4 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
A Game Theory Proof of Optimal Colorings Resilience to Strong Deviations
This paper provides a formal proof of the conjecture stating that optimal colorings in max k-cut games over unweighted and undirected graphs do not allow the formation of any strongly divergent coalition, i.e., a subset of nodes able to increase their own payoffs simultaneously. The result is obtained by means of a new method grounded on game theory, which consists in splitting the nodes of the graph into three subsets: the coalition itself, the coalition boundary and the nodes without relationship with the coalition. Moreover, we find additional results concerning the properties of optimal colorings
Utilitarian Welfare Optimization in the Generalized Vertex Coloring Games: An Implication to Venue Selection in Events Planning
We consider a general class of multi-agent games in networks, namely the
generalized vertex coloring games (G-VCGs), inspired by real-life applications
of the venue selection problem in events planning. Certain utility responding
to the contemporary coloring assignment will be received by each agent under
some particular mechanism, who, striving to maximize his own utility, is
restricted to local information thus self-organizing when choosing another
color. Our focus is on maximizing some utilitarian-looking welfare objective
function concerning the cumulative utilities across the network in a
decentralized fashion. Firstly, we investigate on a special class of the
G-VCGs, namely Identical Preference VCGs (IP-VCGs) which recovers the
rudimentary work by \cite{chaudhuri2008network}. We reveal its convergence even
under a completely greedy policy and completely synchronous settings, with a
stochastic bound on the converging rate provided. Secondly, regarding the
general G-VCGs, a greediness-preserved Metropolis-Hasting based policy is
proposed for each agent to initiate with the limited information and its
optimality under asynchronous settings is proved using theories from the
regular perturbed Markov processes. The policy was also empirically witnessed
to be robust under independently synchronous settings. Thirdly, in the spirit
of ``robust coloring'', we include an expected loss term in our objective
function to balance between the utilities and robustness. An optimal coloring
for this robust welfare optimization would be derived through a second-stage
MH-policy driven algorithm. Simulation experiments are given to showcase the
efficiency of our proposed strategy.Comment: 35 Page
Coalition Resilient Outcomes in Max k-Cut Games
We investigate strong Nash equilibria in the max k-cut game, where we are given an undirected edge-weighted graph together with a set {1,…,k} of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player v consists of the k colors. When players select a color they induce a k-coloring or simply a coloring. Given a coloring, the utility (or payoff) of a player u is the sum of the weights of the edges {u,v} incident to u, such that the color chosen by u is different from the one chosen by v. 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 k-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 [13]. 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 x-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 x. We prove that 1-local strong equilibria always exist. Finally, we show the existence of strong Nash equilibria in several interesting specific scenarios