arXiv subjects

Zhigang Cao

Publications and source records attributed to Zhigang Cao.

21 records · Page 2Linked to original sources

arXiv2012

Rebels Lead to the Doctrine of the Mean: Opinion Dynamic in a Heterogeneous DeGroot Model

We study an extension of the DeGroot model where part of the players may be rebels. The updating rule for rebels is quite different with that of normal players (which are referred to as conformists): at each step a rebel first takes the opposite value of the weighted average of her neighbors' opinions, i.e. 1 minus that average (the opinion space is assumed to be [0,1] as usual), and then updates her opinion by taking another weighted average between that value and her own opinion in the last round. We find that the effect of rebels is rather significant: as long as there is at least one rebel in every closed and strongly connected group, under very weak conditions, the opinion of each player in the whole society will eventually tend to 0.5.

cs.SI↗

arXiv2012

A note on anti-coordination and social interactions

This note confirms a conjecture of [Bramoullé, Anti-coordination and social interactions, Games and Economic Behavior, 58, 2007: 30-49]. The problem, which we name the maximum independent cut problem, is a restricted version of the MAX-CUT problem, requiring one side of the cut to be an independent set. We show that the maximum independent cut problem does not admit any polynomial time algorithm with approximation ratio better than $n^{1-ε}$, where $n$ is the number of nodes, and $ε$ arbitrarily small, unless P=NP. For the rather special case where each node has a degree of at most four, the problem is still MAXSNP-hard.

cs.GT↗

arXiv2009

Selfish Bin Covering

In this paper, we address the selfish bin covering problem, which is greatly related both to the bin covering problem, and to the weighted majority game. What we mainly concern is how much the lack of coordination harms the social welfare. Besides the standard PoA and PoS, which are based on Nash equilibrium, we also take into account the strong Nash equilibrium, and several other new equilibria. For each equilibrium, the corresponding PoA and PoS are given, and the problems of computing an arbitrary equilibrium, as well as approximating the best one, are also considered.

cs.GT↗