Related papers: A dynamic theory of spatial externalities
In this paper, we study the decision making of multiple autonomous vehicles at a roundabout. The behaviours of the vehicles depend on their aggressiveness, which indicates how much they value speed over safety. We propose a distributed…
This paper characterizes differentiable subgame perfect equilibria in a continuous time intertemporal decision optimization problem with non-constant discounting. The equilibrium equation takes two different forms, one of which is…
I develop a comprehensive theoretical framework for dynamic spatial treatment effect boundaries using continuous functional definitions grounded in Navier-Stokes partial differential equations. Rather than discrete treatment effect…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
The paper extends an impulsive control-theoretical framework towards dynamic systems in the space of measures. We consider a transport equation describing the time-evolution of a conservative "mass" (probability measure), which represents…
We consider a dynamic traffic routing game over an urban road network involving a large number of drivers in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates''), followed…
Westudy how a planner can design dynamic interventions to overcome status-quo inertia in living temporal games, where strategic agents control their state (active, sleep, partially dead) on a temporal network. Building on the…
The assumptions of necessary rationality and necessary knowledge of strategies, also known as perfect prediction, lead to at most one surviving outcome, immune to the knowledge that the players have of them. Solutions concepts implementing…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
The timing of strategic exit is one of the most important but difficult business decisions, especially under competition and uncertainty. Motivated by this problem, we examine a stochastic game of exit in which players are uncertain about…
Involution, a phenomenon of excessive competition with diminishing returns, has become a pressing socio-economic concern in contemporary China, prompting both academic inquiry and policy interventions. This paper proposes an evolutionary…
Inspired by the path coordination problem arising from robo-taxis, warehouse management, and mixed-vehicle routing problems, we model a group of heterogeneous players responding to stochastic demands as a congestion game under Markov…
Long-term evolutionary processes can strongly influence common-pool resource conservation by generating new traits or behaviours that modify the feedback between population strategies and the resource state. Here we develop an…
This survey is organized around three main topics: models, econometrics, and empirical applications. Section 2 presents the theoretical framework, introduces the concept of Markov Perfect Nash Equilibrium, discusses existence and…
I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…
Game theory has been widely applied to many areas including economics, biology and social sciences. However, it is still challenging to quantify the global stability and global dynamics of the game theory. We developed a landscape and flux…
This paper examines the spatial agglomeration of workers and income in a continuous space-time framework. Local markets feature spatial spillovers and both exogenous and endogenous amenities. Workers relocate to maximise their instantaneous…
We develop a model based on mean-field games of competitive firms producing similar goods according to a standard AK model with a depreciation rate of capital generating pollution as a byproduct. Our analysis focuses on the widely-used…