14,378 research outputs found
Different Policy Objectives of the Road Pricing Problem – a Game Theory Approach
Using game theory we investigate a new approach to formulate and solve optimal tolls with a focus on different policy objectives of the road authority. The aim is to gain more insight into determining optimal tolls as well as into the behavior of users after tolls have been imposed on the network. The problem of determining optimal tolls is stated and defined using utility maximization theory, including elastic demand on the travelers’ side and different objectives for the road authority. Game theory notions are adopted regarding different games and players, rules and outcomes of the games played between travelers on the one hand and the road authority on the other. Different game concepts (Cournot, Stackelberg and monopoly game) are mathematically formulated and the relationship between players, their payoff functions and rules of the games are defined for very simplistic cases. The games are solved for different scenarios and different objectives for the road authority, using the Nash equilibrium concept. Using the Stackelberg game concept as being most realistic for road pricing, a few experiments are presented illustrating the optimal toll design problem subject to different pricing policies considering different objectives of the road authority. Results show different outcomes both in terms of optimal tolls as well as in payoffs for travelers. There exist multiple optimal solutions and objective function may have a non- continuous shape. The main contribution is the two-level separation between of the users from the road authority in terms of their objectives and influences.
Strong Nash Equilibria in Games with the Lexicographical Improvement Property
We introduce a class of finite strategic games with the property that every
deviation of a coalition of players that is profitable to each of its members
strictly decreases the lexicographical order of a certain function defined on
the set of strategy profiles. We call this property the Lexicographical
Improvement Property (LIP) and show that it implies the existence of a
generalized strong ordinal potential function. We use this characterization to
derive existence, efficiency and fairness properties of strong Nash equilibria.
We then study a class of games that generalizes congestion games with
bottleneck objectives that we call bottleneck congestion games. We show that
these games possess the LIP and thus the above mentioned properties. For
bottleneck congestion games in networks, we identify cases in which the
potential function associated with the LIP leads to polynomial time algorithms
computing a strong Nash equilibrium. Finally, we investigate the LIP for
infinite games. We show that the LIP does not imply the existence of a
generalized strong ordinal potential, thus, the existence of SNE does not
follow. Assuming that the function associated with the LIP is continuous,
however, we prove existence of SNE. As a consequence, we prove that bottleneck
congestion games with infinite strategy spaces and continuous cost functions
possess a strong Nash equilibrium
Resource allocation games of various social objectives
In this paper, we study resource allocation games of two different cost components for individual game players and various social costs. The total cost of each individual player consists of the congestion cost, which is the same for all players sharing the same resource, and resource activation cost, which is proportional to the individual usage of the resource. The social costs we consider are, respectively, the total of costs of all players and the maximum congestion cost plus total resource activation cost.
Using the social costs we assess the quality of Nash equilibria in terms of the price of anarchy (PoA) and the price of stability (PoS). For each problem, we identify one or two problem parameters and provide parametric bounds on the PoA and PoS. We show that they are unbounded in general if the parameter involved are not restricted
A Study of Truck Platooning Incentives Using a Congestion Game
We introduce an atomic congestion game with two types of agents, cars and
trucks, to model the traffic flow on a road over various time intervals of the
day. Cars maximize their utility by finding a trade-off between the time they
choose to use the road, the average velocity of the flow at that time, and the
dynamic congestion tax that they pay for using the road. In addition to these
terms, the trucks have an incentive for using the road at the same time as
their peers because they have platooning capabilities, which allow them to save
fuel. The dynamics and equilibria of this game-theoretic model for the
interaction between car traffic and truck platooning incentives are
investigated. We use traffic data from Stockholm to validate parts of the
modeling assumptions and extract reasonable parameters for the simulations. We
use joint strategy fictitious play and average strategy fictitious play to
learn a pure strategy Nash equilibrium of this game. We perform a comprehensive
simulation study to understand the influence of various factors, such as the
drivers' value of time and the percentage of the trucks that are equipped with
platooning devices, on the properties of the Nash equilibrium.Comment: Updated Introduction; Improved Literature Revie
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