arXiv subjects

Xiaoguang Yang

Publications and source records attributed to Xiaoguang Yang.

23 records · Page 2Linked to original sources

arXiv2012

Complementary cooperation, minimal winning coalitions, and power indices

We introduce a new simple game, which is referred to as the complementary weighted multiple majority game (C-WMMG for short). C-WMMG models a basic cooperation rule, the complementary cooperation rule, and can be taken as a sister model of the famous weighted majority game (WMG for short). In this paper, we concentrate on the two dimensional C-WMMG. An interesting property of this case is that there are at most $n+1$ minimal winning coalitions (MWC for short), and they can be enumerated in time $O(n\log n)$, where $n$ is the number of players. This property guarantees that the two dimensional C-WMMG is more handleable than WMG. In particular, we prove that the main power indices, i.e. the Shapley-Shubik index, the Penrose-Banzhaf index, the Holler-Packel index, and the Deegan-Packel index, are all polynomially computable. To make a comparison with WMG, we know that it may have exponentially many MWCs, and none of the four power indices is polynomially computable (unless P=NP). Still for the two dimensional case, we show that local monotonicity holds for all of the four power indices. In WMG, this property is possessed by the Shapley-Shubik index and the Penrose-Banzhaf index, but not by the Holler-Packel index or the Deegan-Packel index. Since our model fits very well the cooperation and competition in team sports, we hope that it can be potentially applied in measuring the values of players in team sports, say help people give more objective ranking of NBA players and select MVPs, and consequently bring new insights into contest theory and the more general field of sports economics. It may also provide some interesting enlightenments into the design of non-additive voting mechanisms. Last but not least, the threshold version of C-WMMG is a generalization of WMG, and natural variants of it are closely related with the famous airport game and the stable marriage/roommates problem.

cs.GT↗

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↗

arXiv2007

The Mechanisms of Codon Reassignments in Mitochondrial Genetic Codes

Many cases of non-standard genetic codes are known in mitochondrial genomes. We carry out analysis of phylogeny and codon usage of organisms for which the complete mitochondrial genome is available, and we determine the most likely mechanism for codon reassignment in each case. Reassignment events can be classified according to the gain-loss framework. The gain represents the appearance of a new tRNA for the reassigned codon or the change of an existing tRNA such that it gains the ability to pair with the codon. The loss represents the deletion of a tRNA or the change in a tRNA so that it no longer translates the codon. One possible mechanism is Codon Disappearance, where the codon disappears from the genome prior to the gain and loss events. In the alternative mechanisms the codon does not disappear. In the Unassigned Codon mechanism, the loss occurs first, whereas in the Ambiguous Intermediate mechanism, the gain occurs first. Codon usage analysis gives clear evidence of cases where the codon disappeared at the point of the reassignment and also cases where it did not disappear. Codon disappearance is the probable explanation for stop to sense reassignments and a small number of reassignments of sense codons. However, the majority of sense to sense reassignments cannot be explained by codon disappearance. In the latter cases, by analysis of the presence or absence of tRNAs in the genome and of the changes in tRNA sequences, it is sometimes possible to distinguish between the Unassigned Codon and Ambiguous Intermediate mechanisms. We emphasize that not all reassignments follow the same scenario and that it is necessary to consider the details of each case carefully.

q-bio.PE↗