Paper List
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Autonomous Agents Coordinating Distributed Discovery Through Emergent Artifact Exchange
This paper addresses the fundamental limitation of current AI-assisted scientific research by enabling truly autonomous, decentralized investigation w...
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D-MEM: Dopamine-Gated Agentic Memory via Reward Prediction Error Routing
This paper addresses the fundamental scalability bottleneck in LLM agentic memory systems: the O(N²) computational complexity and unbounded API token ...
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Countershading coloration in blue shark skin emerges from hierarchically organized and spatially tuned photonic architectures inside skin denticles
This paper solves the core problem of how blue sharks achieve their striking dorsoventral countershading camouflage, revealing that coloration origina...
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Human-like Object Grouping in Self-supervised Vision Transformers
This paper addresses the core challenge of quantifying how well self-supervised vision models capture human-like object grouping in natural scenes, br...
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Hierarchical pp-Adic Framework for Gene Regulatory Networks: Theory and Stability Analysis
This paper addresses the core challenge of mathematically capturing the inherent hierarchical organization and multi-scale stability of gene regulator...
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Towards unified brain-to-text decoding across speech production and perception
This paper addresses the core challenge of developing a unified brain-to-text decoding framework that works across both speech production and percepti...
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Dual-Laws Model for a theory of artificial consciousness
This paper addresses the core challenge of developing a comprehensive, testable theory of consciousness that bridges biological and artificial systems...
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Pulse desynchronization of neural populations by targeting the centroid of the limit cycle in phase space
This work addresses the core challenge of determining optimal pulse timing and intensity for desynchronizing pathological neural oscillations when the...
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.