106 research outputs found
Cost-sharing in generalised selfish routing
© Springer International Publishing AG 2017. We study a generalisation of atomic selfish routing games where each player may control multiple flows which she routes seek-ing to minimise their aggregate cost. Such games emerge in various set-tings, such as traïŹc routing in road networks by competing ride-sharing applications or packet routing in communication networks by competing service providers who seek to optimise the quality of service of their cus-tomers. We study the existence of pure Nash equilibria in the induced games and we exhibit a separation from the single-commodity per player model by proving that the Shapley value is the only cost-sharing method that guarantees it. We also prove that the price of anarchy and price of stability is no larger than in the single-commodity model for general cost-sharing methods and general classes of convex cost functions. We close by giving results on the existence of pure Nash equilibria of a splittable variant of our model
Budget-restricted utility games with ordered strategic decisions
We introduce the concept of budget games. Players choose a set of tasks and
each task has a certain demand on every resource in the game. Each resource has
a budget. If the budget is not enough to satisfy the sum of all demands, it has
to be shared between the tasks. We study strategic budget games, where the
budget is shared proportionally. We also consider a variant in which the order
of the strategic decisions influences the distribution of the budgets. The
complexity of the optimal solution as well as existence, complexity and quality
of equilibria are analyzed. Finally, we show that the time an ordered budget
game needs to convergence towards an equilibrium may be exponential
The Price of Anarchy for Selfish Ring Routing is Two
We analyze the network congestion game with atomic players, asymmetric
strategies, and the maximum latency among all players as social cost. This
important social cost function is much less understood than the average
latency. We show that the price of anarchy is at most two, when the network is
a ring and the link latencies are linear. Our bound is tight. This is the first
sharp bound for the maximum latency objective.Comment: Full version of WINE 2012 paper, 24 page
Complexity and Approximation of the Continuous Network Design Problem
We revisit a classical problem in transportation, known as the (bilevel) continuous network design problem, CNDP for short. Given a graph for which the latency of each edge depends on the ratio of the edge flow and the capacity installed, the goal is to find an optimal investment in edge capacities so as to minimize the sum of the routing costs of the induced Wardrop equilibrium and the investment costs for installing the edge's capacities. While this problem is considered to be challenging in the literature, its complexity status was still unknown. We close this gap, showing that CNDP is strongly -hard and -hard, both on directed and undirected networks and even for instances with affine latencies. As for the approximation of the problem, we first provide a detailed analysis for a heuristic studied by Marcotte for the special case of monomial latency functions [P. Marcotte, Math. Prog., 34 (1986), pp. 142--162]. We derive a closed form expression of its approximation guarantee for arbitrary sets of latency functions. We then propose a different approximation algorithm and show that it has the same approximation guarantee. Then, we prove that using the better of the two approximation algorithms results in a strictly improved approximation guarantee for which we derive a closed form expression. For affine latencies, for example, this best-of-two approach achieves an approximation factor of , which improves on the factor of that has been shown before by Marcotte
Malicious Bayesian Congestion Games
In this paper, we introduce malicious Bayesian congestion games as an
extension to congestion games where players might act in a malicious way. In
such a game each player has two types. Either the player is a rational player
seeking to minimize her own delay, or - with a certain probability - the player
is malicious in which case her only goal is to disturb the other players as
much as possible.
We show that such games do in general not possess a Bayesian Nash equilibrium
in pure strategies (i.e. a pure Bayesian Nash equilibrium). Moreover, given a
game, we show that it is NP-complete to decide whether it admits a pure
Bayesian Nash equilibrium. This result even holds when resource latency
functions are linear, each player is malicious with the same probability, and
all strategy sets consist of singleton sets. For a slightly more restricted
class of malicious Bayesian congestion games, we provide easy checkable
properties that are necessary and sufficient for the existence of a pure
Bayesian Nash equilibrium.
In the second part of the paper we study the impact of the malicious types on
the overall performance of the system (i.e. the social cost). To measure this
impact, we use the Price of Malice. We provide (tight) bounds on the Price of
Malice for an interesting class of malicious Bayesian congestion games.
Moreover, we show that for certain congestion games the advent of malicious
types can also be beneficial to the system in the sense that the social cost of
the worst case equilibrium decreases. We provide a tight bound on the maximum
factor by which this happens.Comment: 18 pages, submitted to WAOA'0
Computing Approximate Pure Nash Equilibria in Shapley Value Weighted Congestion Games
We study the computation of approximate pure Nash equilibria in Shapley value
(SV) weighted congestion games, introduced in [19]. This class of games
considers weighted congestion games in which Shapley values are used as an
alternative (to proportional shares) for distributing the total cost of each
resource among its users. We focus on the interesting subclass of such games
with polynomial resource cost functions and present an algorithm that computes
approximate pure Nash equilibria with a polynomial number of strategy updates.
Since computing a single strategy update is hard, we apply sampling techniques
which allow us to achieve polynomial running time. The algorithm builds on the
algorithmic ideas of [7], however, to the best of our knowledge, this is the
first algorithmic result on computation of approximate equilibria using other
than proportional shares as player costs in this setting. We present a novel
relation that approximates the Shapley value of a player by her proportional
share and vice versa. As side results, we upper bound the approximate price of
anarchy of such games and significantly improve the best known factor for
computing approximate pure Nash equilibria in weighted congestion games of [7].Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-71924-5_1
Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games
Additively separable hedonic games and fractional hedonic games have received
considerable attention. They are coalition forming games of selfish agents
based on their mutual preferences. Most of the work in the literature
characterizes the existence and structure of stable outcomes (i.e., partitions
in coalitions), assuming that preferences are given. However, there is little
discussion on this assumption. In fact, agents receive different utilities if
they belong to different partitions, and thus it is natural for them to declare
their preferences strategically in order to maximize their benefit. In this
paper we consider strategyproof mechanisms for additively separable hedonic
games and fractional hedonic games, that is, partitioning methods without
payments such that utility maximizing agents have no incentive to lie about
their true preferences. We focus on social welfare maximization and provide
several lower and upper bounds on the performance achievable by strategyproof
mechanisms for general and specific additive functions. In most of the cases we
provide tight or asymptotically tight results. All our mechanisms are simple
and can be computed in polynomial time. Moreover, all the lower bounds are
unconditional, that is, they do not rely on any computational or complexity
assumptions
The Price of Stability of Weighted Congestion Games
We give exponential lower bounds on the Price of Stability (PoS) of weighted congestion games with polynomial cost functions. In particular, for any positive integer we construct rather simple games with cost functions of degree at most which have a PoS of at least , where is the unique positive root of the equation . This almost closes the huge gap between and . Our bound extends also to network congestion games. We further show that the PoS remains exponential even for singleton games. More generally, we provide a lower bound of on the PoS of -approximate Nash equilibria for singleton games. All our lower bounds hold for mixed and correlated equilibria as well. On the positive side, we give a general upper bound on the PoS of -approximate Nash equilibria, which is sensitive to the range of the player weights and the approximation parameter . We do this by explicitly constructing a novel approximate potential function, based on Faulhaber's formula, that generalizes Rosenthal's potential in a continuous, analytic way. From the general theorem, we deduce two interesting corollaries. First, we derive the existence of an approximate pure Nash equilibrium with PoS at most ; the equilibrium's approximation parameter ranges from to in a smooth way with respect to . Second, we show that for unweighted congestion games, the PoS of -approximate Nash equilibria is at most . Read More: https://epubs.siam.org/doi/10.1137/18M120788
Hiring Secretaries over Time: The Benefit of Concurrent Employment
We consider a stochastic online problem where n applicants arrive over time, one per time step. Upon the arrival of each applicant, their cost per time step is revealed, and we have to fix the duration of employment, starting immediately. This decision is irrevocable; that is, we can neither extend a contract nor dismiss a candidate once hired. In every time step, at least one candidate needs to be under contract, and our goal is to minimize the total hiring cost, which is the sum of the applicantsâ costs multiplied with their respective employment durations. We provide a competitive online algorithm for the case that the applicantsâ costs are drawn independently from a known distribution. Specifically, the algorithm achieves a competitive ratio of 2.965 for the case of uniform distributions. For this case, we give an analytical lower bound of 2 and a computational lower bound of 2.148. We then adapt our algorithm to stay competitive even in settings with one or more of the following restrictions: (i) at most two applicants can be hired concurrently; (ii) the distribution of the applicantsâ costs is unknown; (iii) the total number n of time steps is unknown. On the other hand, we show that concurrent employment is a necessary feature of competitive algorithms by proving that no algorithm has a competitive ratio better than Ω(nâââ/logâân) if concurrent employment is forbidden
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