Unilateral Altruism in Network Routing Games with Atomic Players (original) (raw)
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Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing
Abstract. Selfish behavior of nodes of a network such as sensors of a geographically distributed sensor network, each of which owned and operated by a different stakeholder may lead to a game theoretic setting called “selfish routing”. The fact that every node strictly aims at maximizing its own utility can cause degradations of social welfare. An issue of concern would be the quantitative measure of this inefficiency.
Altruism in Atomic Congestion Games
Lecture Notes in Computer Science, 2009
This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting social cost. Our model can be embedded in the framework of congestion games with playerspecific latency functions. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. Previous work shows that for symmetric singleton games with convex delays Nash equilibria are guaranteed to exist. For concave delay functions we observe that there are games without Nash equilibria and provide a polynomial time algorithm to decide existence for symmetric singleton games with arbitrary delay functions. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, then there is always a Nash equilibrium in any congestion game with altruists and any better-response dynamics converges.
From Altruism to NonCooperation in Routing Games
Computing Research Repository, 2008
The paper studies the routing in the network shared by several users. Each user seeks to optimize either its own performance or some combination between its own performance and that of other users, by controlling the routing of its given flow demand. We parameterize the degree of cooperation which allows to cover the fully non-cooperative behavior, the fully cooperative behavior, and even more, the fully altruistic behavior, all these as special cases of the parameter's choice. A large part of the work consists in exploring the impact of the degree of cooperation on the equilibrium. Our first finding is to identify multiple Nash equilibria with cooperative behavior that do not occur in the non-cooperative case under the same conditions (cost, demand and topology). We then identify Braess like paradox (in which adding capacity or adding a link to a network results in worse performance to all users) and study the impact of the degree of cooperation on it. We identify situations where low cooperation results in poorer performance at equilibrium. We then pursue the exploration and carry it on to the setting of Stackelberg equilibrium. We finally obtain some theoretical results that show that for low degree of cooperation the equilibrium is unique, confirming the results of our numerical study.
Partial Altruism is Worse than Complete Selfishness in Nonatomic Congestion Games
2020
We seek to understand the fundamental mathematics governing infrastructure-scale interactions between humans and machines, particularly when the machines' intended purpose is to influence and optimize the behavior of the humans. To that end, this paper investigates the worst-case congestion that can arise in nonatomic network congestion games when a fraction of the traffic is completely altruistic (e.g., benevolent self-driving cars) and the remainder is completely selfish (e.g., human commuters). We study the worst-case harm of altruism in such scenarios in terms of the perversity index, or the worst-case equilibrium congestion cost resulting from the presence of altruistic traffic, relative to the congestion cost which would result if all traffic were selfish. We derive a tight bound on the perversity index for the class of series-parallel network congestion games with convex latency functions, and show three facts: First, the harm of altruism is maximized when exactly half of...
Corr, 2008
This paper studies the effects of introducing altruistic agents into atomic congestion games. Altruistic behavior is modeled by a trade-off between selfish and social objectives. In particular, we assume agents optimize a linear combination of personal delay of a strategy and the resulting increase in social cost. Our model can be embedded in the framework of congestion games with player-specific latency functions. Stable states are the Nash equilibria of these games, and we examine their existence and the convergence of sequential best-response dynamics. Previous work shows that for symmetric singleton games with convex delays Nash equilibria are guaranteed to exist. For concave delay functions we observe that there are games without Nash equilibria and provide a polynomial time algorithm to decide existence for symmetric singleton games with arbitrary delay functions. Our algorithm can be extended to compute best and worst Nash equilibria if they exist. For more general congestion games existence becomes NP-hard to decide, even for symmetric network games with quadratic delay functions. Perhaps surprisingly, if all delay functions are linear, then there is always a Nash equilibrium in any congestion game with altruists and any better-response dynamics converges. In addition to these results for uncoordinated dynamics, we consider a scenario in which a central altruistic institution can motivate agents to act altruistically. We provide constructive and hardness results for finding the minimum number of altruists to stabilize an optimal congestion profile and more general mechanisms to incentivize agents to adopt favorable behavior.
Price of Anarchy in Networks with Heterogeneous Latency Functions
Mathematics of Operations Research
We address the performance of selfish network routing in multi-commodity flows where the latency or delay function on edges is dependent on the flow of individual commodities, rather than on the aggregate flow. An application of this study is the analysis of a network with differentiated traffic, i.e., in transportation networks where there are multiple types of traffic and in networks where traffic is prioritized according to type classification. We consider the inefficiency of equilibrium in this model and provide price of anarchy bounds for networks with k (types of) commodities where each link is associated with heterogeneous polynomial delays, i.e., commodity i on edge e faces delay specified by h e i (f 1 (e), f 2 (e),. .. , f k (e)) where f i (e) is the flow of the ith commodity through edge e and h e i () a polynomial delay function applicable to the ith commodity. We consider both atomic and non-atomic flows and show bounds on the price of anarchy that depend on the relative impact of each type of traffic on the edge delay where the delay functions are polynomials of degree θ, e.g., i a i f i (e) θ. The price of anarchy is unbounded for arbitrary polynomials. For networks with decomposable delay functions where the delay is the same for all commodities using the edge, i.e., delays on edge e are defined by h e (f 1 (e), f 2 (e),. .. , f k (e)), we show improved bounds on the price of anarchy, for both non-atomic and atomic flows. The results illustrate that the inefficiency of selfish routing worsens in the case of heterogeneous delays as compared to the standard delay functions that do not consider type differentiation.
Routing games: From egoism to altruism
2010
Abstract The paper studies the routing in the network shared by several users. Each user seeks to optimize either its own performance or some combination between its own performance and that of other users, by controlling the routing of its given flow demand. We parameterize the degree of cooperation which allows to cover the fully non-cooperative behavior, the fully cooperative behavior, and even more, the fully altruistic behavior, all these as special cases of the parameter's choice.
The Robust Price of Anarchy of Altruistic Games
Lecture Notes in Computer Science, 2011
We study the inefficiency of equilibria for various classes of games when players are (partially) altruistic. We model altruistic behavior by assuming that player i's perceived cost is a convex combination of 1 − αi times his direct cost and αi times the social cost. Tuning the parameters αi allows smooth interpolation between purely selfish and purely altruistic behavior. Within this framework, we study altruistic extensions of linear congestion games, fair cost-sharing games and valid utility games.
Routing selfish unsplittable traffic
ACM Transactions on Algorithms, 2007
We consider general resource assignment games involving selfish users/agents in which users compete for resources and try to be assigned to resources which maximize their own benefits (e.g., try to route their traffic through links which minimize the latency of their own traffic). We propose and study a mechanism design approach in which an allocation mechanism assigns users to resources and charges the users for using the resources so to induce each user to truthfully report a private piece of information he/she holds (e.g., how much traffic he/she needs to transmit). This information is crucial for computing optimal (or close to the optimal) allocations and an agent could misreport his/her information so to induce the underlying allocation algorithm to output a solution which he/she likes more (e.g., which assigns better resources to him/her).
The price of selfish behavior in bilateral network formation
Proceedings of the twenty-fourth annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '05, 2005
Given a collection of selfish agents who wish to establish links to route traffic among themselves, the set of equilibrium network topologies may appear quite different from the centrally enforced optimum. We study the quality (price of anarchy) of equilibrium networks in a game where links require the consent of both participants and are negotiated bilaterally and compare these networks to those generated by an earlier model due to Fabrikant et al. in which links are formed unilaterally. We provide a characterization of stable and efficient networks in the bilateral network formation game, show that the set of stable networks is richer than those in the unilateral game, and that all stable networks of the unilateral game are also stable in the bilateral game. We also provide an upper and lower bound on the price of anarchy (tight in the size of the network n but not the link cost α) of the bilateral game and show that the worst-case price of anarchy of the bilateral model is worse than for the unilateral model. A careful empirical analysis demonstrates that the average price of anarchy is better in the bilateral connection game than in the unilateral game for small link costs but worse as links become more expensive. In the process, a powerful equivalence between link-based graph stability and two game-theoretic equilibrium notions is also discussed. The equivalence establishes necessary and sufficient conditions for an equilibrium in the bilateral game that helps provide a partial geometric characterization of equilibrium graphs.