625 research outputs found
Maximizing Welfare in Social Networks under a Utility Driven Influence Diffusion Model
Motivated by applications such as viral marketing, the problem of influence
maximization (IM) has been extensively studied in the literature. The goal is
to select a small number of users to adopt an item such that it results in a
large cascade of adoptions by others. Existing works have three key
limitations. (1) They do not account for economic considerations of a user in
buying/adopting items. (2) Most studies on multiple items focus on competition,
with complementary items receiving limited attention. (3) For the network
owner, maximizing social welfare is important to ensure customer loyalty, which
is not addressed in prior work in the IM literature. In this paper, we address
all three limitations and propose a novel model called UIC that combines
utility-driven item adoption with influence propagation over networks. Focusing
on the mutually complementary setting, we formulate the problem of social
welfare maximization in this novel setting. We show that while the objective
function is neither submodular nor supermodular, surprisingly a simple greedy
allocation algorithm achieves a factor of of the optimum
expected social welfare. We develop \textsf{bundleGRD}, a scalable version of
this approximation algorithm, and demonstrate, with comprehensive experiments
on real and synthetic datasets, that it significantly outperforms all
baselines.Comment: 33 page
Nonspecific Networking
A new model of strategic network formation is developed and analyzed, where an agent's investment in links is nonspecific. The model comprises a large class of games which are both potential and super- or submodular games. We obtain comparative statics results for Nash equilibria with respect to investment costs for supermodular as well as submodular networking games. We also study logit-perturbed best-response dynamics for supermodular games with potentials. We find that the associated set of stochastically stable states forms a sublattice of the lattice of Nash equilibria and derive comparative statics results for the smallest and the largest stochastically stable state. Finally, we provide a broad spectrum of applications from social interaction to industrial organization. Models of strategic network formation typically assume that each agent selects his direct links to other agents in which to invest. Nonspecific networking means that an agent cannot select a specific subset of feasible links which he wants to establish or strengthen. Rather, each agent chooses an effort level or intensity of networking. In the simplest case, the agent faces a binary choice: to network or not to network. If an agent increases his networking effort, all direct links to other agents are strengthened to various degrees. We assume that benefits accrue only from direct links. The set of agents or players is finite. Each agent has a finite strategy set consisting of the networking levels to choose from. For any pair of agents, their networking levels determine the individual benefits which they obtain from interacting with each other. An agent derives an aggregate benefit from the pairwise interactions with all others. In addition, the agent incurs networking costs, which are a function of the agent's own networking level. The agent's payoff is his aggregate benefit minus his cost.Network Formation, Potential Games, Supermodular Games
Information Structure Design in Team Decision Problems
We consider a problem of information structure design in team decision
problems and team games. We propose simple, scalable greedy algorithms for
adding a set of extra information links to optimize team performance and
resilience to non-cooperative and adversarial agents. We show via a simple
counterexample that the set function mapping additional information links to
team performance is in general not supermodular. Although this implies that the
greedy algorithm is not accompanied by worst-case performance guarantees, we
illustrate through numerical experiments that it can produce effective and
often optimal or near optimal information structure modifications
Cooperative Games with Bounded Dependency Degree
Cooperative games provide a framework to study cooperation among
self-interested agents. They offer a number of solution concepts describing how
the outcome of the cooperation should be shared among the players.
Unfortunately, computational problems associated with many of these solution
concepts tend to be intractable---NP-hard or worse. In this paper, we
incorporate complexity measures recently proposed by Feige and Izsak (2013),
called dependency degree and supermodular degree, into the complexity analysis
of cooperative games. We show that many computational problems for cooperative
games become tractable for games whose dependency degree or supermodular degree
are bounded. In particular, we prove that simple games admit efficient
algorithms for various solution concepts when the supermodular degree is small;
further, we show that computing the Shapley value is always in FPT with respect
to the dependency degree. Finally, we note that, while determining the
dependency among players is computationally hard, there are efficient
algorithms for special classes of games.Comment: 10 pages, full version of accepted AAAI-18 pape
Interaction on Hypergraphs
Interaction on hypergraphs generalizes interaction on graphs, also known as pairwise local interaction. For games played on a hypergraph which are supermodular potential games, logit-perturbed best-response dynamics are studied. We find that the associated stochastically stable states form a sublattice of the lattice of Nash equilibria and derive comparative statics results for the smallest and the largest stochastically stable state. In the special case of networking games, we obtain comparative statics results with respect to investment costs, for Nash equilibria of supermodular games as well as for Nash equilibria of submodular games.
Sharing Non-Anonymous Costs of Multiple Resources Optimally
In cost sharing games, the existence and efficiency of pure Nash equilibria
fundamentally depends on the method that is used to share the resources' costs.
We consider a general class of resource allocation problems in which a set of
resources is used by a heterogeneous set of selfish users. The cost of a
resource is a (non-decreasing) function of the set of its users. Under the
assumption that the costs of the resources are shared by uniform cost sharing
protocols, i.e., protocols that use only local information of the resource's
cost structure and its users to determine the cost shares, we exactly quantify
the inefficiency of the resulting pure Nash equilibria. Specifically, we show
tight bounds on prices of stability and anarchy for games with only submodular
and only supermodular cost functions, respectively, and an asymptotically tight
bound for games with arbitrary set-functions. While all our upper bounds are
attained for the well-known Shapley cost sharing protocol, our lower bounds
hold for arbitrary uniform cost sharing protocols and are even valid for games
with anonymous costs, i.e., games in which the cost of each resource only
depends on the cardinality of the set of its users
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