2,490 research outputs found
Dynamic club formation with coordination
We present a dynamic model of jurisdiction formation in a society of identical people. The process is described by a Markov chain that is defined by myopic optimization on the part of the players. We show that the process will converge to a Nash equilibrium club structure. Next, we allow for coordination between members of the same club,i.e. club members can form coalitions for one period and deviate jointly. We define a Nash club equilibrium (NCE) as a strategy configuration that is immune to such coalitional deviations. We show that, if one exists, this modified process will converge to a NCE configuration with probability one. Finally, we deal with the case where a NCE fails to exist due to indivisibility problems. When the population size is not an integer multiple of the optimal club size, there will be left over players who prevent the process from settling down. We define the concept of an approximate Nash club equilibrium (ANCE), which means that all but k players are playing a Nash club equilibrium, where k is defined by the minimal number of left over players. We show that the modified process converges to an ergodic set of states each of which is ANCE
Asymptotically Truthful Equilibrium Selection in Large Congestion Games
Studying games in the complete information model makes them analytically
tractable. However, large player interactions are more realistically
modeled as games of incomplete information, where players may know little to
nothing about the types of other players. Unfortunately, games in incomplete
information settings lose many of the nice properties of complete information
games: the quality of equilibria can become worse, the equilibria lose their
ex-post properties, and coordinating on an equilibrium becomes even more
difficult. Because of these problems, we would like to study games of
incomplete information, but still implement equilibria of the complete
information game induced by the (unknown) realized player types.
This problem was recently studied by Kearns et al. and solved in large games
by means of introducing a weak mediator: their mediator took as input reported
types of players, and output suggested actions which formed a correlated
equilibrium of the underlying game. Players had the option to play
independently of the mediator, or ignore its suggestions, but crucially, if
they decided to opt-in to the mediator, they did not have the power to lie
about their type. In this paper, we rectify this deficiency in the setting of
large congestion games. We give, in a sense, the weakest possible mediator: it
cannot enforce participation, verify types, or enforce its suggestions.
Moreover, our mediator implements a Nash equilibrium of the complete
information game. We show that it is an (asymptotic) ex-post equilibrium of the
incomplete information game for all players to use the mediator honestly, and
that when they do so, they end up playing an approximate Nash equilibrium of
the induced complete information game. In particular, truthful use of the
mediator is a Bayes-Nash equilibrium in any Bayesian game for any prior.Comment: The conference version of this paper appeared in EC 2014. This
manuscript has been merged and subsumed by the preprint "Robust Mediators in
Large Games": http://arxiv.org/abs/1512.0269
Greedy Selfish Network Creation
We introduce and analyze greedy equilibria (GE) for the well-known model of
selfish network creation by Fabrikant et al.[PODC'03]. GE are interesting for
two reasons: (1) they model outcomes found by agents which prefer smooth
adaptations over radical strategy-changes, (2) GE are outcomes found by agents
which do not have enough computational resources to play optimally. In the
model of Fabrikant et al. agents correspond to Internet Service Providers which
buy network links to improve their quality of network usage. It is known that
computing a best response in this model is NP-hard. Hence, poly-time agents are
likely not to play optimally. But how good are networks created by such agents?
We answer this question for very simple agents. Quite surprisingly, naive
greedy play suffices to create remarkably stable networks. Specifically, we
show that in the SUM version, where agents attempt to minimize their average
distance to all other agents, GE capture Nash equilibria (NE) on trees and that
any GE is in 3-approximate NE on general networks. For the latter we also
provide a lower bound of 3/2 on the approximation ratio. For the MAX version,
where agents attempt to minimize their maximum distance, we show that any
GE-star is in 2-approximate NE and any GE-tree having larger diameter is in
6/5-approximate NE. Both bounds are tight. We contrast these positive results
by providing a linear lower bound on the approximation ratio for the MAX
version on general networks in GE. This result implies a locality gap of
for the metric min-max facility location problem, where n is the
number of clients.Comment: 28 pages, 8 figures. An extended abstract of this work was accepted
at WINE'1
LP-based Covering Games with Low Price of Anarchy
We present a new class of vertex cover and set cover games. The price of
anarchy bounds match the best known constant factor approximation guarantees
for the centralized optimization problems for linear and also for submodular
costs -- in contrast to all previously studied covering games, where the price
of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In
particular, we describe a vertex cover game with a price of anarchy of 2. The
rules of the games capture the structure of the linear programming relaxations
of the underlying optimization problems, and our bounds are established by
analyzing these relaxations. Furthermore, for linear costs we exhibit linear
time best response dynamics that converge to these almost optimal Nash
equilibria. These dynamics mimic the classical greedy approximation algorithm
of Bar-Yehuda and Even [3]
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
Resource Buying Games
In resource buying games a set of players jointly buys a subset of a finite
resource set E (e.g., machines, edges, or nodes in a digraph). The cost of a
resource e depends on the number (or load) of players using e, and has to be
paid completely by the players before it becomes available. Each player i needs
at least one set of a predefined family S_i in 2^E to be available. Thus,
resource buying games can be seen as a variant of congestion games in which the
load-dependent costs of the resources can be shared arbitrarily among the
players. A strategy of player i in resource buying games is a tuple consisting
of one of i's desired configurations S_i together with a payment vector p_i in
R^E_+ indicating how much i is willing to contribute towards the purchase of
the chosen resources. In this paper, we study the existence and computational
complexity of pure Nash equilibria (PNE, for short) of resource buying games.
In contrast to classical congestion games for which equilibria are guaranteed
to exist, the existence of equilibria in resource buying games strongly depends
on the underlying structure of the S_i's and the behavior of the cost
functions. We show that for marginally non-increasing cost functions, matroids
are exactly the right structure to consider, and that resource buying games
with marginally non-decreasing cost functions always admit a PNE
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