among these is agent heterogeneity. Real-world populations consist of diverse individuals possessing persistent yet often unobservable latent traits (c.g., skills, preferences, risk attitudes). which critically influence their responses to incentives [1. Classical models frequently resort to simplifying assumptions of homogeneity or rely on unrealistic full information, leading to suboptimal or ineffective mechanisms.
"Equal contribution
I Equal corresponding authors. Project website: http:///ilesggoogge...o//vveeess
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Principal
Social System
Risky
Costly
Locate at a or b?
Secure
Efficient
6B0
Complex system dy dynamies Heterngeneous
Simulating
Social World Model
Figure I: The AI mechanism designer (principal) makes decisions within complex social system, 4.1for for details) shown on the left of the
exemplified by the facility location problem subsection 4.1 figure, which involves selecting the optimal site from potential locations (a or b). Directly interacting with the real social system is costly and risky. Such social systems typically present two major challenges. (1) Complex system dynamics, where individual interactions and environmental changes give rise to intricate and evolving system behaviors. (2) Heterogeneous agent traits, where individuals possess diverse latent preferences and needs (as illustrated the magnified area on the left, where color intensity indicates preference for a facility, and the overall agent distribution also impacts the optimal location choice). Our proposed Social World Model aids the principal by simulating interaction in a secure and efficient manner.
Furthermore, these systems are characterized by complex system dynamics, which are difficult to capture using static, equilibrium-based analyses. Compounding these issues the pervasive informa- tion asymmetry, where mechanism designers typically lack direct access to the crucial latent traits driving agent behavior. The advent Artificial Intelligence, particularly Reinforcement Learning (RL), has ushered in a new era for mechanism design [39], offering unprecedented capabilities develop adaptive and data-driven mechanisms capable of navigating increasingly complex and dynamic environments.
Model- -aaed Reinforcement Learning (MBRL) has emerged as a promising avenue for enhancing the efficacy and sample efficiency of mechanism design. By learning a model of the environment's dynamies, MBRL allows simulating trial-and-error exploration and counterfactual reasoning 22 significantly reducing the reliance on costly real-world interactions, a critical advantage in high-stakes social systems. Despite this potential, the direct application of existing MBRL techniques to social mechanism design faces considerable hurdles. A primary limitation is the persistent neglect of agent heterogeneity. Many contemporary world models still treat agents homogeneous entities or struggle to effectively represent and leverage their distinguishing latent traits. This oversight directly conflicts with the core need design mechanisms tailored to the characteristics of the diverse agents 26 12]. Moreover, modeling the intricate complexity of social interactions, encompassing cooperation, competition, and influence dynamics that can lead to highly non-ling non-linear and emergent system behaviors, poses a substantial challenge for standard world models [34), especially when individual agents are fundamentally driven by their underlying, unobservable traits.
To address these pressing challenges, we introduce a novel framework, named Social World Model- Augmented Mechanism Design Policy Learning (SWM-AP). Our approach, leveraging a model-based reinforcement learning paradigm, comprises two primary, interconnected components. The first sophisticated Social World Model (SWM), engincered to perform latent trait inference by unearthing agents' persistent hidden characteristies (e.g., skills, preferences) from their interaction trajectories in an unsupervised manner. It also learns trait-conditioned system dynamics, predicting how the social system evolves (i.e., state transitions and reward generation) as function of these inferred traits and deployed mechanisms. The second core component is the Mechanism Design Policy. It is responsible for deploying optimal incentive mechanisms. This policy leverages the capabilities of SWM in two key ways: first, its prior mind tracker module conducts real-time inference of background agents' traits using the posterior mind tracker of SWM the supervision signal;

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second, it interacts with SWM's simulative environment to efficiently explore and refine its strategies. This synergy allows the Mechanism Design Policy devise more adaptive, targeted, and ultimately effective incentive structures, aiming to maximize social welfare while minimizing the need for costly real-world samples, as shown Figure T
The paper is structured as follows. We first review relevant literature on world models and mechanism design. Subsequently, we detail our SWM-AP framework with theoretical analysis of algorithm feasibility. Through extensive numerical experiments across multiple scenarios, including facility location games, team optimization, and tax policy design, we validate our method's effectiveness. We conclude by summarizing contributions and proposing future directions for applying world models to real-world mechanism design research.
2 Related Works
2.1 Mechanism Design in Reinforcement Learning
The integration of Reinforcement Learning (RL) with mechanism design offers powerful paradigm for dynamic systems, overcoming limitations of classical game-theoretic approaches tied to static equilibria and strict rationality. While foundational theories like Mirrlees' theory of optimal taxa- tion [21] exist, they often struggle in dynamic, heterogeneous environments where agent preferences and capabilities evolve [4. RL enables data-driven policy optimization via sequential interaction in complex settings 32
27 However, contemporary RL-based mechanism design often over- simplifies agents as homogeneous, neglecting crucial cognitive traits (e.g., risk tolerance) that drive real-world decisions B While Inverse Reinforcement Learning (IRL) methods like 'Democratic Al' can infer latent preferences, they face scalability issues in co-training [16 [17]. Cognitive-awan RI. advances this frontier: The M framework (31] incorporates psychological states into policy adaptation but relies explicit reward structures. Our work bridges these gaps by introducing a social world model that co-optimizes mechanism design. Many MARI approaches flat social while our hierarchical mechanism design
18
structures for cooperative coordination [33 24
35
15
guides self-interested agents.
2.2 World Model
Model-Based Reinforcement Learning methods learn dynamic models to guide policy optimization, reducing sample complexity while maintaining performance. The learned dynamic models fall into two categories. First is enhancing model-free methods with the learned model. Model-enhanced methods include MBPO [4), which trains the SAC or PPO algorithm using generated and real trajectories. Similar ideas have been extended to offline model-based RL settings [36). Impressive advancements have also been made in learning dynamic changes in latent variable spaces [6] [5] 78. Furthermore, the application of transformers as world models 20 has demonstrated robust performance in humanoid robots 28% 38. The second way is to use the model for planning. TD- MPC 110 [ incorporates terminal value estimates for long-term reward estimates. Some existing works on multi-agent reinforcement learning employ world models to simulate the dynamics of multiple systems [37 34 19). However, due to their lack of modeling complex social relationships among agents or explicit specification of agents' inherent attributes to simplify the problem, these approaches face challenges in deployment to real-world social environments. In contrast, our methodology simulates the dynamics of multi-agent systems characterized by individual heterogeneity and complex interaction relationships.
3 Method
In this paper, we propose Social World Model-Augmenter Mechanism Design Policy Learning (SWM-AP) approach, as illustrated in Figure 2 and Algorithm I In Subsection 3.1, we formally define the research problem through decision- -making processes. Subsection 3.2 details the learning architecture of our SWM-AP approach, including the specifics of the Social World Model with its hidden trait inference tracker, and the training of the Mechanism Design Policy. Subsection 3.3 provides theoretical justification via EI derivation for our approach combining latent trait inference with world model learning, demonstrating the feasibility of jointly learning latent traits
3

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and system dynamics, thereby supporting our approach of using trait inference to enhance the state prediction accuracy.
3.1 Problem Formulation
We formalize AI-driven mechanism design as an episodic Markov game between an institutional planner (principal) and population of background agents. The principal operates as an algorithmic policy designer that dynamically deploys incentive mechanisms to optimize social welfare(the sum of all the background agents' returns). Each background agent maintains a fixed trait (such skill or preference), which regulates the agent's response to the mechanism and shapes its behavior during interactions with other agents. These traits are private and unobservable the principal, constituting a central challenge for adaptive mechanism design.
This problem can be succinctly summarized by the tuple (N, (M.), Sohs .A, P. Rex (1) Here, N the number of background agents, each agent with a latent trait m' E EM,. S represents the principal's comprehensive observation space, encompassing background agents' states (s (s',..s*) that are visible to principal (like agents' locations) and global environment state 8 (like the distribution of resources). The principal acts by selecting mechanism policy
[[(T|sab)). while each background agent i takes action following its policy (aa b म. m²). ). The system transition function P describes how observations evolve given current observations and the deployed mechanism policy. That is
s+1
(5 |
00s m.).
(1)
The principal infers the system transition function P and learns a mechanism policy to maximize the expected cumulative social welfare
max E
Σ 20r000
where y0 E, is principal's reward, named the social welfare, r = 1t' a² a.,,..,a")) ) reward of background agent i, and y is the discount factor.
is the
Thus, our formulation of Al-driven mechanism design presents two fundamental departures from classical mechanism design theory. 1) Principal has prior knowledge of background agents' behavior patterns, which adaptively respond to the policies of principal and other background agents. Principal needs to conduct online inference of these patterns through interactions with them. 2) Agents exhibit heterogeneity, possessing diverse and persistent latent traits that individually shape their behaviors. Consequently, the principal must infer these distinct agent-specific traits and behavioral patterns from interaction trajectories, rather than relying on aggregated or homogeneous population models.
3.2 Social World Model-Augmented Mechanism Design Policy Learning
Our approach to Al-driven mechanism design problems within heterogencous and dynamic multi- agent systems, termed Social World Mogel-Augmented Mechanism Design Policy Learning (SWM- AP), leverages model-based reinforcement learning framework. The core of our method consists of two primary, interconnected components: Social World Model (SWM) that learns the complex dynamics of state transition, and a Mechanism Design Policy that learns to deploy optimal incentive mechanisms. This overall architecture designed address the challenge of unobservable agent traits and to maximize social welfare with a minimized sample.
Social World Model: SWM is tasked with learning a comprehensive model of the state transition function. Specifically, given the current observation sh the deployed mechanism TT, and an estimate of the agents' latent traits In (m .... NV) SWM learns to predict the next observation shh and the immediate social welfare r?
An important component of SWM is the Posterior Trait Tracker. Since the background agents' traits m are latent, accurate modeling of environment dynamics necessitates inferring these traits. The Posterior Trait Tracker is designed to infer these latent traits, mppost by analyzing complete interaction abs trajectories (aghs, To, r:00c ...., 57 .т, TT collected during training. This module processes entire trajectory segments to capture long-term behavioral patterns indicative of the underlying traits. SWM, including its state prediction component, is then trained by minimizing the discrepancy

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Environment
Environment buffer
Sample trajectory
Design decision IT:
Sample Mini-bulch
Lax,tocttionTTamm
T (50 Tg. To
sf HT, Fr)
&
(To Un Taa)
Policy Learning
Observation sobs
Social World Model
Mechanism Design Policy
Posterior Trait Tracker
Prior Trait Tracker (Mf priior. I S Age
(Mpost | ))
Prior
Trait Tracker Learinng
Social World
Trait m post
Interaction
Inferred Trait A prion.1
Model
Learning
State Prediction S n1 mpose)
Imagined trajectories (fo. Ry i b
Decision Making
(3t+1
(M gbs M priion
Policy Leamning
Algorithm diagram of SWM-AP. The Social World Model (SWM) utilizes a Posterior Trait Tracker infer latent agent traits from full trajectories, which subsequently aid in predicting the future states of background agents. Concurrently, the Mechanism Design Policy employs Prior Trait Tracker for real-time inference of agent traits based on partial history, informing its mechanism design. Interactions between the policy and the learned SWM, leveraging imagined trajectories, enhance sample efficiency for policy learning.
Figure 2:
between its predicted future states and the actual observed states, utilizing these inferred traits mostt The objective function of SWM can be expressed as:
Jswma = ETED Σ | (sote , Te, mposs)
obs 112 cDKL (p(Mpos)) (m))
(3)
Here, JswMelb, Φ) represents the loss function for SWM with parameters vi and the Posterior Trait Tracker with parameters db The expectation E,-D is taken over trajectories 7 sampled from a dataset D of past experiences. sybs is the next state observation predicted by SWM, conditioned on the current state tith mechanism Ne, and the traits tñposs inferred by the Posterior Trait Tracker. tgh is the actual observed next state. The term || 1| denotes the squared L2 norm (Euclidean distance), measuring the prediction error. p p(I))t))) is the probability output by the Posterior Trait Tracker, while U ((m) is the uniform distribution for every element in m. the regularization coefficient. This joint optimization allows SWM to learn environment dynamics that are conditioned on a rich understanding of agent traits.
The Mechanism Design Policy, denoted as [1( | mmrror), is respon- sible for selecting and deploying incentive mechanisms to maximize the expected cumulative discounted social welfare, as defined in Equation 2 This policy trained using PPO [29], interacting with the environment (either real simulated by SWM) to gather experiences. The social welfare ri serves directly as the reward signal for policy updates.
Mechanism Design Policy:
A critical challenge during policy deployment is that complete future trajectories are unavailable for the Posterior Trait Tracker. To address this, the policy component incorporates Prior Trait Tracker. This module is trained to perform real-time inference of background agents' traits, mppriors based on the historically observed partial trajectory up to timestep t, i.e., (sght .o...., sohr). ). The Prior Trait Tracker is trained in supervised fashion, typically by minimizing the discrepancy between its predictions i and the "ground truth" traits mpps inferred by the Posterior Trait Tracker from complete trajectories during offline training. For example, a common objective is to minimize cross-entropy loss if traits are categorical or mean squared error if traits are continuous, each
5

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step:
Σ L(in i g<s T2c; act); mpst)
J (E) = E
prior,
Here, Jrrior is the loss for the Prior Trait Tracker with parameters Ç. L is loss function comparing the prior tracker's estimate at time priiuttt which is based on observations up with the more accurate posterior estimate mpos derived from the full trajectory.
During online interaction (policy execution), the inferred trait mmpror from the Prior Trait Tracker is fed as input to both the Mechanism Design Policy II (to inform its decision-making) and to SWM (when SWM used for generating imagined trajectories). This allows the policy adapt its mechanism design strategy dynamically based on its evolving understanding of the agents' latent traits. Furthermore, the policy interacts with the learned SWM enhance sample efficiency. For instance, SWM can generate simulated rollouts under different candidate mechanisms, allowing the policy to refined with significantly more data than direct environment interaction alone would permit. The Prior Trait Tracker's s output can also be probability distribution over possible traits, reflecting its prediction certainty, which the policy can leverage for more robust strategy learning [40]. This two-pronged approach, combining world model that understands agent traits with policy that leverages this understanding for real-time adaptation and efficient learning, forms the backbone of our method.
3.3 Theoretical Analysis
We derive the Evidence Lower Bound (ELBO) to provide theoretical basis for unsupervised learning of latent agent traits from interaction data, within the episodic framework defined in subsection 3.1
We denote the principal's trajectory as (s no, $1 Ti, (m² .... N
.obs ST TT-I, (0 the joint actions
a, (at,-.. a²") and the joint traits of r and m follows a generative process:
We assume the joint distribution
T-1
/ ploot 1sgte Te. 11st
N B. (aalsss..m m))
p(T, m) = pl (mm)p((p)) obs
II E-
P(T
obs
m)
II
da
where p(m) is the prior of the joint traits, and Bi Be(-)s), m², m.) is the agent's 's fixed policy conditioned on its trait m² the deployed mechanism xe.
The
( Te, m) San (p(sch) 1 1spts, Te, a,, m) (IT (a m, m,m.)
world
model
approximates the dynamics da,. The policy of the principal Il (x((
provides p( ((()))))) Thus, the likelihood estimated as
Po.o(T(m) p(sghr
[lg II t=
obs st Te. m).
To generate new trajectories. we need to sample m from the posterior p(m|r) rather than the prior p(m). However, p(m/7) is intractable, and we use the Posterior Trait Tracker qo (m/r)) to approximate it.
To maximize the log evidence log p(T), need to maximize the ELBO:
(ELBO v/, 1,,07)
(og(mm))lloaa)) Pw ssbss Tes m)]
(6)
state prediction likelihood
T Eyg (mir) flog (T DEL (m/r))lp(())
+
regularization
principal policy likelihood
As we use the same principal policy HT, to collect real trajectories and generate simulated trajectories, the principal policy likelihood is always maximized for ELBO. We minimize Equation 3 to maximize

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Equation 6 under assumptions that p(s 1 m) is Gaussian and each element of p(m) is unform. Please check the derivation details in Appendix A
Algorithm SWM-AP Learning framework
1: Initialize:
Mechanism Design Policy ( Migrio,e)), Dynamic
Model
Ma Ma |sth Tg. mppo),, Posterior Trait Tracker qu (Mppos [T), Prior Trait Tracker pe (ipproo.. HH,)
where H, (5 TTt, act), Environment, Model Datasets Denus Dmodel
2: for N Epochs do
3: Collect real trajectories
(s0 To. :............................... ST TT, TT) in Environment using policy IIg and Prior Trait Tracker Pç. Store in Denv.
4: Jointly train Posterior Trait Tracker Oe and Dynamic Model Mg on dataset Denvs using objective based on Equation 3] implicitly training dę to produce mppst
5: Train Prior Trait Tracker P& on dataset Denv using objective based on Equation 4 to align
( (-1+)) with g. (-1r)
6: Generate imagined trajectories f = (s0ts no, PO0 :.... using Dynamic Model Ma. policy oa and Posterior Trait Tracker pę. Store in Doddel-
7: Optimize policy Πy using data from Dear and D maximizing objective Equation
using PPO on combined data.
8: end for
9: Return: Policy 1l,, SWM Pv
4 Experiments
4.1 Facility Location
We designed a facility location game to examine the effectiveness of the methodology, where we developed learning strategies to enhance the capability higher-level agents in selecting optimal facility construction locations for the background populations of rulc-based agents.
Environment Setting: In the facility location game, the mechanism designer is tasked with selecting appropriate facility locations for multiple agents distributed across a map. Different agents exhibit heterogeneous preferences regarding facility locations. Our approach achieves optimal mechanism design by learning dynamic mechanism design strategies to maximize the collective reward of multiple low-level agents. The environment is configured as a matrix where each agent maintains a fixed global position at the beginning of each round, representing their permanent residence in real-world scenarios. The mechanism designer determines facility locations each round with fixed total number of facilities, where each location configuration influences the total visitation frequency of low-level agents to facilities. The reward is defined as the summation of visitation frequencies from low-level agents to facilities. This experimental setup corresponds to the classical facility location game in mechanism design theory. Specifically, we implement a configuration with five facilities and eight agents distributed across an 8 8 grid.
Performance Analysis: We evaluate our proposed SWM-AP method against several baselines: the mbdel- reinforcement learning algorithms Dreamer and MBPO, and the model-free RL algorithm PPO. The comparative results are presented in Figure Figure 3a utilizes dual y-axis plot to illustrate two key performance aspects: sample efficiency and final converged reward. On this plot, the circles, aligned with the right y-axis, represent the mean final reward (+ standard deviation) achieved by each algorithm upon convergence. The bars, corresponding to the left y-axis, indicate the number of training steps required for each method reach predefined performance target, specifically PPO's final converged reward. The results demonstrate that model-based methods generally exhibit superior sample efficiency compared their model-free counterparts. Notably, our method not only achieves the highest sample efficiency, requiring the fewest training steps to meet the performance target, but also attains the highest final converged reward among all evaluated algorithms. Figure 3b) and Figure 3c display the learning loss curves for system states and immediate rewards, respectively. We find that our SWM achieves more accurate predictions for both metrics when compared to other baselines.
7

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Algorithm Comparison: Sample Efficiency and Final Performance
DEEARO
9008
700K
2,099
(b) State prediction loss
408K
Steas
2008
DREADO
200K
100K
Oheamar
SWAM
(a) Facility location: Sample efficiency and final performance
(c) Reward prediction loss
Figure 3: Facility location performance analysis. (a) Comparison of sample efficiency and final converged performance. (b) State prediction loss and (c) Reward prediction loss curves for our SWM compared to baselines.
4.2 Team Structure Optimization
Team structure optimization, where the team structure background agents can be dynamically adjusted by principal, is another widely studied mechanism design problem. We conduct the experiments in AdaSociety [3], a highly customizable multi-agent environment supporting dynamic social relationships and heterogeneous agents with open-ended tasks. By controlling the relationships between background agents, principal aims to maximize the collective reward of background agents.
Environment Setting: The environment consists of an 8 x 8 grid with four types of basic resources (10 units each, positioned at the corners), where two basic resources can be converted into one advanced resource (valued at 5, compared to for basic resources). Four agent types exist, each capable of producing a specific basic resource unable to store it. Instead, they can store one other predefined resource type. Agents form teams of arbitrary size, with each agent restricted to one team, and incur maintenance cost 0.05(z 1) per step, where æ is the team size. Agents produce resources matching their type and only store resources to earn rewards if teammate can produce their storable types. In each episode, four background agents are initialized with randomly assigned types. Principal observes the current map without knowing agents' types, and then reassigns the team structure every 10 steps starting at step 5, aiming to maximize total group reward. Each episode lasts for 50 timesteps. The task challenges principal to optimize collective efficiency in resource- constrained multi multi-agent system, where principal must balance production, storage dependencies, and team coordination costs.
Nntermene Compurbon
Myrrttin Contune offiaan meee use untir Sitioiet
10
4% 10-1
3x 1p-
Trx
(a) Performance
(b) State loss
(c) example
Figure 4: Performance comparison in team structure optimization
Performance Analysis: We evaluate our SWM-AP method against representative model-based and model-free RL baselines in the dynamic team structure optimization task within AdaSociety. The comparative results are presented in Figure 4 Figure 4a highlights key performance metrics: sample efficiency (bars, left y-axis), indicating training steps reach a target performance, and final converged group reward (circles/points, right y-axis, with + standard deviation). Consistent with findings other domains, model-based approaches demonstrate superior sample efficiency. Notably, our method not only achieves the highest sample efficiency, requiring the fewest steps to reach the target, but also secures the highest final converged group reward, showcasing effectiveness in optimizing team configurations under resource constraints and dynamic reassignments. Figure 4b

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depicts the learning curves for the predictive components of the world model. These plots indicate that our SWM, which explicitly infers and uses agent traits to model team dynamics, achieves lower prediction errors compared to model-based baselines. Figure 4c illustrates an example of SWM and MBPO in this environment. Both algorithms take the current state (left sub-graph) as input and predict the location of each agent in the next timestep. These predictions are shown in the right sub-graph, with our SWM's prediction marked in pink and MBPO's in yellow. The right sub-graph also displays the actual location of the agent in the next timestep for comparison. Overall, SWM's predictions are more accurate. For instance, for the agent in the lower right corner, SWM correctly predicts that the agent will move the grid on the right, where resources located, while MBPO predicts that the agent will stay in its current position, where the manufacturing of advanced resources is taking place. This accuracy is likely because SWM has better understanding of background agents' traits, enabling it to more precisely infer these agents' action plans.
4.3 Tax Adjustment
In this experimental setup, low-level agents are trained using reinforcement learning. As a result, the planner interacts with continually adapting and improving population of agents, making the environment increasingly complex over time.
Environment Setting: In Al-Economist [39]. background agents engage in activities such as collecting materials (specifically wood and stone) to construct houses in exchange for income. They can also trade resources on the market. Agents possess varying levels of skills in house construction, and their primary objective is maximize individual utility. This utility positively influenced by income but negatively affected by labor effort. Therefore, agents make decisions by considering several economic variables, including their construction skills, resource endowments, and applicable tax rates. These factors influence both their work and consumption choices. Principal, whose role is to design tax policies, seeks to enhance social welfare by balancing overall economic productivity with income equality. Notably, principal lacks visibility into the agents' specific construction skills. For this experiment, the environment consists of four low-level agents operating within 25 x 25 map. Each episode spans 1000 time steps, while principal updates tax policies every 100 steps.
Mean perforance Camparison
Mean Equality Comparison
Kean Produrtivity Comparison
Performatce Comparieze (5AM MEROO)
1510
X000
13
parformants
2,000
2000
350
(a) Overall performance
(b) Equality
(c) Productivity
(d) State loss
Figure 5: Performance comparison in Al-Economist
Performance Analysis: We assess the effectiveness of our SWM-AP by comparing it with two baseline algorithms: the model-based MBPO and the model-free PPO. The evaluation is based on three social metrics recorded after 1,000 agent steps: equality, productivity, and their product, equality x productivity. The product metric serves as an indicator of overall social welfare within the simulated environment. The comparative results presented in FFiuure 3 As shown, our method exhibits effective control over taxation, enabling principal to optimize social welfare. Notably, our method attains level of productivity comparable to that of PPO while significantly enhancing equality. This suggests that our SWM is capable of promoting more equitable society without compromising economic output. In contrast, MBPO yields suboptimal performance. Although attempts to increase equality, this comes at the cost of a marked decline in productivity, ultimately resulting in lower overall social welfare relative to our method. We attribute the superior performance of our method to its ability to reduce state prediction eтror more efficiently during the early phases of training (as shown in (Figure 5d). This improved predictive accuracy facilitates more effective principal optimization, thereby leading to better overall outcomes.
5 Conclusion
This paper proposes a social world model-augmented mechanism design policy learning method, named SWM-AP, which employs unsupervised learning to infer the hidden trait of background

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agents, thereby enhancing the prediction of group dynamics and mechanism design policy learning. Experimental results in facility location, team structure optimization, and taxation setting tasks demonstrate that our method outperforms both model-based and model-free reinforcement learning approaches. Our approach inspires new directions for world model research towards more complex and realistic social world.
Limitations and Future Work: Current limitations include the scalability of SWM extremely large-scale systems and the challenge of ensuring the direct interpretability of all inferred latent traits. Future work will focus on developing more scalable SWM architectures, potentially leverag- ing structured priors, and on enhancing trait interpretability through techniques like disentangled representation learning.
Acknowledgments and Disclosure of Funding
This work is supported by the National Science and Technology Major Project (No. 2022/D0014404))
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A ELBO Derivation
We denote the principal's trajectory as (si No. 51 m1,"" as a, = (a) ... ),), and the joint traits as m = (m² ... , N. We assume the joint distribution of and follows generative process:
ST 1 -1 s7g), the joint actions
m
/. ( 1s2 1stth Te. a m)
p(T, m) p(m)p(((
Il p
II B.(atls) m', me) da
where p(m) is the prior of the joint traits, and Bi(+)s), m², xe) is the agent's fixed policy conditioned on its trait m' the deployed mechanism
The
world
model
Pr Ne, m) approximates
the dynamics da. The policy of the principal IIg (
Say (p(sph 1sthe, Te, a,, m) (II," (aaalss) m. mT)
provides p(Tellge)) Thus, the likelihood is estimated
T-1 II t=0
Po.0(r|m) p(s)tt))
obs ooh
Te. m).
To generate new trajectories, we need sample m from the posterior p(m/r) rather than the prior p(m). However, p(m[T) is intractable, and we use the Posterior Trait Tracker qu (m//) to approximate
Here, we derive a lower bound for the log evidence log (p)).
log Pv. = yg (m)))) (m)))) Pv.o (T)]
Pe.0 m)
gg (m/r))
Pv. (m T)
Po. m)
+ Eg go (ml) flog (m(/))
(m/r))log
(m(
p
Po.0(T, m)
-Eg (m/r)(lo
+
96 (m/T)
Po.a(T m)
gg (m/)))])
16 (m|T)
(m)r)) Pr.0 (T; m) log go (m|
(oo.../o))lloppoooo. + logg(m) log go (m [T)
20(m) rT)
(m)r)) (lagmm))oooopp..o (T[m) E (m))
p(m)
(mor P. ( (r|m)
D (mg
T
= logg(ss abs
E go (m//) Ilog Pi (sgtt 1st m)]
State Prediction Likelihood
T-1
+
E (m/ ( 3e B s - DKL (gs (m) (mppm////)//)p)))/)l) (p(m))
Regularization
principol policy likelihnod
20

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B Trait Inference Confusion Matrices
In our framework, a "trait" (m) represents a persistent, intrinsic characteristic of an agent. In tasks such AdaSociety, manifests as an agent's inherent production capability, while the SWM-AP method infers these unobservable attributes (e.g., skills, preferences, or risk attitudes) from agent interaction trajectories, shaping their behavior. This trait not directly encapsulated in the observation space (sz), rendering it inaccessible to the principal. We argue that the necessity of modeling such traits is directly tied to the degree of observational ambiguity in system. In real-world scenarios, a principal (e.g., government or platform) must make decisions under conditions of incomplete and ambiguous information. An individual's observable state (st) at any given moment, such as their current location or recent purchase, is often a highly ambiguous signal of their underlying trait (m), such as risk aversion, long-term preferences, or intrinsic skills. For instance, two individuals might be observed in the same location (st), but one is risk-averse local resident (trait m 1) while the other an adventurous tourist (trait m2). Their immediate responses (a,) and future state (#1+1) to a new incentive (e.g., dynamic pricing) will diverge drastically, and predicting this divergence is impossible without inferring their underlying traits.
To test this hypothesis and explore trait interpretability under observational ambiguity, we conducted diagnostic experiments in the AdaSociety task. In standard training, the Posterior Trait Tracker produces a confusion matrix with clear diagonal dominance, indicating successful differentiation between agent types(Figure 6| left). However, non-trivial off-diagonal values suggest room for improvement, attributable "modeling shortcuts". In later episode stages, the environment's predictability allows the model to rely on state history rather than precise trait inference, achieving low prediction error. To address this, we trained the tracker exclusively on high-ambiguity initial states, where agents' fixed starting positions provide minimal clues about their randomly assigned types. The resulting confusion matrix (Figure 6] right) exhibits stronger diagonal dominance. This demonstrates that SWM-AP's ability to learn interpretable traits is significantly enhanced under high-ambiguity conditions, which directly addresses persistent informational asymmetry in real-world scenarios.
Standard Training (Mixed Ambiguity States)
High-Ambiquity Training (Initial States)
Type
0.3819
0.2623
0.1751
0.1806
O.5635
0,1889
0.0000
0.2476
0.6
Typo
0.1314
0.6041
0.1840
0.0805
0.3079
0.4348
0.2313
0.0260
0.4
0.3
Type
0.2344
0.1239
0.3932
0.2464
0.0270
0.2182
0.4215
0.3332
0.1
0.2082
0.1047
0.2147
0.4724
0.2732
0.0000
0.1996
0.5272
Type
Type 2
Type
Type
Type
Type 2
Type
Type
Inferred
Inferred
Figure 6: Confusion matrices for trait inference in AdaSociety. Left: Standard training on mixed- ambiguity states, showing moderate diagonal dominance due modeling shorteuts in low-ambiguity late-episode states. Right: High-ambiguity training on initial states, demonstrating improved trait disentanglement with stronger diagonal dominance.
C Performance and Efficiency Results
To assess the scalability of SWM-AP in larger multi-agen settings, we extended the Facility Location task to 32 agents on 7x7 grid with placeable facilities. Each agent was randomly assigned one of two unobservable latent traits at the start of each episode, governing their behavior based on distance and congestion, with fixed home locations. The principal made mechanism design decisions per episode. Results, averaged over 3 independent runs with different random seeds, are presented in Table T Efficiency is measured as the number of training steps required to reach MBPO's final performance (reward of 6.43), with lower values indicating better sample efficiency.
21

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Table 1: Performance and efficiency results for the 32-agent Facility Location task.
Algorithm
Final Reward (Mean + Std) Steps to MBPO Final Perf.
PPO
6.55 + 0.03
353,600
MBPO
6,43 = 0.04
433,600
Dreamer
6.57 = 0.06
300,800
SWM-AP
6.62 = 0.06
274,667
These results demonstrate that SWM-AP achieves a superior sample efficiency compared to baselines.
D Computational Benchmarks
We report the runtime and memory usage benchmarked against the number of agents. The results indicate that both the runtime and memory footprint of our method fall within an acceptable range.
Table 2: Computational benchmarks for the Facility Location task across different agent numbers, per 100k training steps.
Agents
Training Time (hrs)
Memory Footprint (MB)
2
0.91
538
4
1.15
618
8
1.93
898
16
3.45
1786
32
5.25
5104
E
Experimental Details
This appendix provides essential details for reproducibility. Key configurations and hyperparameters are summarized below. Table summarizes crucial parameters for the experimental environments and core algorithms.
Table 3: Key Environment and Algorithm Configurations.
Calcanty Parander
Facility Location
Teun Structure Oytiniiativn
Taa Adjistmnnt
Exninnnen Apectiis
Agcel Couss
Tatral Coore
200
paint Maycaes)
Audgg smongg sypes
Tyeade
1000 (the 10 the planser)
SWM-AP: Socal Ris Madie (SMM)
H1512) LSTM
(1.2,
H.512 (1.2, H552)
Prefett SWM Oytnsen & L.R
MLP.L.3.PP 18250)
CCN (L.3 128)) 12..2. (.128)
GCN 1250) MLP
Aaan 80
Alkin, 10
Almm, 10
Mesfassion Dusige
sunn))
GCN
MMP (L..
MLP
1.S.5LL..H. (L.1H125))
Cytimies & LR
Adan. 2.5
Aduas, 6.x 10
Alaas, 1 10
DiSSARE Ixagited (5Wb)
0.50
0.99
0.09
Stteps
30
Aego
Bandiatr PPO
Pelkcy/blac Aack. Optimaerr
MLP:L.2 1280 Adams
GCN (LA. Hi14 64) MLP (L.,, H:250)
MLP (L.2, H 250) L5 LSTTLLLLEEE 1.8:50) MLP (L.1
Bsvilar:: MIPO
Phiacy/hils Anck.
MLFIL2
GATN 11114, 646) MLP (1226) 0.99
GUNILI 10185, 64)) qu2 11/209
1090
Geverl Thansing Compuae
Ntms. Randor Stads
Timer Bun.
XUM ower name
SUM over mu NVDIA KUX 3000/1 MR1
NEMM over STaze NVDIAA ATIIL permi))
NYSIHA RTX 3001 i1 perrus)
Further Details on SWM-AP: SWM trained to minimize Mean Squared Error for dynamics prediction. potentially with an additional VAE-like loss for trait inference if applicable. Further Details on Baselines: Model-free baselines like PPO implemented with standard configurations. For PPO, clipping epsilon of 0.2 was used.
22


Reviews:
[{"review_id": "Hlk2sW9y4y", "reviewer": "Reviewer_ggqb", "summary": "This paper proposes a method to learn a social world model based on inferred agent-specific traits. The method leverages model-based RL to train the underlying policy in a sample efficient way. The proposed approach is backed by the derivation of the ELBO for the agents traits. The performance is validated on 3 environments.", "questions": "- I assume that $\\hat{m}\\_{post}$ depends on $\\tau$ in (3), is that correct? In any case, it would be good to define $\\hat{m}\\_{post}$ more explicitly before (3).\n- Have you checked the performance of the algorithm in scenarios where there is no agent heterogeneity? Obviously, the performance cannot be expected to be much better in this case, and the sample efficiency could be decreased, but it would be nice to see that the asymptotic performance is not worse than the baselines.\n- In MBPO, the length of the rollouts is typically controlled to avoid the accumulation of errors. Is this not an issue in the proposed method?\n- In Figure 5.d, the loss seems to be re-increasing for the proposed method. I appreciate that this is already a lot of training steps, but it would be good to ensure that the loss does not diverge further.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The motivation of the paper is clear\n- The performance assessment is convincing with multiple environments and relevant baselines being included.\n- The theoretical motivation via the ELBO, although simple, gives additional confidence in the proposal method\n\nWeaknesses:\n- The notations need to be fixed, there are many inconsistencies, e.g., $N$ is sometimes a number of agents and sometimes a set, the action space is sometimes $A$ and sometimes $\\mathcal{A}$, the policy space is introduced as $\\Psi$ but the objective in (2) is maximisation over $\\Pi$, etc. \n- The performance assessment could be improved, e.g. by including a scenario/case with no agent heterogeneity", "was_revised": true, "final_justification": "The authors have done additional performance assessments that address the concerns I had about the performance of the algorithm.", "rebuttal": "We thank Reviewer ggqb for their thoughtful feedback and positive assessment of our core motivation. Their keen eye for detail and suggestions for additional experiments have been instrumental in helping us improve the manuscript's rigor and clarity. We provide detailed responses to each point below.\n\n> **Response to Weakness 1**:\n\nApologies for any confusion caused by the notations! We will address the following issues: In Line 127, $N$ is used as a set, which will be corrected to $[N]$ to represent the set ${1, \\cdots, N}$. Additionally, in Line 129, $A$ is used to denote the action space of the background agents, and this will be updated to $\\mathcal{A}$ for consistency.\n\nRegarding formula (2), we would like to clarify that $\\Psi$ represents the mechanism space (the action space of the principal), while $\\Pi$ denotes the policy space of the principal. On the other hand, $\\mathcal{A}$ refers to the action space of the background agents, not the principal. Therefore, the objective in formula (2) involves maximization over the policy space $\\Pi$.\nWe will add necessary explanations for these notations in the revised manuscript to minimize confusion.\n\n>**Response to Question 1**: \n\nThank you for this excellent suggestion for improving clarity. You are absolutely correct: $\\hat{m}_{\\text{post}}$ indeed inferred from the complete interaction trajectory $\\tau$. \n\nIn our framework, $\\hat{m}_{\\text{post}}$  presents the posterior estimation of the agents' latent traits. It is generated by a specific component of our Social World Model (SWM) called the Posterior Trait Tracker. As you rightly pointed out, this tracker takes the entire trajectory $\\tau = (s_0^{\\text{obs}}, \\pi_0, r_0^{\\text{soc}}, \\dots)$ as input and infers the most likely latent traits that explain the observed agent behaviors throughout the episode.\n\nWe agree that defining this explicitly before its first appearance in Equation (3) would significantly enhance the paper's readability. In the revised manuscript, we will move the detailed description of the Posterior Trait Tracker and the definition of $\\hat{m}_{\\text{post}}$  to appear just before Equation (3), ensuring the notation is clear before being used in the objective function.\n\n>**Response to  Weakness 2 & Question 2**: \n\nAs you correctly anticipated, the primary advantage of our SWM-AP framework lies in handling heterogeneity, so we would not expect a significant performance gain in a homogeneous scenario. The most important outcome, as you noted, is to ensure that our method does not underperform the baselines in terms of asymptotic reward. We have conducted this experiment in the Facility Location setting by assigning all agents the identical ground-truth trait. Our results confirm your hypothesis:\n\nMBPO's converged reward of 0.89 ± 0.05. SWM-AP achieves a final performance level statistically on par with the MBPO baseline(0.87 ± 0.04). MBPO reached its final performance level (a reward of 0.89) at approximately 269k training steps, while SWM-AP reached this performance threshold (a reward of 0.89) at around 301k steps. The sample efficiency of SWM-AP is slightly lower than MBPO in this setting, as the model initially expends capacity to model non-existent trait variations. However, the asymptotic performance of SWM-AP converges to a level that is statistically on par with the MBPO baselines.\n\nThis demonstrates that our framework is robust; while it is specialized for heterogeneous systems, it does not suffer a significant performance degradation in simpler, homogeneous environments. We will add a new subsection in the appendix of the revised paper to present these results and the corresponding learning curves.\n\n>**Response to Question 3**:  \n\nThank you for raising this critical point regarding error accumulation in model-based methods. This is indeed a fundamental challenge. Our approach mitigates this issue, primarily due to the hierarchical decision-making structure and time-scale separation that are central to our mechanism design formulation.\n\nIn our framework, the mechanism design policy (the \"Principal\") operates at a much slower time scale than the background agents. For instance, in the AI-Economist experiment, the Principal updates the tax policy only once every 100 agent-level steps. This means that for the principal's policy optimization, the effective \"horizon\" it needs to look ahead is naturally bounded. To evaluate a potential policy change, our SWM only needs to simulate the system's evolution over this relatively short, high-level decision interval . This structure naturally limits the required rollout length for the Principal's policy learning, thereby preventing the catastrophic accumulation of prediction errors that plagues methods requiring very long-horizon rollouts.\n\nThis structural advantage is complemented by the higher intrinsic accuracy of our SWM. By conditioning on inferred agent traits, our model achieves a lower single-step prediction error (as shown in Figures 3b and 4b), which further enhances the reliability of these necessary short-to-medium-horizon simulations.\n\nFor future work on problems that might require even longer-term strategic planning by the Principal, we agree that more advanced techniques would be beneficial. Methods such as incorporating a learned terminal value function to bootstrap long-term reward estimates, or leveraging more sophisticated trajectory optimization techniques, would be promising directions to further enhance robustness. We will add a brief note on this to the discussion section in our paper.\n\n>**Response to Question 4**: \n\nThank you for raising this important point. We have extended the training to 5e8 steps and observed that the state loss for our proposed method (SWM) stabilizes at **0.72 ± 0.02**, remaining consistently lower than the MBPO baseline, which achieves **0.83 ± 0.03**. We will include the extended results and updated figure in the camera-ready version to provide a clearer illustration of the training dynamics and confirm that the loss does not diverge further."}, {"review_id": "RpqTAagXvw", "reviewer": "Reviewer_w2JX", "summary": "This paper introduces a hierarchical, model-based reinforcement learning framework that addresses two challenges in settings with many agents: (1) agents have unobserved, persistent traits and (2) exploring real social environments is costly and risky. The proposed method couples a social world model, which predicts future states and rewards while conditioning on latent agent traits, with a mechanism-design policy trained by PPO. Empirical studies in three domains demonstrate that the proposed method achieves higher cumulative social rewards in fewer real-environment steps than baseline model-free and model-based methods. Additionally, its learned world model exhibits lower prediction errors.", "questions": "1. Can the authors provide a thorough literature review of the relevant areas from the techique side and clearly highlight their own contribution?\n2. Can the authors include experimental results that compare their method with current state-of-the-art approaches?\n3. Can the authors report a comparison of computational efficiency?\n4. Can the authors scale up the experiments to involve a larger number of agents?", "limitations": "The experiments use at most eight agents, yet the method is intended for large-population settings (e.g., public-policy platforms). The authors should discuss failure modes or computational bottlenecks expected when scaling to hundreds or thousands of agents, and outline mitigation strategies (e.g., hierarchical clustering, distributed roll-outs).", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strengths\n- The paper lays out the background, algorithmic components, and training pipeline in a logical sequence, with helpful figures that make the core ideas easy to grasp.\n- By explicitly modelling latent agent traits and positioning the work within mechanism-design applications, the authors demonstrate a genuine concern for practical deployment.\n- Experiments span three distinct benchmarks, highlighting the method’s versatility and robustness across heterogeneous tasks.\n\n## Weaknesses\n- Latent modeling has already been explored in recent multi-agent RL work (e.g., [1–3]), so it is crucial for the authors to articulate exactly how their approach diverges from—and advances beyond—these prior methods.\n- Comparative results rely on methods that are more than 5 years old. Without head-to-head evaluations against current SOTA algorithms, the performance claims remain unconvincing.\n- Model-based RL is already sensitive to modelling inaccuracies, the extra complexity introduced by the dual-tracker architecture (posterior + prior) could amplify instability and incur significant compute overhead. However, the paper provides no comparision measurements of training time, memory footprint, or convergence speed, so the method’s computational efficiency and practical scalability remain unclear.\n- All test scenarios involve only 4/8 agents. Such limited scale makes it hard to judge whether the approach would stay stable and performant in the larger populations typical of real-world social systems, and therefore its broader contribution to world-model research remains to be demonstrated.\n\n[1] Venugopal A, Milani S, Fang F, et al. MABL: Bi-Level Latent-Variable World Model for Sample-Efficient Multi-Agent Reinforcement Learning[J]. arXiv preprint arXiv:2304.06011, 2023.\n\n[2] Na H, Moon I. LAGMA: latent goal-guided multi-agent reinforcement learning[J]. arXiv preprint arXiv:2405.19998, 2024.\n\n[3] Xie A, Losey D, Tolsma R, et al. Learning latent representations to influence multi-agent interaction[C]//Conference on robot learning. PMLR, 2021: 575-588.", "was_revised": true, "final_justification": "After the rebuttal, most of my concerns were addressed by the authors. However, since the code is not accessible (which the authors claim will be released once the paper is published) and the design of the network framework is oversimplified, I still question the reproducibility of the work. So my final decision is Borderline accept.", "rebuttal": "We sincerely thank Reviewer w2JX for their detailed and constructive feedback. Their clear, actionable suggestions have been invaluable in strengthening our manuscript. We have conducted new experiments and analyses to address every concern raised.\n\n>**Response to Weakness 1 & Question 1:**\n\nWe thank the reviewer for highlighting these important related works in multi-agent latent modeling. We agree that it is crucial to articulate our unique contribution. Our work diverges from these cited papers in its fundamental problem setting and objective.\n\nThe methods cited (MABL, LAGMA and LILI) primarily focus on improving the decentralized policies of low-level, cooperative agents by inferring the latent goals or types of their peers. Their goal is to enhance coordination among the agents themselves.\n\nIn contrast, our work addresses a hierarchical Mechanism Design problem. Our objective is not to train the low-level agents, but to learn an optimal policy for a Principal who aims to guide a population of self-interested, heterogeneous agents towards a socially desirable outcome (e.g., maximizing social welfare). The latent traits in our framework are inferred by the Principal to better predict the population's response to incentives, which is a fundamentally different information flow and use case. This self-interest fundamentally complicates the learning problem. Unlike in cooperative settings, the dynamics are more complex and less predictable, as background agents may act strategically or competitively.\n\nTherefore, while we share the technical tool of latent modeling, our core contribution lies in formulating and solving a Social World Model-Augmented Mechanism Design problem, a distinct and less explored area compared to cooperative MARL. We will revise our related work section to more explicitly draw this distinction and clarify our unique positioning, and we will certainly include and discuss these valuable references suggested by the reviewer.\n\n\n>**Response to Weakness 2 & 4, and Questions 2 & 4:**\n\nWe appreciate the reviewer's concerns regarding the choice of baselines and the scalability of our method. We would like to address these interconnected points.\n\n**1. On the Choice of Baselines (W2, Q2):** We chose MBPO and Dreamer as representatives for state-based and pixel-based model-based RL, respectively. While MBPO is an established algorithm, it remains a strong and widely-used baseline for sample-efficient state-space MBRL, which is the setting for our tasks. We did include Dreamer, a more recent and powerful model-based approach, in our comparisons for the Facility Location task, demonstrating that our SWM outperforms it in both sample efficiency and final reward.\n\n**2. On Scalability (W4, Q4):** We acknowledge that demonstrating scalability is crucial. To address this, we have conducted a new, larger-scale experiment in the Facility Location environment with 32 agents.\n\n| Algorithm | Performance | Efficiency (Steps to reach Dreamer Final Perf.) |\n|---|---|---|\n| Dreamer | 6.56 $\\pm$ 0.08 | 374400 |\n| SWM-AP (Ours) | 6.68 $\\pm$ 0.05 | 304000 |\n\nEven in this more challenging 32-agent scenario, our SWM-AP maintains its performance advantage, outperforming Dreamer. This finding underscores the scalability of our approach, demonstrating its robustness as the complexity of the multi-agent system increases. We will add this new experiment to the appendix of the revised paper.\n\n**Future Directions for Massive-Scale Systems:** We completely agree with the reviewer that scaling to hundreds or thousands of agents, as mentioned in the \"Limitations\" section, presents a common and significant challenge for the entire field of multi-agent learning. The mitigation strategies suggested, such as hierarchical clustering of agents or leveraging structured models for distributed rollouts, are indeed highly promising future research directions.\n\n- Our framework provides a natural foundation for such extensions. For instance, the inferred latent traits from our SWM could be used directly as input for a hierarchical clustering algorithm to group agents with similar behaviors. This would allow the Principal to design semi-targeted mechanisms for agent clusters rather than individuals, drastically reducing the policy's output space.\n- We will explicitly incorporate this discussion into our \"Limitations and Future Work\" section, crediting these ideas as promising pathways to scale our framework to massive population sizes.\n\n\n>**Response to Weakness 3 & Question 3:**\n\nThe dual-tracker architecture does introduce additional computational components. To provide full transparency on the practical costs, we have benchmarked the computational efficiency of our method against the baselines in the Facility Location task(8 agents). We will include the following table in the appendix:\n\n| Method | Training Time (per 100K steps) | Memory Footprint (MB) |\n|---|---|---|\n| PPO | $\\sim$ 1.6 hours | $\\sim$564 MB |\n| MBPO | $\\sim$1.87 hours | $\\sim$1102 MB |\n| Dreamer | $\\sim$1.85 hours | $\\sim$1094 MB |\n| SWM-AP (Ours) | $\\sim$1.93 hours | $\\sim$898 MB |\n\nThe results show that while SWM-AP incurs a moderate overhead in training time and model size, this additional cost is justified by its significant gains in sample efficiency and final task performance, which are often the primary bottlenecks in costly real-world interactions. Our approach trades some computational resources for a substantial reduction in the amount of expensive environment interaction data needed."}, {"review_id": "Jfd18OdERD", "reviewer": "Reviewer_ksZ8", "summary": "The paper proposes SWM-AP, a novel framework combining a Social World Model (SWM) with policy learning for mechanism design in multi-agent systems. By inferring agents’ latent traits from interaction trajectories, the model predicts agent behavior and improves the efficiency and adaptability of mechanism design policies. Experiments across diverse scenarios (tax policy, facility location, team coordination) show SWM-AP outperforms both model-free and model-based RL baselines in sample efficiency and social welfare outcomes.", "questions": "How does SWM-AP scale computationally with the number of agents and complexity of traits?\n\nCan latent traits be interpreted or validated meaningfully (e.g., via human-aligned categories)?\n\nHow would the framework adapt to real-world applications, especially where traits evolve over time?\n\nWhat are the risks of bias or exploitation in learned mechanisms, and how can these be mitigated?", "limitations": "While the authors acknowledge key limitations, including scalability and interpretability, they do not sufficiently elaborate on their practical implications or propose concrete mitigation strategies. To improve, the authors should expand the scalability discussion by reporting runtime and memory usage as a function of agent count. Trait interpretability can be strengthened through the use of structured priors, a taxonomy of traits, or alignment with established psychological constructs. The ethical section should be deepened to address fairness, potential bias, and safeguards for uncertainty-aware policies, particularly in socially sensitive applications.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths: The paper presents several notable strengths. Its originality lies in the integration of latent trait inference with policy learning, marking a clear innovation over prior approaches in reinforcement learning and economic mechanism design. The methodology is technically rigorous, supported by a solid theoretical foundation grounded in variational inference and validated through ELBO derivations. Experimental results across diverse domains demonstrate consistent performance gains, reinforcing the framework’s robustness. Furthermore, the paper is well-written and logically structured, with clear figures and diagrams that enhance comprehension. Its relevance extends broadly to social systems, with promising applications in areas such as public policy, resource allocation, and potentially digital mental health.\n\nWeaknesses: The work also presents some limitations. The most prominent concern is scalability. There is insufficient analysis or evidence showing how the approach handles large agent populations or complex environments. A second issue relates to interpretability: while latent traits are central to the model, their meaning and impact remain opaque, limiting practical transparency. Additionally, the evaluation is restricted to synthetic settings, with no real-world data or deployment case studies to assess generalizability. Finally, ethical considerations, including fairness and misuse of trait-based modeling, are only superficially addressed. This is particularly concerning for potential applications in sensitive contexts, such as mental health, where rigorous safeguards would be essential.", "was_revised": true, "final_justification": "The authors' rebuttal successfully resolved my primary concerns regarding scalability (demonstrated through new 32-agent experiments and comprehensive runtime benchmarks) and provided solid theoretical grounding for trait learning through their observational ambiguity framework, with diagnostic experiments validating improved trait disentanglement under high-ambiguity conditions. While ethical safeguards and real-world deployment readiness remain partially addressed, with composite objectives providing some protection but lacking concrete frameworks for sensitive applications, and synthetic environments still leaving questions about handling noisy real-world data, I assign high weight to the excellent technical innovation and experimental validation across diverse domains, viewing the deployment concerns as natural limitations for foundational research rather than fundamental flaws. The integration of latent trait inference with mechanism design represents a significant algorithmic contribution with strong empirical support that merits acceptance, though future work should consider validation frameworks against established behavioral models and more concrete safeguarding mechanisms for sensitive applications.", "rebuttal": "We are deeply grateful to Reviewer ksZ8 for their excellent and supportive review. The reviewer's forward-looking questions and constructive suggestions on limitations are invaluable, and we are pleased to provide new experimental results and further clarifications that address every point raised.\n\n>**Response to Q1:**\n\nWe have conducted a new, larger-scale experiment in the Facility Location environment with 32 agents to empirically assess this.\n\n| Algorithm | Performance | Efficiency (Steps to reach Dreamer Final Perf.) |\n|---|---|---|\n| Dreamer | 6.56 $\\pm$ 0.08 | 374400 |\n| SWM-AP (Ours) | 6.68 $\\pm$ 0.05 | 304000 |\n\nEven in this more challenging 32-agent scenario, our SWM-AP maintains its performance advantage, outperforming Dreamer. This finding underscores the scalability of our approach, demonstrating its robustness as the complexity of the multi-agent system increases. We will add this new experiment to the appendix of the revised paper.\n\n>**Response to Q2:**\n\nWe sincerely thank the reviewer for this insightful question, which has prompted us to clarify a core motivation of our work. The necessity of learning latent traits is not an artifact of a specific experimental design but rather a fundamental characteristic of real-world mechanism design problems. Our deeper analysis confirms that the key determinant for learning interpretable traits is the degree of observational ambiguity, a condition that is pervasive in the complex, real-world social systems that mechanism designers face.\n\nTo clarify, in our framework, a 'trait' represents a persistent, intrinsic characteristic of an agent that is distinct from the transient system dynamics. For instance, in AdaSociety, it represents an agent's inherent production capability. This trait is **unobservable** to the principal, as it is not directly encapsulated in the observation space ($s_t$). \n\nThe necessity of modeling such traits, we argue, is directly tied to the degree of **observational ambiguity** in a system. In many real-world scenarios, a principal (e.g., a government or a platform) must make decisions under conditions of incomplete and ambiguous information. An individual's observable state ($s_t$) at any given moment, such as their current location or recent purchase, is often a highly ambiguous signal of their underlying, persistent trait ($m$), such as their risk aversion, long-term preferences, or intrinsic skills. For instance, two individuals might be observed in the same location ($s_t$), but one is a risk-averse local resident (trait $m_1$) while the other is an adventurous tourist (trait $m_2$). Their immediate responses ($a_{t}$) and future state ($s_{t+1}$) to a new incentive (e.g., dynamic pricing) will diverge drastically, and predicting this divergence is impossible without inferring their underlying traits.\n\nOur current experiments, while controlled, already demonstrate the model's ability to capture these unobservable traits. When trained on the complete trajectories of the AdaSociety task, our trait tracker produces a confusion matrix with clear diagonal dominance, indicating that it successfully learns to differentiate between agent types. However, we acknowledge there is room for improvement, as some off-diagonal values are non-trivial.\n\n(Confusion Matrix from current main experiment, 4 agents average)\n| | **Inferred  Type 1** | **Inferred  Type 2** | **Inferred  Type 3** | **Inferred  Type 4** |\n|:---:|:---:|:---:|:---:|:---:|\n| **True Type 1** | **0.3819** | 0.2623 | 0.1751 | 0.1806 |\n| **True Type 2** | 0.1314 | **0.6041** | 0.1840 | 0.0805 |\n| **True Type 3** | 0.2344 | 0.1239 | **0.3932** | 0.2484 |\n| **True Type 4** | 0.2082 | 0.1047 | 0.2147 | **0.4724** |\n\nOur analysis suggests this imperfect disentanglement stems from a 'modeling shortcut' (consistent with Occam's Razor). In later stages of the episode, the environment becomes more predictable, and the model can achieve low prediction error by relying on state history rather than precise trait inference.\n\nTo test this hypothesis, we conducted an additional **diagnostic experiment**. In this experiment, we trained the trait inference module **exclusively on data from high-ambiguity states**—specifically, the initial episode steps where agents' fixed starting positions offer few clues about their randomly assigned types. The resulting confusion matrix exhibits a stronger diagonal dominance\n\n(Confusion Matrix from diagnostic experiment using only high-ambiguity states)\n| | **Inferred  Type 1** | **Inferred  Type 2** | **Inferred  Type 3** | **Inferred  Type 4** |\n|:---:|:---:|:---:|:---:|:---:|\n| **True Type 1** | **0.5635** | 0.1889 | 0.0000 | 0.2476 |\n| **True Type 2** | 0.3079 | **0.4348** | 0.2313 | 0.0260 |\n| **True Type 3** | 0.0270 | 0.2182 | **0.4215** | 0.3332 |\n| **True Type 4** | 0.2732 | 0.0000 | 0.1996 | **0.5272** |\n\nThis diagnostic result confirms that the model's capacity for learning interpretable traits is significantly enhanced when it is forced to operate in ambiguous conditions. The improved diagonal dominance strongly suggests that the limitation lies not in our model's architecture, but in the nature of the training data provided by the simplified environment.\n\nThis insight directly motivates our plan to incorporate two enhanced experimental settings into the final paper, which are designed to maintain this crucial ambiguity persistently and more faithfully represent real-world complexity:\n\nThe first task involves augmenting the existing Facility Location task with latent behavioral norms. We consider a scenario with behavioral dispositions as traits, which are inherently more ambiguous than the static preferences in the current Facility Location task. The trait will be a 'patience' or 'responsiveness' factor that dictates how an agent reacts to dynamic conditions like queues, reflecting real-world heterogeneity in responses to friction. In such cases, predicting an agent's future visit probability merely from the current queuing status becomes infeasible.\n\nThe second task is designed to ensure persistent informational asymmetry within the AdaSociety environment. We will ensure the informational gap between the principal and agents is persistent. By randomizing initial positions and resource locations in every episode, we simulate a scenario where the principal constantly faces new, unfamiliar agent configurations, a common challenge in dynamic markets or online platforms.\n\nThese enhanced experiments will showcase SWM-AP's core strength in handling ambiguity. Since real-world systems exhibit far greater ambiguity than our simulations, we expect the performance gains of our approach to be even more significant in practice.\n\n>**Response to Q3:**\n\nWe acknowledge that in many real-world scenarios, agent traits can be dynamic and evolve over time.\n\nThe current version of our framework, SWM-AP, assumes persistent traits within an episode to ensure experimental control and tractability. This allows us to establish a strong baseline for the core challenge of inferring static hidden traits.\n\nAdapting to evolving traits is a significant and exciting direction for future work. Our framework could be extended to handle this by modifying the trait inference mechanism. For example, instead of a single posterior over the whole trajectory, one could use a sequential inference model to track the trait distribution over time. The \"Prior Trait Tracker\" used by the policy would then naturally provide the most up-to-date trait estimate for decision-making. We believe our current work provides a solid foundation for these future explorations into more dynamic social environments. We will add this to our \"Limitations and Future Work\" section.\n\n>**Response to Q4:**\n\nMitigating bias and exploitation is paramount for any AI system intended for social applications. We address this in our work through several layers:\n\n1.  Our framework's behavior is fundamentally guided by the principal's objective function. As demonstrated in the AI-Economist experiment (Figure 5), we do not naively maximize a single metric like productivity. Instead, we use a composite reward function that explicitly balances productivity and equality. This forces the learned mechanism to avoid exploitative strategies that might increase overall output at the cost of fairness. We believe this principle of carefully designing socially-aware objectives is the primary tool for mitigation. For real-world deployment, this objective would need to be co-designed with domain experts and sociologists to incorporate broader ethical values.\n2.  In the current experiments, the planner's action space (e.g., setting tax brackets) is well-defined and constrained, which naturally limits the potential for unforeseen exploitative behaviors.\n3.  We agree that real-world deployment would require rigorous safeguards. Our trait inference is based on aggregated, anonymized behavioral data within the simulation. In any real-world application, ensuring individual privacy and data security would be a prerequisite. The mechanisms would operate on population-level dynamics rather than targeting identifiable individuals in a harmful way.\n\nWe will expand our ethics discussion in the paper to more thoroughly cover these points, emphasizing the role of objective engineering as a key mitigation strategy.\n\n>**Response to Limitations:**  \n\nWe report the runtime and memory usage benchmarked against the number of agents. The results indicate that both the runtime and memory footprint of our method fall within an acceptable range.\n\n| Agent Num | Training Time (per 100K steps)\t| Memory Footprint (MB) |\n|---|---|---|\n| 2 | $\\sim$ 0.91 hours | $\\sim$538 MB |\n| 4 | $\\sim$1.15 hours | $\\sim$618 MB |\n| 8 | $\\sim$1.93 hours | $\\sim$898 MB |\n| 16 | $\\sim$ 3.45 hours | $\\sim$1786 MB |\n| 32 | $\\sim$  5.25 hours | $\\sim$5104 MB |"}]

Author rebuttal:

Meta-review: The paper proposes a hierarchical model-based RL framework for mechanism design in multi-agent systems with latent traits (like skills or preferences). Motivation is clear, the method is theoretically grounded, and evaluation is convincing.

The discussion period has been useful and has helped the authors to improve their work. In particular, they improved evaluation to demonstrate the efficiency and scalability of the proposed framework and have committed to include many clarifications about the experiments in the final version of their paper.

I recommend acceptance because the paper tackles an important and challenging problem, the proposed method is sound both in terms of theoretically motivated and empirical evaluation, and the paper has interesting ideas that might inspire other communities, like those working on agentic frameworks.
Decision: Accept (poster)