Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1612.07878

Markov-Nash Equilibria in Mean-Field Games with Discounted Cost

Naci Saldi·Tamer Başar·Maxim Raginsky
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish space. At each time, the agents are coupled through the empirical distribution of their states, which affects both the agents' individual costs and their state transition probabilities. We introduce a new solution concept of the Markov-Nash equilibrium, under which a policy is player-by-player optimal in the class of all Markov policies. Under mild assumptions, we demonstrate the existence of a mean-field equilibrium in the infinite-population limit $N \to \infty$, and then show that the policy obtained from the mean-field equilibrium is approximately Markov-Nash when the number of agents $N$ is sufficiently large.

Explore related subjects

eess.SYcs.SYmath.OC

Keep this discovery

BibTeXRIS

Naci Saldi, Tamer Başar, Maxim Raginsky. 2016-12-23. Markov-Nash Equilibria in Mean-Field Games with Discounted Cost. https://arxiv.org/abs/1612.07878

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Structured Stochastic Representations of Integrated Dynamic Strategies

Dynamic allocation decisions couple present resource use to evolving internal conditions, delayed returns, and future costs. We represent this interaction by four probability localizations linked through regime-indexed, graph-constrained column-stochastic operators. Pre-action state or context selects a locally affine model, while action-dependent changes update subsequent regimes, yielding a causal switched representation of nonlinear evolution. We characterize operator identifiability relative to the graph, the stochastic constraints, and the sampled embedding, separating coefficient recovery from predictive equivalence on the decision domain. Decision making is then formulated through implementable return--cost acceptability regions. Finite-horizon error propagation supplies conservative classification margins, and simultaneous intervals distinguish model-relative near-optimality from certified $\epsilon$-optimality over a declared finite policy class. Regime-indexed stochastic feedback is admitted when it satisfies the same certification test. Reproducible synthetic laboratories for personal preparation, supplier participation, and customer retention illustrate exact, operator-supplied, and noisy feedback cases. Multinomial experiments show improving recovery of the feedback function and fewer unresolved decisions with increasing sample size, while unrestricted off-policy recovery remains limited. The contribution is a structure-preserving representation--identification--decision workflow, not a domain-specific physiological or commercial calibration.

eess.SY↗
arXiv2026

Fusion Estimation in Multi-sensor Systems for Data Packets with Disrupted Identities

In this paper, we explore the problem of fusion estimation for a multi-sensor system where the identity of the data packet received by each sensor may be disrupted or incorrect due to confusion in device identity allocation, communication protocol defects, or the lack of a clear sensor identifier. This can result in a random shuffle of the data components during the fusion estimation process, compromising the performance of the fusion estimation. To address this issue, we introduce the concepts of permutations and symmetry groups to describe this phenomenon as data packet permutation. We construct statistics to simplify the information set, developing two algorithms: a Bayesian approach, which performs fusion using posterior arrangement probabilities, and a greedy approach, which effectively improves estimation performance by guessing the likely data arrangement. We compare these two algorithms and demonstrate that both are expectation error-bounded. We improve algorithms for information-scarce scenarios. By employing the expectation-maximization algorithm, we fill in the prior information of data arrangement where the correct convergence is proven. Finally, we present numerical simulations to validate our results.

eess.SY↗
arXiv2026

Quantifying the Reality Gap for RL-Based UAV Placement at mmWave and Sub-THz

Reinforcement learning (RL) policies for unmanned aerial vehicle (UAV) placement in mmWave and sub-terahertz networks are typically trained on simplified analytical channels. We quantify the resulting sim-to-real gap on a real urban map of Doha, Qatar, at carriers {28, 140, 183, 300} GHz and altitudes {50, 75, 100, 125} m, evaluating three channel pipelines: an analytical model (FSPL + atmospheric absorption + cuboid LoS), full Monte-Carlo ray tracing in Sionna RT with ITU-R P.676-13 absorption, and a deterministic-LoS hybrid that reuses Sionna's mesh under a closed-form path-gain expression. We formalize the gap on the spatial SNR distribution via four metrics, namely bias, RMSE, Jensen-Shannon divergence, and optimum-deployment displacement. Three findings emerge: at 28/140 GHz, $\sim$70% of the apparent -5.6/-4.8 dB Sionna bias is Monte-Carlo undersampling and shrinks to -1.7/-1.5 dB after mitigation; at 183 GHz a -9.2 dB residual isolates the atmospheric absorption / ITU-R P.676 line-shape disagreement; at 300 GHz the stochastic ray tracer agrees with the analytical model only coincidentally, with a +3.8 dB structural offset exposed by the deterministic-LoS pipeline. Across all carriers the linear-domain regret of the analytical-trained policy stays $\geq$ 0.93, indicating practical near-optimality but with a carrier-resolved SNR bias that warrants explicit reporting.

eess.SY↗