Mahdi Takalloo, Changhyun Kwon
For single-commodity networks, the increase of the price of anarchy is bounded by a factor of $(1+ε)^p$ from above, when the travel demand is increased by a factor of $1+ε$ and the latency functions are polynomials of degree at most $p$. We show that the same upper bound holds for multi-commodity networks and provide a lower bound as well.
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We develop an algorithm that computes for a given undirected or directed network with flow-dependent piece-wise linear edge cost functions all Wardrop equilibria as a function of the flow demand. Our algorithm is based on Katzenelson's homotopy method for electrical networks. The algorithm uses a bijection between vertex potentials and flow excess vectors that is piecewise linear in the potential space and where each linear segment can be interpreted as an augmenting flow in a residual network. The algorithm iteratively increases the excess of one or more vertex pairs until the bijection reach…
Correlated Equilibria in Large Anonymous Bayesian Games
本研究将贝叶斯相关均衡扩展到大规模非原子博弈，提出贝叶斯相关沃德罗普均衡，证明其作为有限博弈均衡的极限，并揭示凸势博弈中相关均衡收敛到沃德罗普均衡的性质。
Nash and Wardrop equilibria in aggregative games with coupling constraints
研究纳什与沃德罗普均衡在聚合游戏中关系及收敛算法，分析其与种群规模的关系，并应用于电动汽车充电和道路网络路径选择。
Aggregative games have many industrial applications, and computing an equilibrium in those games is challenging when the number of players is large. In the framework of atomic aggregative games with coupling constraints, we show that variational Nash equilibria of a large aggregative game can be approximated by a Wardrop equilibrium of an auxiliary population game of smaller dimension. Each population of this auxiliary game corresponds to a group of atomic players of the initial large game. This approach enables an efficient computation of an approximated equilibrium, as the variational inequa…
We consider massively dense ad hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the non-cooperative routing problem among a large population of users where each user seeks a path from its origin to its destination so as to minimize its individual cost. Finally, we seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scal…
We consider the question of whether, and in what sense, Wardrop equilibria provide a good approximation for Nash equilibria in atomic unsplittable congestion games with a large number of small players. We examine two different definitions of small players. In the first setting, we consider games where each player's weight is small. We prove that when the number of players goes to infinity and their weights to zero, the random flows in all (mixed) Nash equilibria for the finite games converge in distribution to the set of Wardrop equilibria of the corresponding nonatomic limit game. In the seco…
Wardrop equilibrium and Braess's paradox for varying demand
该研究针对仿射成本单起终点路由博弈，刻画了Wardrop均衡随需求变化的分段仿射特性并给出高需求下均衡求解流程，同时提出Braess悖论的易计算充分检测条件，揭示了致悖路径的需求依赖特性。
We study a two-sided network investment game consisting of two sets of players, called providers and users. The game is set in two stages. In the first stage, providers aim to maximize their profit by investing in bandwidth of cloud computing services. The investments of the providers yield a set of usable services for the users. In the second stage, each user wants to process a task and therefore selects a bundle of services so as to minimize the total processing time. We assume the total processing time to be separable over the chosen services and the processing time of each service to depen…
We study the distribution of traffic in networks whose users try to minimise their delays by adhering to a simple learning scheme inspired by the replicator dynamics of evolutionary game theory. The stable steady states of these dynamics coincide with the network's Wardrop equilibria and form a convex polytope whose dimension is determined by the network's redundancy (an important concept which measures the "linear dependence" of the users' paths). Despite this abundance of stationary points, the long-term behaviour of the replicator dynamics turns out to be remarkably simple: every solution o…
We explore issues of dynamic supply and demand in ride sharing services such as Lyft and Uber, where demand fluctuates over time and geographic location. We seek to maximize social welfare which depends on taxicab and passenger locations, passenger valuations for service, and the distances between taxicabs and passengers. Our only means of control is to set surge prices, then taxicabs and passengers maximize their utilities subject to these prices. We study two related models: a continuous passenger-taxicab setting, similar to the Wardrop model, and a discrete passenger-taxicab setting. In the…
Stability Analysis of Transportation Networks with Multiscale Driver Decisions
针对受多时空尺度信息影响的驾驶员路径选择行为，提出耦合常微分方程模型，证明当路径偏好更新频率远小于交通流动态频率时，网络状态趋近于Wardrop均衡的邻域。
Pricing Traffic Networks with Mixed Vehicle Autonomy
本文研究了通过定价机制消除混合自动驾驶交通网络中均衡的低效率问题，探讨了统一定价和差异化定价对社会延迟的影响，并证明了在道路容量不对称度均匀时，边际成本税收定价可实现最小社会延迟。
Simple binary-state coordination models are widely used to study collective socio-economic phenomena such as the spread of innovations or the adoption of products on social networks. The common trait of these systems is the occurrence of large-scale coordination events taking place abruptly, in the form of a cascade process, as a consequence of small perturbations of an apparently stable state. The conditions for the occurrence of cascade instabilities have been largely analysed in the literature, however for the same coordination models no sufficient attention was given to the relation betwee…
Pure Nash Equilibria in Graphical Games of Bounded Width Revisited
重新审视判定图形博弈是否有纯纳什均衡的复杂性，指出相关算法缺陷，确定问题细粒度复杂性，给出新算法依赖关系，还表明算法可能最优，改进算法等同于证伪pw - SETH。
The price of anarchy has become a standard measure of the efficiency of equilibria in games. Most of the literature in this area has focused on establishing worst-case bounds for specific classes of games, such as routing games or more general congestion games. Recently, the price of anarchy in routing games has been studied as a function of the traffic demand, providing asymptotic results in light and heavy traffic. The aim of this paper is to study the price of anarchy in nonatomic routing games in the intermediate region of the demand. To achieve this goal, we begin by establishing some smo…
Carbon Pricing in Traffic Networks
研究交通网络中通过碳定价引导交通达到满足排放预算的 Wardrop 均衡，证明其可行性与可处理性，并给出多项式时间算法计算均衡与最小价格。
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