Manh Hong Duong

The Anh Han, Manh Hong Duong, Matjaz Perc

Understanding the emergence of prosocial behaviours among self-interested individuals is an important problem in many scientific disciplines. Various mechanisms have been proposed to explain the evolution of such behaviours, primarily seeking the conditions under which a given mechanism can induce highest levels of cooperation. As these mechanisms usually involve costs that alter individual payoffs, it is however possible that aiming for highest levels of cooperation might be detrimental for social welfare -- the later broadly defined as the total population payoff, taking into account all costs involved for inducing increased prosocial behaviours. Herein, by comparatively analysing the social welfare and cooperation levels obtained from stochastic evolutionary models of two well-established mechanisms of prosocial behaviour, namely, peer and institutional incentives, we demonstrate exactly that. We show that the objectives of maximising cooperation levels and the objectives of maximising social welfare are often misaligned. We argue for the need of adopting social welfare as the main optimisation objective when designing and implementing evolutionary mechanisms for social and collective goods.

Van An Nguyen, Vuong Khang Huynh, Huu Loi Bui et al.

Institutional incentives are widely used to promote cooperation among autonomous, self-regarding agents, from human societies to multi-agent and AI systems. Existing work typically treats incentive design as a bi-objective problem: minimise institutional cost while achieving a high long-run frequency of cooperation. Whether such schemes also maximise social welfare - total population payoff net of institutional expenditure - has remained largely unexplored. We develop a welfare-centric framework for institutional incentives in finite, well-mixed populations playing a social dilemma (Donation Game and Public Goods Game), considering both rewards for cooperators and punishments for defectors. For each mechanism, we derive explicit expressions for expected social welfare and characterise how it depends on incentive efficiency and selection intensity. Analytically, we identify parameter regimes where social welfare has a single optimal incentive level and regimes with qualitative phase transitions, in which welfare becomes non-monotonic with multiple local optima. We prove that any welfare-maximising incentive is either zero or concentrated around a simple closed-form target, and we provide an efficient algorithm to compute these optima. Comparing reward and punishment, we further derive close-formed conditions under which reward outperform punishment in terms of social welfare for any given budget. Overall, our results reveal a systematic gap between incentives optimised for cost or cooperation frequency and those that maximise welfare.

Manh Hong Duong, Adrian Muntean, Omar Richardson

We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.

Matthew Dobson, Manh Hong Duong, Christoph Ortner

We develop a rigorous error analysis for coarse-graining of defect-formation free energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the rate of convergence. We then construct a sequence of coarse-grained energies with the same rate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.

Iason Zisis, Joep H. M. Evers, Bas van der Linden et al.

This paper presents the derivation of SPH from principles of continuum mechanics via a measure-based formu- lation. Additionally, it discusses a theoretical convergence result, the extensions achieved from previous works and the current limitations of the proof. In support of the theoretical result, numerical experiments show that SPH converges with respect to the Wasserstein distance as the number of particles grows to infinity. Convergence is still observed for those numerical experiments which are not covered by the hypotheses of the theoretical result. The latter finding suggests that it should be possible to prove the theoretical result under weaker conditions.

Adeela Bashir, Zhao Song, Ndidi Bianca Ogbo et al.

AI safety is an increasingly urgent concern as the capabilities and adoption of AI systems grow. Existing evolutionary models of AI governance have primarily examined incentives for safe development and effective regulation, typically representing users' trust as a one-shot adoption choice rather than as a dynamic, evolving process shaped by repeated interactions. We instead model trust as reduced monitoring in a repeated, asymmetric interaction between users and AI developers, where checking AI behaviour is costly. Using evolutionary game theory, we study how user trust strategies and developer choices between safe (compliant) and unsafe (non-compliant) AI co-evolve under different levels of monitoring cost and institutional regimes. We complement the infinite-population replicator analysis with stochastic finite-population dynamics and reinforcement learning (Q-learning) simulations. Across these approaches, we find three robust long-run regimes: no adoption with unsafe development, unsafe but widely adopted systems, and safe systems that are widely adopted. Only the last is desirable, and it arises when penalties for unsafe behaviour exceed the extra cost of safety and users can still afford to monitor at least occasionally. Our results formally support governance proposals that emphasise transparency, low-cost monitoring, and meaningful sanctions, and they show that neither regulation alone nor blind user trust is sufficient to prevent evolutionary drift towards unsafe or low-adoption outcomes.

Nataliya Balabanova, Adeela Bashir, Paolo Bova et al.

This paper investigates the complex interplay between AI developers, regulators, users, and the media in fostering trustworthy AI systems. Using evolutionary game theory and large language models (LLMs), we model the strategic interactions among these actors under different regulatory regimes. The research explores two key mechanisms for achieving responsible governance, safe AI development and adoption of safe AI: incentivising effective regulation through media reporting, and conditioning user trust on commentariats' recommendation. The findings highlight the crucial role of the media in providing information to users, potentially acting as a form of "soft" regulation by investigating developers or regulators, as a substitute to institutional AI regulation (which is still absent in many regions). Both game-theoretic analysis and LLM-based simulations reveal conditions under which effective regulation and trustworthy AI development emerge, emphasising the importance of considering the influence of different regulatory regimes from an evolutionary game-theoretic perspective. The study concludes that effective governance requires managing incentives and costs for high quality commentaries.

Alessio Buscemi, Daniele Proverbio, Paolo Bova et al.

There is general agreement that fostering trust and cooperation within the AI development ecosystem is essential to promote the adoption of trustworthy AI systems. By embedding Large Language Model (LLM) agents within an evolutionary game-theoretic framework, this paper investigates the complex interplay between AI developers, regulators and users, modelling their strategic choices under different regulatory scenarios. Evolutionary game theory (EGT) is used to quantitatively model the dilemmas faced by each actor, and LLMs provide additional degrees of complexity and nuances and enable repeated games and incorporation of personality traits. Our research identifies emerging behaviours of strategic AI agents, which tend to adopt more "pessimistic" (not trusting and defective) stances than pure game-theoretic agents. We observe that, in case of full trust by users, incentives are effective to promote effective regulation; however, conditional trust may deteriorate the "social pact". Establishing a virtuous feedback between users' trust and regulators' reputation thus appears to be key to nudge developers towards creating safe AI. However, the level at which this trust emerges may depend on the specific LLM used for testing. Our results thus provide guidance for AI regulation systems, and help predict the outcome of strategic LLM agents, should they be used to aid regulation itself.

Henrique Correia da Fonseca, António Fernandes, Zhao Song et al.

When developers of artificial intelligence (AI) products need to decide between profit and safety for the users, they likely choose profit. Untrustworthy AI technology must come packaged with tangible negative consequences. Here, we envisage those consequences as the loss of reputation caused by media coverage of their misdeeds, disseminated to the public. We explore whether media coverage has the potential to push AI creators into the production of safe products, enabling widespread adoption of AI technology. We created artificial populations of self-interested creators and users and studied them through the lens of evolutionary game theory. Our results reveal that media is indeed able to foster cooperation between creators and users, but not always. Cooperation does not evolve if the quality of the information provided by the media is not reliable enough, or if the costs of either accessing media or ensuring safety are too high. By shaping public perception and holding developers accountable, media emerges as a powerful soft regulator -- guiding AI safety even in the absence of formal government oversight.

Zainab Alalawi, Paolo Bova, Theodor Cimpeanu et al.

There is general agreement that some form of regulation is necessary both for AI creators to be incentivised to develop trustworthy systems, and for users to actually trust those systems. But there is much debate about what form these regulations should take and how they should be implemented. Most work in this area has been qualitative, and has not been able to make formal predictions. Here, we propose that evolutionary game theory can be used to quantitatively model the dilemmas faced by users, AI creators, and regulators, and provide insights into the possible effects of different regulatory regimes. We show that creating trustworthy AI and user trust requires regulators to be incentivised to regulate effectively. We demonstrate the effectiveness of two mechanisms that can achieve this. The first is where governments can recognise and reward regulators that do a good job. In that case, if the AI system is not too risky for users then some level of trustworthy development and user trust evolves. We then consider an alternative solution, where users can condition their trust decision on the effectiveness of the regulators. This leads to effective regulation, and consequently the development of trustworthy AI and user trust, provided that the cost of implementing regulations is not too high. Our findings highlight the importance of considering the effect of different regulatory regimes from an evolutionary game theoretic perspective.