13,472 research outputs found
On the Structure of Equilibria in Basic Network Formation
We study network connection games where the nodes of a network perform edge
swaps in order to improve their communication costs. For the model proposed by
Alon et al. (2010), in which the selfish cost of a node is the sum of all
shortest path distances to the other nodes, we use the probabilistic method to
provide a new, structural characterization of equilibrium graphs. We show how
to use this characterization in order to prove upper bounds on the diameter of
equilibrium graphs in terms of the size of the largest -vicinity (defined as
the the set of vertices within distance from a vertex), for any
and in terms of the number of edges, thus settling positively a conjecture of
Alon et al. in the cases of graphs of large -vicinity size (including graphs
of large maximum degree) and of graphs which are dense enough.
Next, we present a new swap-based network creation game, in which selfish
costs depend on the immediate neighborhood of each node; in particular, the
profit of a node is defined as the sum of the degrees of its neighbors. We
prove that, in contrast to the previous model, this network creation game
admits an exact potential, and also that any equilibrium graph contains an
induced star. The existence of the potential function is exploited in order to
show that an equilibrium can be reached in expected polynomial time even in the
case where nodes can only acquire limited knowledge concerning non-neighboring
nodes.Comment: 11 pages, 4 figure
Playing Stackelberg Opinion Optimization with Randomized Algorithms for Combinatorial Strategies
From a perspective of designing or engineering for opinion formation games in
social networks, the "opinion maximization (or minimization)" problem has been
studied mainly for designing subset selecting algorithms. We furthermore define
a two-player zero-sum Stackelberg game of competitive opinion optimization by
letting the player under study as the first-mover minimize the sum of expressed
opinions by doing so-called "internal opinion design", knowing that the other
adversarial player as the follower is to maximize the same objective by also
conducting her own internal opinion design.
We propose for the min player to play the "follow-the-perturbed-leader"
algorithm in such Stackelberg game, obtaining losses depending on the other
adversarial player's play. Since our strategy of subset selection is
combinatorial in nature, the probabilities in a distribution over all the
strategies would be too many to be enumerated one by one. Thus, we design a
randomized algorithm to produce a (randomized) pure strategy. We show that the
strategy output by the randomized algorithm for the min player is essentially
an approximate equilibrium strategy against the other adversarial player
Selfish Network Creation with Non-Uniform Edge Cost
Network creation games investigate complex networks from a game-theoretic
point of view. Based on the original model by Fabrikant et al. [PODC'03] many
variants have been introduced. However, almost all versions have the drawback
that edges are treated uniformly, i.e. every edge has the same cost and that
this common parameter heavily influences the outcomes and the analysis of these
games.
We propose and analyze simple and natural parameter-free network creation
games with non-uniform edge cost. Our models are inspired by social networks
where the cost of forming a link is proportional to the popularity of the
targeted node. Besides results on the complexity of computing a best response
and on various properties of the sequential versions, we show that the most
general version of our model has constant Price of Anarchy. To the best of our
knowledge, this is the first proof of a constant Price of Anarchy for any
network creation game.Comment: To appear at SAGT'1
Social Data Offloading in D2D-Enhanced Cellular Networks by Network Formation Games
Recently, cellular networks are severely overloaded by social-based services,
such as YouTube, Facebook and Twitter, in which thousands of clients subscribe
a common content provider (e.g., a popular singer) and download his/her content
updates all the time. Offloading such traffic through complementary networks,
such as a delay tolerant network formed by device-to-device (D2D)
communications between mobile subscribers, is a promising solution to reduce
the cellular burdens. In the existing solutions, mobile users are assumed to be
volunteers who selfishlessly deliver the content to every other user in
proximity while moving. However, practical users are selfish and they will
evaluate their individual payoffs in the D2D sharing process, which may highly
influence the network performance compared to the case of selfishless users. In
this paper, we take user selfishness into consideration and propose a network
formation game to capture the dynamic characteristics of selfish behaviors. In
the proposed game, we provide the utility function of each user and specify the
conditions under which the subscribers are guaranteed to converge to a stable
network. Then, we propose a practical network formation algorithm in which the
users can decide their D2D sharing strategies based on their historical
records. Simulation results show that user selfishness can highly degrade the
efficiency of data offloading, compared with ideal volunteer users. Also, the
decrease caused by user selfishness can be highly affected by the cost ratio
between the cellular transmission and D2D transmission, the access delays, and
mobility patterns
The Price of Anarchy for Network Formation in an Adversary Model
We study network formation with n players and link cost \alpha > 0. After the
network is built, an adversary randomly deletes one link according to a certain
probability distribution. Cost for player v incorporates the expected number of
players to which v will become disconnected. We show existence of equilibria
and a price of stability of 1+o(1) under moderate assumptions on the adversary
and n \geq 9.
As the main result, we prove bounds on the price of anarchy for two special
adversaries: one removes a link chosen uniformly at random, while the other
removes a link that causes a maximum number of player pairs to be separated.
For unilateral link formation we show a bound of O(1) on the price of anarchy
for both adversaries, the constant being bounded by 10+o(1) and 8+o(1),
respectively. For bilateral link formation we show O(1+\sqrt{n/\alpha}) for one
adversary (if \alpha > 1/2), and \Theta(n) for the other (if \alpha > 2
considered constant and n \geq 9). The latter is the worst that can happen for
any adversary in this model (if \alpha = \Omega(1)). This points out
substantial differences between unilateral and bilateral link formation
Designing cost-sharing methods for Bayesian games
We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players
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