Hamidou Tembiné

Hamidou Tembine, Quanyan Zhu, Tamer Basar

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function described by a Hamilton-Jacobi-Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics.

Quanyan Zhu, Hamidou Tembine, Tamer Basar

Learning algorithms are essential for the applications of game theory in a networking environment. In dynamic and decentralized settings where the traffic, topology and channel states may vary over time and the communication between agents is impractical, it is important to formulate and study games of incomplete information and fully distributed learning algorithms which for each agent requires a minimal amount of information regarding the remaining agents. In this paper, we address this major challenge and introduce heterogeneous learning schemes in which each agent adopts a distinct learning pattern in the context of games with incomplete information. We use stochastic approximation techniques to show that the heterogeneous learning schemes can be studied in terms of their deterministic ordinary differential equation (ODE) counterparts. Depending on the learning rates of the players, these ODEs could be different from the standard replicator dynamics, (myopic) best response (BR) dynamics, logit dynamics, and fictitious play dynamics. We apply the results to a class of security games in which the attacker and the defender adopt different learning schemes due to differences in their rationality levels and the information they acquire.

Quanyan Zhu, Hamidou Tembine, Tamer Basar

In this paper, we formulate an evolutionary multiple access channel game with continuous-variable actions and coupled rate constraints. We characterize Nash equilibria of the game and show that the pure Nash equilibria are Pareto optimal and also resilient to deviations by coalitions of any size, i.e., they are strong equilibria. We use the concepts of price of anarchy and strong price of anarchy to study the performance of the system. The paper also addresses how to select one specifc equilibrium solution using the concepts of normalized equilibrium and evolutionary stable strategies. We examine the long-run behavior of these strategies under several classes of evolutionary game dynamics such as Brown-von Neumann-Nash dynamics, and replicator dynamics.

Quanyan Zhu, Hamidou Tembine, Tamer Basar

In this paper, we formulate an evolutionarymultiple access control game with continuousvariable actions and coupled constraints. We characterize equilibria of the game and show that the pure equilibria are Pareto optimal and also resilient to deviations by coalitions of any size, i.e., they are strong equilibria. We use the concepts of price of anarchy and strong price of anarchy to study the performance of the system. The paper also addresses how to select one specific equilibrium solution using the concepts of normalized equilibrium and evolutionarily stable strategies. We examine the long-run behavior of these strategies under several classes of evolutionary game dynamics, such as Brown-von Neumann-Nash dynamics, Smith dynamics and replicator dynamics. In addition, we examine correlated equilibrium for the single-receiver model. Correlated strategies are based on signaling structures before making decisions on rates. We then focus on evolutionary games for hybrid additive white Gaussian noise multiple access channel with multiple users and multiple receivers, where each user chooses a rate and splits it over the receivers. Users have coupled constraints determined by the capacity regions. Building upon the static game, we formulate a system of hybrid evolutionary game dynamics using G-function dynamics and Smith dynamics on rate control and channel selection, respectively. We show that the evolving game has an equilibrium and illustrate these dynamics with numerical examples.

H. Tembine

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean field limit and dynamical system viewpoints. Under regularity assumptions and specific time-scaling techniques, the evolution of the mean field limit can be expressed in terms of deterministic or stochastic equation or inclusion (difference or differential). In this paper, we overview recent advances of large-scale games in large-scale systems. We focus in particular on population games, stochastic population games and mean field stochastic games. Considering long-term payoffs, we characterize the mean field systems using Bellman and Kolmogorov forward equations.

Hamidou Tembine

This article develops an intergenerational mean-field-type game (MFTG) to model Mali's and neighbouring countries multi-actor conflict ecosystem, which includes formal state forces, traditional hunters, nonstate militias, jihadists, criminal networks, civil societies, and international proxies. Each decision-maker (agent, a group of agents or representative agent) is defined by a type, state, information structure, and action, with payoffs dependent not only on individual decisions but also on the evolving distribution of all agents' profiles. The model reveals that cycles of violence can persist across multiple generations due to the embedded presence of retaliatory types such as revenger child-soldiers whose trauma-conditioned best-responses favor conflict, and whose behavior reinforces intergenerational transmission of violence. The model also captures the strategic exploitation of institutional fragility by war entrepreneurs who profit from sustained instability through arms sales, militia contracting, and unregistered market mediation. These actors inject minimal resources to trigger profitable escalations, turning latent tensions into self-reinforcing violence economies. We show that in the absence of structural counterincentives, peaceful strategies are non-absorbing, and violence remains dynamically rewarding for war entrepreneurs. However, by embedding incentive-compatible, information-adaptive transfers directly into instantaneous payoffs, rewarding verifiable peacebuilding and penalizing aggression, it is possible to shift the mean-field-type equilibrium distribution intergenerationally toward more peaceful types and drive systemic de-escalation. We also discuss about the funding and the real implementation of such mechanisms in the field.

Elham Rostami, Taous-Meriem Laleg-Kirati, Hamidou Tembine

We study training-free flow matching between two Gaussian mixture models (GMMs) using explicit velocity fields that transport one mixture into the other over time. Our baseline approach constructs component-wise Gaussian paths with affine velocity fields satisfying the continuity equation, which yields to a closed-form surrogate for the pairwise kinetic transport cost. In contrast to the exact Gaussian Wasserstein cost, which relies on matrix square-root computations, the surrogate admits a simple analytic expression derived from the kinetic energy of the induced flow. We then analyze how closely this surrogate approximates the exact cost. We prove second-order agreement in a local commuting regime and derive an explicit cubic error bound in the local commuting regime. To handle nonlocal regimes, we introduce a path-splitting strategy that localizes the covariance evolution and enables piecewise application of the bound. We finally compare the surrogate with an exact construction based on the Gaussian Wasserstein geodesic and summarize the results in a practical regime map showing when the surrogate is accurate and the exact method is preferable.

Daryl Noupa Yongueng, Hamidou Tembine

Normalization is a key point in transformer training . In Dynamic Tanh (DyT), the author demonstrated that Tanh can be used as an alternative layer normalization (LN) and confirmed the effectiveness of the idea. But Tanh itself faces orthogonality, linearity and distortion problems. Due to that, his proposition cannot be reliable. So we propose a Holonorm (hn) which has residual connections and nonlinearity. Holonorm is suitable for replacing Tanh in the context of normalization. Although the HoloNorm expression could be similar to the softsign function in dimension one, softsign is a componentwise function which is not good for tensors and vectors of great dimension. Holonorm preserves the orthogonality, the direction, the invertibility of the signal. Holonorm is also a suitable metric, maps all vectors into the open unit ball. This prevents exploding activations and improves stability in deep Transformer models. In this work, we have meticulously examined the normalization in transformers and say that Holonorm, a generalized form of softsign function suited as a normalization function first.Second, defined between 0 and 1 hn serves as a percentage, and $1 - \text{Holonorm}$ is its complement, making it better understandable in evaluating a model.

Hamidou Tembine

Persistent instability in Mali and neighboring countries is not a temporary security crisis but a self-reproducing conflict system sustained by intergenerational grievances, climatic shocks, predatory resource extraction, and decentralized war economies. We develop a novel intergenerational Volterra mean-field-type game framework in which historical memory, inherited distrust, revenge incentives, and evolving institutional responses jointly shape future conflict dynamics. The analysis reveals how war entrepreneurs recycle illicit resource revenues through global financial networks, while blunt regulatory interventions can inadvertently accelerate recruitment into armed groups. We design optimal policies that alter the system's long-run geometry, severing the financial and psychological feedback loops of violence. The resulting framework provides a predictive and actionable architecture for durable peace, civilian protection, and multi-generational structural stabilization in the Sahel and beyond.

Allahsera Auguste Tapo, Ali Traore, Sidy Danioko et al.

In the last 5 years, the availability of large audio datasets in African countries has opened unlimited opportunities to build machine intelligence (MI) technologies that are closer to the people and speak, learn, understand, and do businesses in local languages, including for those who cannot read and write. Unfortunately, these audio datasets are not fully exploited by current MI tools, leaving several Africans out of MI business opportunities. Additionally, many state-of-the-art MI models are not culture-aware, and the ethics of their adoption indexes are questionable. The lack thereof is a major drawback in many applications in Africa. This paper summarizes recent developments in machine intelligence in Africa from a multi-layer multiscale and culture-aware ethics perspective, showcasing MI use cases in 54 African countries through 400 articles on MI research, industry, government actions, as well as uses in art, music, the informal economy, and small businesses in Africa. The survey also opens discussions on the reliability of MI rankings and indexes in the African continent as well as algorithmic definitions of unclear terms used in MI.

Jian Gao, Deep Chakraborty, Hamidou Tembine et al.

We propose a nonparallel data-driven emotional speech conversion method. It enables the transfer of emotion-related characteristics of a speech signal while preserving the speaker's identity and linguistic content. Most existing approaches require parallel data and time alignment, which is not available in most real applications. We achieve nonparallel training based on an unsupervised style transfer technique, which learns a translation model between two distributions instead of a deterministic one-to-one mapping between paired examples. The conversion model consists of an encoder and a decoder for each emotion domain. We assume that the speech signal can be decomposed into an emotion-invariant content code and an emotion-related style code in latent space. Emotion conversion is performed by extracting and recombining the content code of the source speech and the style code of the target emotion. We tested our method on a nonparallel corpora with four emotions. Both subjective and objective evaluations show the effectiveness of our approach.

Brian Powers, Michalis Smyrnakis, Hamidou Tembine

Although the definition of what empathetic preferences exactly are is still evolving, there is a general consensus in the psychology, science and engineering communities that the evolution toward players' behaviors in interactive decision-making problems will be accompanied by the exploitation of their empathy, sympathy, compassion, antipathy, spitefulness, selfishness, altruism, and self-abnegating states in the payoffs. In this article, we study one-shot bimatrix games from a psychological game theory viewpoint. A new empathetic payoff model is calculated to fit empirical observations and both pure and mixed equilibria are investigated. For a realized empathy structure, the bimatrix game is categorized among four generic class of games. Number of interesting results are derived. A notable level of involvement can be observed in the empathetic one-shot game compared the non-empathetic one and this holds even for games with dominated strategies. Partial altruism can help in breaking symmetry, in reducing payoff-inequality and in selecting social welfare and more efficient outcomes. By contrast, partial spite and self-abnegating may worsen payoff equity. Empathetic evolutionary game dynamics are introduced to capture the resulting empathetic evolutionarily stable strategies under wide range of revision protocols including Brown-von Neumann-Nash, Smith, imitation, replicator, and hybrid dynamics. Finally, mutual support and Berge solution are investigated and their connection with empathetic preferences are established. We show that pure altruism is logically inconsistent, only by balancing it with some partial selfishness does it create a consistent psychology.

Hamidou Tembine

We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game framework does not apply. We depart from most of the mean-field games literature by presuming that a decision-maker may include its own-state distribution in its decision. This leads to the class of mean-field-type games. In mean-field-type situations, a single decision-maker may have a big impact on the mean-field terms for which new type of optimality equations are derived. We establish a finite dimensional stochastic maximum principle for mean-field-type games where the drift functions have a p-norm structure which weaken the classical Lipschitz and differentiability assumptions. Sufficient optimality equations are established via Dynamic Programming Principle but in infinite dimension. Using de Finetti-Hewitt-Savage theorem, we show that a propagation of chaos property with 'virtual' particles holds for the non-linear McKean-Vlasov dynamics.

Boualem Djehiche, Hamidou Tembine

We establish a stochastic maximum principle (SMP) for control problems of partially observed diffusions of mean-field type with risk-sensitive performance functionals.

Djehiche Boualem, Tembine Hamidou

In this paper we formulate and solve a mean-field game described by a linear stochastic dynamics and a quadratic or exponential-quadratic cost functional for each generic player. The optimal strategies for the players are given explicitly using a simple and direct method based on square completion and a Girsanov-type change of measure. This approach does not use the well-known solution methods such as the Stochastic Maximum Principle and the Dynamic Programming Principle with Hamilton-Jacobi-Bellman-Isaacs equation and Fokker-Planck-Kolmogorov equation. In the risk-neutral linear-quadratic mean-field game, we show that there is unique best response strategy to the mean of the state and provide a simple sufficient condition of existence and uniqueness of mean-field equilibrium. This approach gives a basic insight into the solution by providing a simple explanation for the additional term in the robust or risk-sensitive Riccati equation, compared to the risk-neutral Riccati equation. Sufficient conditions for existence and uniqueness of mean-field equilibria are obtained when the horizon length and risk-sensitivity index are small enough. The method is then extended to the linear-quadratic robust mean-field games under small disturbance, formulated as a minimax mean-field game.

Hamidou Tembine, Raul Tempone, Pedro Vilanova

In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the Banach-Picard iteration converges with geometrical convergence rate. When the best reply map is not a contraction, Ishikawa-based learning is proposed. The algorithm is shown to behave well for Lipschitz continuous and pseudo-contractive maps. However, the convergence rate is still unsatisfactory. Several acceleration techniques are presented. We explain how cognitive users can improve the convergence rate based only on few number of measurements. The methodology provides nice properties in mean field games where the payoff function depends only on own-action and the mean of the mean-field (first moment mean-field games). A learning framework that exploits the structure of such games, called, mean-field learning, is proposed. The proposed mean-field learning framework is suitable not only for games but also for non-convex global optimization problems. Then, we introduce mean-field learning without feedback and examine the convergence to equilibria in beauty contest games, which have interesting applications in financial markets. Finally, we provide a fully distributed mean-field learning and its speedup versions for satisfactory solution in wireless networks. We illustrate the convergence rate improvement with numerical examples.

A. F. Hanif, H. Tembine, M. Assaad et al.

Distributed strategic learning has been getting attention in recent years. As systems become distributed finding Nash equilibria in a distributed fashion is becoming more important for various applications. In this paper, we develop a distributed strategic learning framework for seeking Nash equilibria under stochastic state-dependent payoff functions. We extend the work of Krstic et.al. in [1] to the case of stochastic state dependent payoff functions. We develop an iterative distributed algorithm for Nash seeking and examine its convergence to a limiting trajectory defined by an Ordinary Differential Equation (ODE). We show convergence of our proposed algorithm for vanishing step size and provide an error bound for fixed step size. Finally, we conduct a stability analysis and apply the proposed scheme in a generic wireless networks. We also present numerical results which corroborate our claim.