12 research outputs found
Coalition Resilient Outcomes in Max k-Cut Games
We investigate strong Nash equilibria in the \emph{max -cut game}, where
we are given an undirected edge-weighted graph together with a set of colors. Nodes represent players and edges capture their mutual
interests. The strategy set of each player consists of the colors. When
players select a color they induce a -coloring or simply a coloring. Given a
coloring, the \emph{utility} (or \emph{payoff}) of a player is the sum of
the weights of the edges incident to , such that the color chosen
by is different from the one chosen by . Such games form some of the
basic payoff structures in game theory, model lots of real-world scenarios with
selfish agents and extend or are related to several fundamental classes of
games.
Very little is known about the existence of strong equilibria in max -cut
games. In this paper we make some steps forward in the comprehension of it. We
first show that improving deviations performed by minimal coalitions can cycle,
and thus answering negatively the open problem proposed in
\cite{DBLP:conf/tamc/GourvesM10}. Next, we turn our attention to unweighted
graphs. We first show that any optimal coloring is a 5-SE in this case. Then,
we introduce -local strong equilibria, namely colorings that are resilient
to deviations by coalitions such that the maximum distance between every pair
of nodes in the coalition is at most . We prove that -local strong
equilibria always exist. Finally, we show the existence of strong Nash
equilibria in several interesting specific scenarios.Comment: A preliminary version of this paper will appear in the proceedings of
the 45th International Conference on Current Trends in Theory and Practice of
Computer Science (SOFSEM'19
Approximate Equilibrium and Incentivizing Social Coordination
We study techniques to incentivize self-interested agents to form socially
desirable solutions in scenarios where they benefit from mutual coordination.
Towards this end, we consider coordination games where agents have different
intrinsic preferences but they stand to gain if others choose the same strategy
as them. For non-trivial versions of our game, stable solutions like Nash
Equilibrium may not exist, or may be socially inefficient even when they do
exist. This motivates us to focus on designing efficient algorithms to compute
(almost) stable solutions like Approximate Equilibrium that can be realized if
agents are provided some additional incentives. Our results apply in many
settings like adoption of new products, project selection, and group formation,
where a central authority can direct agents towards a strategy but agents may
defect if they have better alternatives. We show that for any given instance,
we can either compute a high quality approximate equilibrium or a near-optimal
solution that can be stabilized by providing small payments to some players. We
then generalize our model to encompass situations where player relationships
may exhibit complementarities and present an algorithm to compute an
Approximate Equilibrium whose stability factor is linear in the degree of
complementarity. Our results imply that a little influence is necessary in
order to ensure that selfish players coordinate and form socially efficient
solutions.Comment: A preliminary version of this work will appear in AAAI-14:
Twenty-Eighth Conference on Artificial Intelligenc
Efficient Local Search in Coordination Games on Graphs
We study strategic games on weighted directed graphs, where the payoff of a
player is defined as the sum of the weights on the edges from players who chose
the same strategy augmented by a fixed non-negative bonus for picking a given
strategy. These games capture the idea of coordination in the absence of
globally common strategies. Prior work shows that the problem of determining
the existence of a pure Nash equilibrium for these games is NP-complete already
for graphs with all weights equal to one and no bonuses. However, for several
classes of graphs (e.g. DAGs and cliques) pure Nash equilibria or even strong
equilibria always exist and can be found by simply following a particular
improvement or coalition-improvement path, respectively. In this paper we
identify several natural classes of graphs for which a finite improvement or
coalition-improvement path of polynomial length always exists, and, as a
consequence, a Nash equilibrium or strong equilibrium in them can be found in
polynomial time. We also argue that these results are optimal in the sense that
in natural generalisations of these classes of graphs, a pure Nash equilibrium
may not even exist.Comment: Extended version of a paper accepted to IJCAI1
Topological Price of Anarchy bounds for clustering games on networks
We consider clustering games in which the players are embedded in a network and want to coordinate (or anti-coordinate) their choices with their neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding (worst-case) Price of Anarchy bounds. As one of our main results, we derive (tight) bounds on the Price of Anarchy for clustering games on Erdős-Rényi random graphs, which, depending on the graph density, stand in stark contrast to the known Price of Anarchy bounds
Synchronisation Games on Hypergraphs
We study a strategic game model on hypergraphs where players, modelled by nodes, try to coordinate or anti-coordinate their choices within certain groups of players, modelled by hyperedges. We show this model to be a strict generalisation of symmetric additively separable hedonic games to the hypergraph setting and that such games always have a pure Nash equilibrium, which can be computed in pseudo-polynomial time. Moreover, in the pure coordination setting, we show that a strong equilibrium exists and can be computed in polynomial time when the game possesses a certain acyclic structure.</jats:p