Price Of Anarchy Research Articles

A Game-Theoretic Analysis of Joint Mobile Edge Caching and Peer Content Sharing

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Mobile edge caching</i> allows edge devices to cache popular contents and deliver them to end-users directly, and hence can effectively alleviate the increasingly heavy backbone loads and improve the quality-of-service of end-users. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Peer content sharing</i> enables edge devices to share the cached contents with each other, and can further increase the caching capability and efficiency. While lots of research efforts have been made to edge caching or content sharing, it remains largely open to devise a joint caching and sharing framework and study the complicated technical and economic interplay between both technologies. In this paper, we propose a joint framework for mobile edge caching and peer content sharing, and focus on studying the strategic behaviors and interactions of edge devices in the joint framework. Specifically, we model their interactions as a non-cooperative game, where each edge device ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">player</i> ) can choose to be an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">agent</i> (who caches and shares contents with others) or a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">requester</i> (who doesn't cache but requests contents from other devices) of each content. We characterize the game equilibrium under a generic usage-based pricing scheme (for content sharing) and analyze its existence and uniqueness systematically. We further design a best response based iterative learning algorithm for players to update their behaviors and reach the equilibrium in a self-enforcing manner. Moreover, we analyze the Price of Anarchy (PoA) of the game equilibrium to measure the system performance degradation due to the selfish strategic behaviors of game players, based on which we further design a pricing scheme (for content sharing) to reduce such performance degradation. Simulations show that our framework can reduce the total system cost by up to 60%, comparing with the benchmark pure caching system without peer content sharing.

Resource-Aware Cost-Sharing Methods for Scheduling Games

In large distributed systems, ensuring the efficient utilization of the available resources is a very challenging task. Given limited information regarding the state of the system and no centralized control over the outcome, decentralized scheduling mechanisms are unable to enforce optimal utilization. To better understand such systems, some classic papers that introduced game theoretic models used the “price of anarchy” measure to evaluate the system’s performance. The paper “Resource-Aware Cost-Sharing Methods for Scheduling Games” by Christodoulou, Gkatzelis, and Sgouritsa overcomes some of the overly pessimistic results shown in this prior work by enhancing the scheduling mechanisms with access to some additional information regarding the state of the system: a “resource-aware” mechanism knows what machines are available in the system and uses this information to carefully incentivize the users toward more efficient Nash equilibrium outcomes.

How Bad is Selfish Driving? Bounding the Inefficiency of Equilibria in Urban Driving Games

We consider the interaction among agents engaging in a driving task and we model it as general-sum game. This class of games exhibits a plurality of different equilibria posing the issue of equilibrium selection. While selecting the most efficient equilibrium (in term of social cost) is often impractical from a computational standpoint, in this work we study the (in)efficiency of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">any</i> equilibrium players might agree to play. More specifically, we bound the equilibrium inefficiency by modeling driving games as particular type of congestion games over spatio-temporal resources. We obtain novel guarantees that refine existing bounds on the Price of Anarchy (PoA) as a function of problem-dependent game parameters. For instance, the relative trade-off between proximity costs and personal objectives such as comfort and progress. Although the obtained guarantees concern open-loop trajectories, we observe efficient equilibria even when agents employ closed-loop policies trained via decentralized multi-agent reinforcement learning.

Simultaneous 2nd price item auctions with no-underbidding

The literature on the Price of Anarchy (PoA) of simple auctions employs a no-overbidding assumption but has completely overlooked the no-underbidding phenomenon, which is evident in empirical studies on variants of the second price auction. In this work, we provide a theoretical foundation for the no-underbidding phenomenon. We study the PoA of simultaneous 2nd price auctions (S2PA) under a new natural condition of no underbidding, meaning that agents never bid on items less than their marginal values. We establish improved (mostly tight) bounds on the PoA of S2PA under no-underbidding for different valuation classes, in both full-information and incomplete information settings. Specifically, we show that the PoA is at least 1/2 for general monotone valuations, which extends to Bayesian PoA with arbitrary correlated distributions. We also establish a tight PoA bound of 2/3 for S2PA with XOS valuations, under no-overbidding and no-underbidding, which extends to Bayesian PoA with independent distributions.

Incentivizing Collaboration in Heterogeneous Teams via Common-Pool Resource Games

We consider a team of heterogeneous agents, which is collectively responsible for servicing, and subsequently reviewing a stream of homogeneous tasks. Each agent has an associated mean service time and a mean review time for servicing and reviewing the tasks, respectively. Agents receive a reward based on their service and review admission rates. The team objective is to collaboratively maximize the number of “serviced and reviewed” tasks. We formulate a common-pool resource game, and design utility functions to incentivize collaboration among heterogeneous agents in a decentralized manner. We show the existence of a unique pure Nash equilibrium (PNE), and establish convergence of the best response dynamics to this unique PNE. Finally, we establish an analytic upper bound on three inefficiency measures of the PNE, namely the price of anarchy, the ratio of the total review admission rate, and the ratio of latency.

How does trip frequency distort time value to impact congestion charging schemes?

Abstract A notable feature of a city or region with close economic and social connections with its neighbours is its highly mixed local and external traffic, and in some cases the external traffic volume is almost as high as that of local traffic. Whilst local traffic volume may be largely made up of the same regular local commuters making frequent trips, external traffic from outside of the city (region) may not be the same people making regular trips to/from the city. However, from a large pool of people making infrequent trips to/from the city, the existence of external traffic is proven by data from the licence plate recognition system of road vehicles in Changde, China. The function of value of time correlated with the income/wage rate and trip frequency is exploited and verified statistically. The time value distorted by trip frequency is defined as perceived time value (PTV), which also influences the way travellers perceive any travel impedance such as congestion delay and toll charges. This paper analyses the price of anarchy (POA) when explicitly considering the travel frequency of the trip-makers and their PTV, and compares with previous analysis without considering travel frequency. We show that when travel frequency is considered, the optimal toll of congested road pricing schemes which converts road traffic flow from user equilibrium into system optimization is much lower than that without considering travel frequency. The cost of licence plate auction cannot be treated as a congestion toll, which is only a threshold of vehicle ownership. That travellers choose routes by PTV rather than TV (time value) is proven by an example of Heishipu Bridge in Changsha, Hunan Province, China.

Efficiency and inefficiency of Nash equilibrium for scheduling games on batching-machines with activation cost

We study two scheduling games on parallel-batching machines with activation cost, where each game involves n jobs being processed on m parallel-batching identical machines. Each job, as an agent, selects a machine (more precisely, a batch on a machine) for processing to minimize his disutility. For the former game, on the basis of previous results, we find the conditions for the existence of Nash equilibrium, and present the parametric upper bounds of price of anarchy (PoA) and the price of stability (PoS) for the minimax and minisum objectives, and provide some mixed strategy Nash equilibria for two special cases. For the latter game, we first analyze the conditions for the nonexistence of Nash equilibrium, and provide tight approximate Nash equilibrium. Then, the conditions for the existence of Nash equilibrium are studied, and the constant-bounds of PoA and PoS for the minimax objective are given.

Efficient Distributed Threshold-Based Offloading for Large-Scale Mobile Cloud Computing

Mobile cloud computing enables compute-limited mobile devices to perform real-time intensive computations such as speech recognition or object detection by leveraging powerful cloud servers. An important problem in large-scale mobile cloud computing is computational offloading, where each mobile device decides when and how much computation should be uploaded to cloud servers by considering the local processing delay and the cost of using cloud servers. In this paper, we develop a distributed threshold-based offloading algorithm where it uploads an incoming computing task to cloud servers if the number of tasks queued at the device reaches the threshold and processes it locally otherwise. The threshold is updated iteratively based on the computational load and the cost of using cloud servers. We formulate the problem as a symmetric game, and characterize the sufficient and necessary conditions for the existence and uniqueness of the Nash Equilibrium (NE) assuming exponential service times. Then, we show the convergence of our proposed distributed algorithm to the NE when the NE exists. Further, we characterize the performance gap between cost under our proposed distributed algorithm and the minimum cost in terms of Price of Anarchy (PoA) when the cost of using cloud servers is high. Finally, we perform extensive simulations to validate our theoretical findings, demonstrate the efficiency of our proposed distributed algorithm under various scenarios such as hyperexponential service times, imperfect server utilization estimation, and asynchronous threshold updates, and reveal the superior performance of threshold-based policies over their probabilistic counterpart.

Social Distancing Network Creation

During a pandemic people have to find a trade-off between meeting others and staying safely at home. While meeting others is pleasant, it also increases the risk of infection. We consider this dilemma by introducing a game-theoretic network creation model in which selfish agents can form bilateral connections. They benefit from network neighbors, but at the same time, they want to maximize their distance to all other agents. This models the inherent conflict that social distancing rules impose on the behavior of selfish agents in a social network. Besides addressing this familiar issue, our model can be seen as the inverse to the well-studied Network Creation Game by Fabrikant et al. (in: PODC 2003, pp 347–351, 2003. https://doi.org/10.1145/872035.872088), where agents aim at being as central as possible in the created network. We look at two variants of network creation governed by social distancing. Firstly, a variant without connection restrictions, where we characterize optimal and equilibrium networks, and derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant allows connection restrictions. As our main result, we prove that Swap-Maximal Routing-Cost Spanning Trees, an efficiently computable weaker variant of Maximum Routing-Cost Spanning Trees, actually resemble equilibria for a significant range of the parameter space. Moreover, we give almost tight bounds on the Price of Anarchy and Price of Stability. These results imply that under social distancing the agents’ selfishness has a strong impact on the quality of the equilibria.

The price of Anarchy as a classifier for mechanism design in a Pareto-Bayesian-Nash context

The complex interaction of fixed incentives for multiple agents can lead to inefficient results. The Price of Anarchy (PoA) is a concept employed in economics and game theory to quantify how, in the worst-case scenario, a system's efficiency diminishes due to the selfish behavior of its actors. It evaluates the outcomes obtained by perfect coordination to that obtained by self-interested players in a Nash equilibrium.This paper investigates the PoA in mechanism design for Pareto-Bayesian-Markov (PBN) games in which the players privately know their information. Our approach is restricted to the development of algorithmic mechanisms. We consider an ergodic finite Markov chain in which players' transitions are independent and decisions are made across a finite number of periods. As a key outcome, we completely characterize the Pareto frontier and calculate an efficient, ex-post incentive-compatible technique. We employ Tikhonov's regularization technique, for assuring that the original problem's solution converges to a unique solution. The ratio equilibria of the PoA is found employing a projection-gradient method, which is our main result. We compute the PoA using an auxiliary variable and present the formulas for retrieving the variables of interest. We show that our theoretical conclusions ensure convergence and we provide a numerical example to demonstrate the method's utility.

Decentralized Scheduling in Edge Computing Paradigms: End-to-End Decision Analytics and the Price of Anarchy

Decentralized Scheduling in Edge Computing Paradigms: End-to-End Decision Analytics and the Price of Anarchy

Risk-Averse Equilibria for Vehicle Navigation in Stochastic Congestion Games

The fast-growing market of autonomous vehicles, unmanned aerial vehicles, and fleets in general necessitates the design of smart and automatic navigation systems considering the stochastic latency along different paths in the traffic network. The longstanding shortest path problem in a deterministic network, whose counterpart in a congestion game setting is Wardrop equilibrium, has been studied extensively, but it is well known that finding the notion of an optimal path is challenging in a traffic network with stochastic arc delays. In this work, we propose three classes of risk-averse equilibria for an atomic stochastic congestion game in its general form where the arc delay distributions are load dependent and not necessarily independent of each other. The three classes are risk-averse equilibrium (RAE), mean-variance equilibrium (MVE), and conditional value at risk level <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> equilibrium ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{CVaR}_{\alpha}\text{E}$ </tex-math></inline-formula> ) whose notions of risk-averse best responses are based on maximizing the probability of taking the shortest path, minimizing a linear combination of mean and variance of path delay, and minimizing the expected delay at a specified risky quantile of the delay distributions, respectively. We prove that for any finite stochastic atomic congestion game, the risk-averse, mean-variance, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{CVaR}_{\alpha}$ </tex-math></inline-formula> equilibria exist. We show that for risk-averse travelers, the Braess paradox may not occur to the extent presented originally since players do not necessarily travel along the shortest path in expectation, but they take the uncertainty of travel time into consideration as well. We show through some examples that the price of anarchy can be improved when players are risk-averse and travel according to one of the three classes of risk-averse equilibria rather than the Wardrop equilibrium.

A Sensitivity Analysis of the Price of Anarchy in Nonatomic Congestion Games

The price of anarchy (PoA) is a standard measure to quantify the inefficiency of equilibria in nonatomic congestion games. Most publications have focused on worst-case bounds for the PoA. Only a few have analyzed the sensitivity of the PoA against changes of the demands or cost functions, although that is crucial for empirical computations of the PoA. We analyze the sensitivity of the PoA with respect to (w.r.t.) simultaneous changes of demands and cost functions. The key to this analysis is a metric for the distance between two games that defines a topological metric space consisting of all games with the same combinatorial structure. The PoA is then a locally pointwise Hölder continuous function of the demands and cost functions, and we analyze the Hölder exponent for different classes of cost functions. We also apply our approach to the convergence analysis of the PoA when the total demand tends to zero or infinity. Our results further develop the recent seminal work on the sensitivity of the PoA w.r.t. changes of only the demands under special conditions. Funding: This work was supported by the Science Foundation of Anhui Science and Technology Department [Grant 1908085QF262]; Science Foundation of the Anhui Education Department [Grant KJ2019A0834]; National Science Foundation of China [Grants 61906062, 72271085]; Talent Foundation of Hefei University [Grant 1819RC29].

Efficient Multi-Channel Computation Offloading for Mobile Edge Computing: A Game-Theoretic Approach

Mobile edge computing is emerging to provide cloud-computing capabilities to mobile users, so that they can offload computation intensive tasks to close proximity for execution. However, most existing works imply that a transmission-finished task still occupies the channel until all users on the same channel finish the transmission, leading to severe channel resource waste. To solve this problem, we propose an efficient computation offloading mechanism which releases the channel resources of transmission-finished tasks for transmission-unfinished tasks, and aims to minimize the response time and energy consumption for each user. Specifically, we formulate the computation offloading problem as a game, analyze its structural properties and show how it possesses a Nash equilibrium and admits the finite improvement property, in the cases of elastic cloud and non-elastic cloud respectively. We then propose a <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> istributed <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</b> ulti-channel <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b> omputation <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</b> ffloading (DMCO) algorithm, which can converge to a Nash equilibrium, and find the upper bound of the convergence time. We further evaluate the performance of DMCO using the price of anarchy. Numerical results show that DMCO scales well with the number of users, and outperforms existing works, for example, benefits 13.3 percent more users and reduces cost by 23.7 percent than CO, one of the best existing works.

Efficiency of Ad Auctions with Price Displaying

Most economic reports suggest that almost half of the market value unlocked by artificial intelligence (AI) by the next decade (about 9 trillion USD per year) will be in marketing&amp;sales. In particular, AI will allow the optimization of more and more intricate economic settings in which multiple different activities can be automated jointly. A relatively recent example is that one of ad auctions in which similar products or services are displayed together with their price, thus merging advertising and pricing in a unique website. This is the case, e.g., of Google Hotel Ads and TripAdvisor. More precisely, as in a classical ad auction, the ranking of the ads depends on the advertisers' bids, while, differently from classical ad auctions, the price is displayed together with the ad, so as to provide a direct comparison among the prices and thus dramatically affect the behavior of the users. This paper investigates how displaying prices and ads together conditions the properties of the main economic mechanisms such as VCG and GSP. Initially, we focus on the direct-revelation mechanism, showing that prices are chosen by the mechanisms once given the advertisers' reports. We also provide an efficient algorithm to compute the optimal allocation given the private information reported by the advertisers. Then, with both VCG and GSP payments, we show the inefficiency in terms of Price of Anarchy (PoA) and Stability (PoS) over the social welfare and mechanism's revenue when the advertisers choose the prices. The main results show that, with both VCG and GSP, PoS over the revenue may be unbounded even with two slots, while PoA over the social welfare may be as large as the number of slots. Finally, we show that, under some assumptions, simple modifications to VCG and GSP allow us to obtain a better PoS over the revenue.

A convergence analysis of the price of anarchy in atomic congestion games

We analyze the convergence of the price of anarchy (PoA) of Nash equilibria in atomic congestion games with growing total demand T. When the cost functions are polynomials of the same degree, we obtain explicit rates for a rapid convergence of the PoAs of pure and mixed Nash equilibria to 1 in terms of 1/T and d_{max}/T, where d_{max} is the maximum demand controlled by an individual. Similar convergence results carry over to the random inefficiency of the random flow induced by an arbitrary mixed Nash equilibrium. For arbitrary polynomial cost functions, we derive a related convergence rate for the PoA of pure Nash equilibria (if they exist) when the demands fulfill certain regularity conditions and d_{max} is bounded as Trightarrow infty . In this general case, also the PoA of mixed Nash equilibria converges to 1 as Trightarrow infty when d_{max} is bounded. Our results constitute the first convergence analysis for the PoA in atomic congestion games and show that selfish behavior is well justified when the total demand is large.

The price of Anarchy in series-parallel network congestion games

The price of Anarchy in series-parallel network congestion games

Algorithmic-gradient approach for the Price of Anarchy and Stability for incomplete information

In game theory, the Price of Anarchy (PoA) and the Price of Stability (PoS) are excellent tools for characterizing the loss of competition’s efficiency. This paper investigates the PoA and PoS for incomplete information in Bayesian-Markov games. The development of computationally effective optimization tools is essential for the investigation of these equilibria. To attain this goal, the difficulty of computing the PoA and PoS is presented as a tractable nonlinear programming problem. We look at regularized cost-minimization issues and present a framework for building projection-gradient algorithms that have near-optimal a priori performance guarantees. For the constrained Lagrange technique, we use Tikhonov’s regularization approach, for which the original problem converges to a single solution. Then we suggest a framework for computing the difference between the ‘best equilibrium’ and the ‘optimal solution’, as well as the ratio between the ‘worst equilibrium’ and the ‘optimal solution’. To solve these issues, we use a game-theoretic method, assigning agents cost functions to maximize (PoA) or minimize (PoS) the equilibrium efficiency. After the agents’ regularized-cost functions have been established, every algorithm capable of discovering a Nash equilibrium of the system inherits a performance guarantee matching the PoA and Pos. The convergence of the suggested projection-gradient method under mild conditions is established. Finally, we consider the implications of our findings when this paradigm is applied to convex systems.

Quality-speed trade-offs in customer-intensive services with boundedly rational customers and retrials

We consider a system in which one server provides customer-intensive services and the service reward increases in the length of service time. However, longer service times also lead to longer waits for customers and more congestion for the system. Considering the trade-off between the service speed and service quality, in this paper, we investigate the optimal service speed and service fee from the perspectives of revenue maximization and social welfare maximization. The customers are boundedly rational and decide whether to join the system or not according to a logit model. We find that under the revenue maximization, a decrease in the degree of rationality can alleviate congestion, but harms the social welfare. If the social planner determines the service speed and price directly, we show that bounded rationality is detrimental to service managers but beneficial to customers, while social welfare remains constant. Defining the ratio between the social welfare under the revenue-optimal strategy and socially optimal strategy as the price of anarchy (PoA), which quantifies the inefficiency of the strategy of the service provider, we obtain its upper bound and lower bound and demonstrate that the PoA is decreasing when customers become more boundedly rational and the sign of customer’s actual utility is determined by both the level of customer rationality and retrial rate. Moreover, when customers are heterogeneous in terms of perceiving service, we classify customers into two classes and the revenue maximization problem is investigated through the Particle Swarm Optimization algorithm.

The price of anarchy in truckload transportation spot markets

A concept of relevance to spot markets for truck-based freight transportation services is the price of anarchy ( PoA ) , which defines the performance inferiority of decentralized market mechanisms for consummating transactions (vis-à-vis centralized mechanisms). To examine this concept in the context of transportation spot markets, this study uses a combination of behavioral experiments and mathematical optimization. The paper's contributions to the research literature for that context involve (1) addressing the case of freight transportation service providers having service requests information spanning multiple periods; (2) analyzing multiple performance measures; (2) accounting for the performance effects of human behavior; and (3) introducing new behavioral experiments as well as novel and effective analytical procedures to tackle truck-to-load assignment problems. Among the paper's most salient findings is that when performance is measured as the market participants' financial outcome, human behavior in buyer-seller interactions could result in a doubling of the PoA . • Models the Price of Anarchy (PoA) for decentralized spot market transactions. • Considers three PoA metrics: private profits, customer service, eco-efficiency. • Models the impact of human bounded rationality on the PoA. • Develops and solves mathematical models of multi-day truck-to-load assignments. • Introduces an on-line tool for human behavior experiments to study spot markets.