3,440 research outputs found
Achievable Outcomes in Smooth Dynamic Contribution Games
This paper studies a class of dynamic voluntary contribution games in a setting with discounting and neoclassical payoffs (differentiable, strictly concave in the public good, and quasilinear in the private good). An achievable profile is the limit point of a subgame perfect equilibrium path -- the ultimate cumulative contribution vector of the players. A profile is shown to be achievable only if it is in the undercore of the underlying coalitional game, i.e., the profile cannot be blocked by a coalition using a component-wise smaller profile. Conversely, if free-riding incentives are strong enough that contributing zero is a dominant strategy in the stage games, then any undercore profile is the limit of achievable profiles as the period length shrinks. Thus, in this case when the period length is very short, (i) the set of achievable contributions does not depend on whether the players can move simultaneously or only in a round-robin fashion; (ii) an efficient profile can be approximately achieved if and only if it is in the core of the underlying coalitional game; and (iii) any achievable profile can be achieved almost instantly.dynamic games, monotone games, core, public goods, voluntary contribution, gradualism
Complexity of coalition structure generation
We revisit the coalition structure generation problem in which the goal is to
partition the players into exhaustive and disjoint coalitions so as to maximize
the social welfare. One of our key results is a general polynomial-time
algorithm to solve the problem for all coalitional games provided that player
types are known and the number of player types is bounded by a constant. As a
corollary, we obtain a polynomial-time algorithm to compute an optimal
partition for weighted voting games with a constant number of weight values and
for coalitional skill games with a constant number of skills. We also consider
well-studied and well-motivated coalitional games defined compactly on
combinatorial domains. For these games, we characterize the complexity of
computing an optimal coalition structure by presenting polynomial-time
algorithms, approximation algorithms, or NP-hardness and inapproximability
lower bounds.Comment: 17 page
Efficient computation of the Shapley value for game-theoretic network centrality
The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo
Stochastic Coalitional Better-response Dynamics and Strong Nash Equilibrium
We consider coalition formation among players in an n-player finite strategic
game over infinite horizon. At each time a randomly formed coalition makes a
joint deviation from a current action profile such that at new action profile
all players from the coalition are strictly benefited. Such deviations define a
coalitional better-response (CBR) dynamics that is in general stochastic. The
CBR dynamics either converges to a strong Nash equilibrium or stucks in a
closed cycle. We also assume that at each time a selected coalition makes
mistake in deviation with small probability that add mutations (perturbations)
into CBR dynamics. We prove that all strong Nash equilibria and closed cycles
are stochastically stable, i.e., they are selected by perturbed CBR dynamics as
mutations vanish. Similar statement holds for strict strong Nash equilibrium.
We apply CBR dynamics to the network formation games and we prove that all
strongly stable networks and closed cycles are stochastically stable
Spectrum Leasing as an Incentive towards Uplink Macrocell and Femtocell Cooperation
The concept of femtocell access points underlaying existing communication
infrastructure has recently emerged as a key technology that can significantly
improve the coverage and performance of next-generation wireless networks. In
this paper, we propose a framework for macrocell-femtocell cooperation under a
closed access policy, in which a femtocell user may act as a relay for
macrocell users. In return, each cooperative macrocell user grants the
femtocell user a fraction of its superframe. We formulate a coalitional game
with macrocell and femtocell users being the players, which can take individual
and distributed decisions on whether to cooperate or not, while maximizing a
utility function that captures the cooperative gains, in terms of throughput
and delay.We show that the network can selforganize into a partition composed
of disjoint coalitions which constitutes the recursive core of the game
representing a key solution concept for coalition formation games in partition
form. Simulation results show that the proposed coalition formation algorithm
yields significant gains in terms of average rate per macrocell user, reaching
up to 239%, relative to the non-cooperative case. Moreover, the proposed
approach shows an improvement in terms of femtocell users' rate of up to 21%
when compared to the traditional closed access policy.Comment: 29 pages, 11 figures, accepted at the IEEE JSAC on Femtocell Network
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