Paper List
-
Ill-Conditioning in Dictionary-Based Dynamic-Equation Learning: A Systems Biology Case Study
This paper addresses the critical challenge of numerical ill-conditioning and multicollinearity in library-based sparse regression methods (e.g., SIND...
-
Hybrid eTFCE–GRF: Exact Cluster-Size Retrieval with Analytical pp-Values for Voxel-Based Morphometry
This paper addresses the computational bottleneck in voxel-based neuroimaging analysis by providing a method that delivers exact cluster-size retrieva...
-
abx_amr_simulator: A simulation environment for antibiotic prescribing policy optimization under antimicrobial resistance
This paper addresses the critical challenge of quantitatively evaluating antibiotic prescribing policies under realistic uncertainty and partial obser...
-
PesTwin: a biology-informed Digital Twin for enabling precision farming
This paper addresses the critical bottleneck in precision agriculture: the inability to accurately forecast pest outbreaks in real-time, leading to su...
-
Equivariant Asynchronous Diffusion: An Adaptive Denoising Schedule for Accelerated Molecular Conformation Generation
This paper addresses the core challenge of generating physically plausible 3D molecular structures by bridging the gap between autoregressive methods ...
-
Omics Data Discovery Agents
This paper addresses the core challenge of making published omics data computationally reusable by automating the extraction, quantification, and inte...
-
Single-cell directional sensing at ultra-low chemoattractant concentrations from extreme first-passage events
This work addresses the core challenge of how a cell can rapidly and accurately determine the direction of a chemoattractant source when the signal is...
-
SDSR: A Spectral Divide-and-Conquer Approach for Species Tree Reconstruction
This paper addresses the computational bottleneck in reconstructing species trees from thousands of species and multiple genes by introducing a scalab...
Social Distancing Equilibria in Games under Conventional SI Dynamics
Department of Mathematics, Pennsylvania State University | Huck Institute of Life Sciences, Pennsylvania State University
30秒速读
IN SHORT: This paper solves the core problem of proving the existence and uniqueness of Nash equilibria in finite-duration SI epidemic games, showing they are always bang-bang strategies.
核心创新
- Methodology Introduces a novel change of variables that simplifies the geometry and analysis of the SI social-distancing game, enabling explicit integration and closed-form solutions.
- Theory Proves that for the specified SI game with threshold-linear costs, the unique strategic equilibrium is always a time-dependent bang-bang strategy (wait-then-lockdown), with no singular solutions.
- Theory Demonstrates that in the restricted strategy space of two-phase (off-on) strategies, the bang-bang Nash equilibrium is also an Evolutionarily Stable Strategy (ESS), and that it coincides with the socially optimal policy, eliminating free-riding.
主要结论
- For all parameter tuples (m, I0, tf), there exists one and only one equilibrium point x* (Theorem 10), proving uniqueness in the SI game.
- The equilibrium strategy is explicitly given by x*(m, I0, tf) = m - 1 - W((1/I0 - 1)e^{m-1-tf}) for intermediate parameters, utilizing the Lambert W function (Eq. 13).
- The optimal public policy (minimizing population disutility ℰ(x̄)) exactly corresponds with the individual Nash equilibrium strategy (Eq. 18), showing no conflict between individual and social optima in this model.
摘要: The mathematical characterization of social-distancing games in classical epidemic theory remains an important question, for their applications to both infectious-disease theory and memetic theory. We consider a special case of the dynamic finite-duration SI social-distancing game where payoffs are accounted using Markov decision theory with zero-discounting, while distancing is constrained by threshold-linear running-costs, and the running-cost of perfect-distancing is finite. In this special case, we are able construct strategic equilibria satisfying the Nash best-response condition explicitly by integration. Our constructions are obtained using a new change of variables which simplifies the geometry and analysis. As it turns out, there are no singular solutions, and a time-dependent bang-bang strategy consisting of a wait-and-see phase followed by a lock-down phase is always the unique strategic equilibrium. We also show that in a restricted strategy space the bang-bang Nash equilibrium is an ESS, and that the optimal public policy exactly corresponds with the equilibrium strategy.