Altruism in Atomic Congestion Games (original) (raw)
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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.
Optimizing the Social Cost of Congestion Games by Imposing Variable Delays
We describe a new coordination mechanism for non-atomic congestion games that leads to a (selfish) social cost which is arbitrarily close to the non-selfish optimal. This mechanism does not incur any additional extra cost, like tolls, which are usually differentiated from the social cost as expressed in terms of delays only.
Atomic congestion games among coalitions
ACM Transactions on Algorithms, 2008
We consider algorithmic questions concerning the existence, tractability and quality of atomic congestion games, among users that are considered to participate in (static) selfish coalitions. We carefully define a coalitional congestion model among atomic players. Our findings in this model are quite interesting, in the sense that we demonstrate many similarities with the non-cooperative case. For example, there exist potentials proving the existence of Pure Nash Equilibria (PNE) in the (even unrelated) parallel links setting; the Finite Improvement Property collapses as soon as we depart from linear delays, but there is an exact potential (and thus PNE) for the case of linear delays, in the network setting; the Price of Anarchy on identical parallel links demonstrates a quite surprising threshold behavior: it persists on being asymptotically equal to that in the case of the non-cooperative KP-model, unless we enforce a sublogarithmic number of coalitions. We also show crucial differences, mainly concerning the hardness of algorithmic problems that are solved efficiently in the non-cooperative case. Although we demonstrate convergence to robust PNE, we also prove the hardness of computing them. On the other hand, we can easily construct a generalized fully mixed Nash Equilibrium. Finally, we propose a new improvement policy that converges to PNE that are robust against (even dynamically forming) coalitions of small size, in pseudo-polynomial time.
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...
Atomic Congestion Games: Fast, Myopic and Concurrent
Theory of Computing Systems / Mathematical Systems Theory, 2008
We study here the effect of concurrent greedy moves of players in atomic congestion games where n selfish agents (players) wish to select a resource each (out of m resources) so that her selfish delay there is not much. The problem of “maintaining” global progress while allowing concurrent play is exactly what is examined and answered here. We examine two orthogonal settings : (i) A game where the players decide their moves without global information, each acting “freely” by sampling resources randomly and locally deciding to migrate (if the new resource is better) via a random experiment. Here, the resources can have quite arbitrary latency that is load dependent. (ii) An “organised” setting where the players are pre-partitioned into selfish groups (coalitions) and where each coalition does an improving coalitional move. Our work considers concurrent selfish play for arbitrary latencies for the first time. Also, this is the first time where fast coalitional convergence to an approximate equilibrium is shown.
Congestion games with malicious players
Games and Economic Behavior, 2009
We study the equilibria of non-atomic congestion games in which there are two types of players: rational players, who seek to minimize their own delay, and malicious players, who seek to maximize the average delay experienced by the rational players. We study the existence of pure and mixed Nash equilibria for these games, and we seek to quantify the impact of the malicious players on the equilibrium. One counterintuitive phenomenon which we demonstrate is the "windfall of malice": paradoxically, when a myopically malicious player gains control of a fraction of the flow, the new equilibrium may be more favorable for the remaining rational players than the previous equilibrium.
Unilateral Altruism in Network Routing Games with Atomic Players
2011
We study a routing game in which one of the players unilaterally acts altruistically by taking into consideration the latency cost of other players as well as his own. By not playing selfishly, a player can not only improve the other players' equilibrium utility but also improve his own equilibrium utility. To quantify the effect, we define a metric called the Value of Unilateral Altruism (VoU) to be the ratio of the equilibrium utility of the altruistic user to the equilibrium utility he would have received in Nash equilibrium if he were selfish. We show by example that the VoU, in a game with nonlinear latency functions and atomic players, can be arbitrarily large. Since the Nash equilibrium social welfare of this example is arbitrarily far from social optimum, this example also has a Price of Anarchy (PoA) that is unbounded. The example is driven by there being a small number of players since the same example with non-atomic players yields a Nash equilibrium that is fully efficient.
Congestion Games with Player-Specific Constants
Lecture Notes in Computer Science
We consider a special case of weighted congestion games with playerspecific latency functions where each player uses for each particular resource a fixed (non-decreasing) delay function together with a player-specific constant. For each particular resource, the resource-specific delay function and the playerspecific constant (for that resource) are composed by means of a group operation (such as addition or multiplication) into a player-specific latency function. We assume that the underlying group is a totally ordered abelian group. In this way, we obtain the class of weighted congestion games with player-specific constants; we observe that this class is contained in the new intuitive class of dominance weighted congestion games. We obtain the following results: Games on parallel links:-Every unweighted congestion game has a generalized ordinal potential.-There is a weighted congestion game with 3 players on 3 parallel links that does not have the Finite Best-Improvement Property.-There is a particular best-improvement cycle for general weighted congestion games with player-specific latency functions and 3 players whose outlaw implies the existence of a pure Nash equilibrium. This cycle is indeed outlawed for dominance weighted congestion games with 3 players-and hence for weighted congestion games with player-specific constants and 3 players. Network congestion games: For unweighted symmetric network congestion games with player-specific additive constants, it is PLS-complete to find a pure Nash equilibrium. Arbitrary (non-network) congestion games: Every weighted congestion game with linear delay functions and player-specific additive constants has a weighted potential.
Bounding the inefficiency of equilibria in nonatomic congestion games
Games and Economic Behavior, 2004
Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma. In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a "best possible" outcome. We study a nonatomic version of the congestion games defined by Rosenthal , and identify games in which equilibria are approximately optimal in the sense that no other outcome achieves a significantly larger total payoff to the players-games in which optimization by individuals approximately optimizes the social good, in spite of the lack of coordination between players. Our results extend previous work on traffic routing games . * We thank Lou Billera for encouraging us to explore generalizations of our previous work on traffic routing, and Robert Rosenthal for introducing us to his congestion games. The first author thanks Amir Ronen for comments on a previous paper [16] that facilitated a generalization of the results therein to the nonatomic congestion games of this paper.