20 research outputs found
The Complexity of Welfare Maximization in Congestion Games
We investigate issues of complexity related to welfare maximization in congestion games. In particular, we provide a full classification of complexity results for the problem of finding a minimum cost solution to a congestion game, under the model of Rosenthal. We consider both network and general congestion games, and we examine several variants of the problem concerning the structure of the game and the properties of its associated cost functions. Many of these problem variants turn out to be NP-hard, and some are hard to approximate to within any finite factor, unless P = NP. We also identify several versions of the problem that are solvable in polynomial time.United States. Dept. of Energy (Grant Number: DE-AC52-07NA27344)Lawrence Livermore National Laboratory (Grant Number: LLNL-JRNL-410585)United States. Office of Naval Research (Grant Number: N000141110056
Maximizing Social Welfare Subject to Network Externalities: A Unifying Submodular Optimization Approach
We consider the problem of allocating multiple indivisible items to a set of
networked agents to maximize the social welfare subject to network
externalities. Here, the social welfare is given by the sum of agents'
utilities and externalities capture the effect that one user of an item has on
the item's value to others. We first provide a general formulation that
captures some of the existing models as a special case. We then show that the
social welfare maximization problem benefits some nice diminishing or
increasing marginal return properties. That allows us to devise polynomial-time
approximation algorithms using the Lovasz extension and multilinear extension
of the objective functions. Our principled approach recovers or improves some
of the existing algorithms and provides a simple and unifying framework for
maximizing social welfare subject to network externalities
Signaling in Bayesian Network Congestion Games: the Subtle Power of Symmetry
Network congestion games are a well-understood model of multi-agent strategic
interactions. Despite their ubiquitous applications, it is not clear whether it
is possible to design information structures to ameliorate the overall
experience of the network users. We focus on Bayesian games with atomic
players, where network vagaries are modeled via a (random) state of nature
which determines the costs incurred by the players. A third-party entity---the
sender---can observe the realized state of the network and exploit this
additional information to send a signal to each player. A natural question is
the following: is it possible for an informed sender to reduce the overall
social cost via the strategic provision of information to players who update
their beliefs rationally? The paper focuses on the problem of computing optimal
ex ante persuasive signaling schemes, showing that symmetry is a crucial
property for its solution. Indeed, we show that an optimal ex ante persuasive
signaling scheme can be computed in polynomial time when players are symmetric
and have affine cost functions. Moreover, the problem becomes NP-hard when
players are asymmetric, even in non-Bayesian settings
Maximizing social welfare in congestion games via redistribution
It is well-known that efficient use of congestible resources can be achieved via marginal pricing; however, payments collected from the agents generate a budget surplus, which reduces social welfare. We show that an asymptotically first-best solution in the number of agents can be achieved by the appropriate redistribution of the budget surplus back to the agents
In Congestion Games, Taxes Achieve Optimal Approximation
In this work, we consider the problem of minimising the social cost in atomic congestion games. For this problem, we provide tight computational lower bounds along with taxation mechanisms yielding polynomial time algorithms with optimal approximation. Perhaps surprisingly, our results show that indirect interventions, in the form of efficiently computed taxation mechanisms, yield the same performance achievable by the best polynomial time algorithm, even when the latter has full control over the agents' actions. It follows that no other tractable approach geared at incentivizing desirable system behavior can improve upon this result, regardless of whether it is based on taxations, coordination mechanisms, information provision, or any other principle. In short: Judiciously chosen taxes achieve optimal approximation. Three technical contributions underpin this conclusion. First, we show that computing the minimum social cost is NP-hard to approximate within a given factor depending solely on the admissible resource costs. Second, we design a tractable taxation mechanism whose efficiency (price of anarchy) matches this hardness factor, and thus is worst-case optimal. As these results extend to coarse correlated equilibria, any no-regret algorithm inherits the same performances, allowing us to devise polynomial time algorithms with optimal approximation
Fragility of the Commons under Prospect-Theoretic Risk Attitudes
We study a common-pool resource game where the resource experiences failure
with a probability that grows with the aggregate investment in the resource. To
capture decision making under such uncertainty, we model each player's risk
preference according to the value function from prospect theory. We show the
existence and uniqueness of a pure Nash equilibrium when the players have
heterogeneous risk preferences and under certain assumptions on the rate of
return and failure probability of the resource. Greater competition, vis-a-vis
the number of players, increases the failure probability at the Nash
equilibrium; we quantify this effect by obtaining bounds on the ratio of the
failure probability at the Nash equilibrium to the failure probability under
investment by a single user. We further show that heterogeneity in attitudes
towards loss aversion leads to higher failure probability of the resource at
the equilibrium.Comment: Accepted for publication in Games and Economic Behavior, 201