scholarly journals Stackelberg pricing games with congestion effects

2021 ◽  
Author(s):  
Tobias Harks ◽  
Anja Schedel
Keyword(s):  
Cost Function ◽  
Stackelberg Game ◽  
Pure Strategy ◽  
Closed Form Expression ◽  
Social Optimum ◽  
Service Capacity ◽  
Worst Case ◽  
Congestion Cost ◽  
Pricing Games ◽  
Congestion Effects

AbstractWe study a Stackelberg game with multiple leaders and a continuum of followers that are coupled via congestion effects. The followers’ problem constitutes a nonatomic congestion game, where a population of infinitesimal players is given and each player chooses a resource. Each resource has a linear cost function which depends on the congestion of this resource. The leaders of the Stackelberg game each control a resource and determine a price per unit as well as a service capacity for the resource influencing the slope of the linear congestion cost function. As our main result, we establish existence of pure-strategy Nash–Stackelberg equilibria for this multi-leader Stackelberg game. The existence result requires a completely new proof approach compared to previous approaches, since the leaders’ objective functions are discontinuous in our game. As a consequence, best responses of leaders do not always exist, and thus standard fixed-point arguments á la Kakutani (Duke Math J 8(3):457–458, 1941) are not directly applicable. We show that the game is C-secure (a concept introduced by Reny (Econometrica 67(5):1029–1056, 1999) and refined by McLennan et al. (Econometrica 79(5):1643–1664, 2011), which leads to the existence of an equilibrium. We furthermore show that the equilibrium is essentially unique, and analyze its efficiency compared to a social optimum. We prove that the worst-case quality is unbounded. For identical leaders, we derive a closed-form expression for the efficiency of the equilibrium.

scholarly journals Ratio-based multi-level resistive memory cells

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Miguel Angel Lastras-Montaño ◽  
Osvaldo Del Pozo-Zamudio ◽  
Lev Glebsky ◽  
Meiran Zhao ◽  
Huaqiang Wu ◽  
...  
Keyword(s):  
Error Probability ◽  
Resistance Switching ◽  
Closed Form Expression ◽  
Memory Cells ◽  
Resistive Memory ◽  
Worst Case ◽  
Information Encoding ◽  
Bit Error Probability ◽  
Multi Level ◽  
Switching Devices

AbstractRatio-based encoding has recently been proposed for single-level resistive memory cells, in which the resistance ratio of a pair of resistance-switching devices, rather than the resistance of a single device (i.e. resistance-based encoding), is used for encoding single-bit information, which significantly reduces the bit error probability. Generalizing this concept for multi-level cells, we propose a ratio-based information encoding mechanism and demonstrate its advantages over the resistance-based encoding for designing multi-level memory systems. We derive a closed-form expression for the bit error probability of ratio-based and resistance-based encodings as a function of the number of levels of the memory cell, the variance of the distribution of the resistive states, and the ON/OFF ratio of the resistive device, from which we prove that for a multi-level memory system using resistance-based encoding with bit error probability x, its corresponding bit error probability using ratio-based encoding will be reduced to $$x^2$$ x 2 at the best case and $$x^{\sqrt{2}}$$ x 2 at the worst case. We experimentally validated these findings on multiple resistance-switching devices and show that, compared to the resistance-based encoding on the same resistive devices, our approach achieves up to 3 orders of magnitude lower bit error probability, or alternatively it could reduce the cell’s programming time and programming energy by up 5–10$$\times$$ × , while achieving the same bit error probability.

scholarly journals The price of anarchy in routing games as a function of the demand

2021 ◽  
Author(s):  
Roberto Cominetti ◽  
Valerio Dose ◽  
Marco Scarsini
Keyword(s):  
Price Of Anarchy ◽  
Heavy Traffic ◽  
Scaling Law ◽  
Congestion Games ◽  
Social Optimum ◽  
Asymptotic Results ◽  
Worst Case ◽  
Traffic Demand ◽  
Break Points ◽  
Routing Games

AbstractThe 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 smoothness properties of Wardrop equilibria and social optima for general smooth costs. In the case of affine costs we show that the equilibrium is piecewise linear, with break points at the demand levels at which the set of active paths changes. We prove that the number of such break points is finite, although it can be exponential in the size of the network. Exploiting a scaling law between the equilibrium and the social optimum, we derive a similar behavior for the optimal flows. We then prove that in any interval between break points the price of anarchy is smooth and it is either monotone (decreasing or increasing) over the full interval, or it decreases up to a certain minimum point in the interior of the interval and increases afterwards. We deduce that for affine costs the maximum of the price of anarchy can only occur at the break points. For general costs we provide counterexamples showing that the set of break points is not always finite.

scholarly journals Stackelberg Interdependent Security Game in Distributed and Hierarchical Cyber-Physical Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-19
Author(s):  
Jiajun Shen ◽  
Dongqin Feng
Keyword(s):  
Pure Strategy ◽  
Cyber Physical Systems ◽  
Payoff Function ◽  
Social Optimum ◽  
Physical Systems ◽  
Experiment Platform ◽  
Physical Plant ◽  
Interdependent Security ◽  
Security Game ◽  
Security Configuration

With the integration of physical plant and network, cyber-physical systems (CPSs) are increasingly vulnerable due to their distributed and hierarchical framework. Stackelberg interdependent security game (SISG) is proposed for characterizing the interdependent security in CPSs, that is, the interactions between individual CPSs, which are selfish but nonmalicious with the payoff function being formulated from a cross-layer perspective. The pure-strategy equilibria for two-player symmetric SISG are firstly analyzed with the strategy gap between individual and social optimum being characterized, which is known as negative externalities. Then, the results are further extended to the asymmetric and m-player SISG. At last, a numerical case of practical experiment platform is analyzed for determining the comprehensively optimal security configuration for administrator.

scholarly journals Impact of Carbon Tax Scheme and CO2 Control Technologies on Bangladesh Aviation Industry

2020 ◽  
Vol 9 (3) ◽  
pp. 54-62
Keyword(s):  
Co2 Emission ◽  
Alternative Fuels ◽  
Stackelberg Game ◽  
Carbon Tax ◽  
Fuel Efficiency ◽  
Aviation Industry ◽  
Worst Case ◽  
Control Technologies ◽  
Carbon Dioxide Co2 ◽  
Global Emissions

Aviation transport action group reported that carbon dioxide (CO2 ) emission of airlines in 2017 was 859 million tons which is 2% of global emissions, (Akça, Z. 2018). It adds that the bank has calculated that “under the worst case ‘carbon intensive’ scenario, living standards will fall by 6.7% for Bangladesh by 2050”. This paper investigates how Bangladesh can respond to best optimize to the EU’s Aviation Carbon Tax Scheme proposed by the Stackelberg game model. The analytic result shows that the strategy “refusal of pay” is the best one which Bangladesh is taking step of. Numerical simulations specify a quantitative visual of the consequences found. The policy is found to be effectively not flying as much would reduce the CO2 emission and consequently, purchase of new aircraft, retrofitting and upgrade improvements on existing aircraft, latest designs in aircraft/engines, fuel efficiency standards and alternative fuels etc. reducing the overall emissions. The main contribution of this paper is to study a new international issue for developing country on aviation carbon tax and CO2 emissions policy suggestions for the aviation technology.

scholarly journals Who Should Pay the Cost: A Game-theoretic Model for Government Subsidized Investments to Improve National Cybersecurity

2019 ◽  
Author(s):  
Xinrun Wang ◽  
Bo An ◽  
Hau Chan
Keyword(s):  
Optimal Allocation ◽  
Stackelberg Game ◽  
Pure Strategy ◽  
General Setting ◽  
Cyber Attacks ◽  
Allocation Problem ◽  
Theoretic Model ◽  
Game Theoretic ◽  
Game Theoretic Model ◽  
The Government

Due to the recent cyber attacks, cybersecurity is becoming more critical in modern society. A single attack (e.g., WannaCry ransomware attack) can cause as much as $4 billion in damage. However, the cybersecurity investment by companies is far from satisfactory. Therefore, governments (e.g., in the UK) launch grants and subsidies to help companies to boost their cybersecurity to create a safer national cyber environment. The allocation problem is hard due to limited subsidies and the interdependence between self-interested companies and the presence of a strategic cyber attacker. To tackle the government's allocation problem, we introduce a Stackelberg game-theoretic model where the government first commits to an allocation and the companies/users and attacker simultaneously determine their protection and attack (pure or mixed) strategies, respectively. For the pure-strategy case, while there may not be a feasible allocation in general, we prove that computing an optimal allocation is NP-hard and propose a linear reverse convex program when the attacker can attack all users. For the mixed-strategy case, we show that there is a polynomial time algorithm to find an optimal allocation when the attacker has a single-attack capability. We then provide a heuristic algorithm, based on best-response-gradient dynamics, to find an effective allocation in the general setting. Experimentally, we show that our heuristic is effective and outperforms other baselines on synthetic and real data.

Bi-objective optimization models for network interdiction

2019 ◽  
Vol 53 (2) ◽  
pp. 461-472 ◽  
Author(s):  
Yan Chen ◽  
Cheng Guo ◽  
Shenghan Yu
Keyword(s):  
Cost Function ◽  
Optimization Methods ◽  
Network Interdiction ◽  
Optimization Models ◽  
Congestion Cost ◽  
Multi Stage

This paper designs models for the network interdiction problem. The interdiction problem under study has two contradicting goals: disrupting the network to minimize the profit of one set of agents, while as much as possible preserve the profit of another set of agents. Three bi-objective optimization methods are employed to form the optimal objectives. Also, we develop two formulations (MILP and multi-stage LP) used to deal with congestion cost which is a piecewise cost function. A numerical instance is also presented to better illustrate those models.

scholarly journals A Robust Longitudinal Control Strategy of Platoons under Model Uncertainties and Time Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Na Chen ◽  
Meng Wang ◽  
Tom Alkim ◽  
Bart van Arem
Keyword(s):  
Cost Function ◽  
Traffic Safety ◽  
Control Strategy ◽  
Time Delays ◽  
System Stability ◽  
Feedback Delay ◽  
Automated Vehicles ◽  
Model Uncertainties ◽  
Worst Case ◽  
And Performance

Automated vehicles are designed to free drivers from driving tasks and are expected to improve traffic safety and efficiency when connected via vehicle-to-vehicle communication, that is, connected automated vehicles (CAVs). The time delays and model uncertainties in vehicle control systems pose challenges for automated driving in real world. Ignoring them may render the performance of cooperative driving systems unsatisfactory or even unstable. This paper aims to design a robust and flexible platooning control strategy for CAVs. A centralized control method is presented, where the leader of a CAV platoon collects information from followers, computes the desired accelerations of all controlled vehicles, and broadcasts the desired accelerations to followers. The robust platooning is formulated as a Min-Max Model Predictive Control (MM-MPC) problem, where optimal accelerations are generated to minimize the cost function under the worst case, where the worst case is taken over the possible models. The proposed method is flexible in such a way that it can be applied to both homogeneous platoon and heterogeneous platoon with mixed human-driven and automated controlled vehicles. A third-order linear vehicle model with fixed feedback delay and stochastic actuator lag is used to predict the platoon behavior. Actuator lag is assumed to vary randomly with unknown distributions but a known upper bound. The controller regulates platoon accelerations over a time horizon to minimize a cost function representing driving safety, efficiency, and ride comfort, subject to speed limits, plausible acceleration range, and minimal net spacing. The designed strategy is tested by simulating homogeneous and heterogeneous platoons in a number of typical and extreme scenarios to assess the system stability and performance. The test results demonstrate that the designed control strategy for CAV can ensure the robustness of stability and performance against model uncertainties and feedback delay and outperforms the deterministic MPC based platooning control.

Plastic Energy Dissipation in Lumbar Spine Implants: A Contact Mechanics Point of View

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
M. Hodaei ◽  
A. Bahari ◽  
P. Maghoul ◽  
V. Rabbani
Keyword(s):  
Lumbar Spine ◽  
Energy Dissipation ◽  
Energy Loss ◽  
Gaussian Function ◽  
Least Square ◽  
Closed Form Expression ◽  
Metal Debris ◽  
Worst Case ◽  
Plastic Energy ◽  
Wide Range

In this study, an elastoplastic contact model is developed for L1–L5 lumbar spine implants. Roughness effect is included to estimate energy loss which is an indication of wear and subsequently the issue of metal debris in body. A Gaussian function is assumed for the distribution of asperities. The contact surfaces of the implants are assumed to be spherical caps. Subsequently, a least-square approach is applied to obtain an approximate expression for the contact force using the data from integration over contact zone. The energy loss is calculated, next, which is due to plastic deformations of asperities. The numerical results indicate that for a given loading–unloading condition, the amount of energy dissipation increases in L1–L4 lumbar spine implants, while it decreases from L4 to L5 implants. The implants geometrical specifications are chosen to cover a wide range of patients' age. Finally, a closed-form expression is obtained for the plastic energy dissipation per cycle in terms of plasticity index for the lumbar spine L4, as the worst-case scenario. Such a function can serve as a very useful tool for implant designers and manufacturers.

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