The Game Model Analysis between the Individual and the Group

This paper analyses the game model between the individual and the group that has the characteristics of Stackelberg model in traditional game theory and replicator dynamic model in evolutionary game theory. In the first phase of game, the bounded rationality group players adopt the replicator dynamic behavior. Secondly, the full rationality individual player decides the own response function by the strategies distribution of group players. The shortsighted individual player will take the risk-dominant strategy. This model has some unique characteristics.

Group control for procedural rules:parameterized complexity and consecutive domains

We consider GROUP CONTROL BY ADDING INDIVIDUALS(GCAI)in the setting of group identification for two procedural rules-the consensus-start-respecting rule and the liberal-start-respecting rule.It is known that GCAI for both rules are NP-hard,but whether they are fixed-parameter tractable with respect to the number of distinguished individuals remained open.We resolve both open problems in the affirmative.In addition,we strengthen the NP-hardness of GCAI by showing that,with respect to the natural parameter the number of added individuals,GCAI for both rules are W[2]-hard.Notably,the W[2]-hardness for the liberal-startrespecting rule holds even when restricted to a very special case where the qualifications of individuals satisfy the so-called consecutive ones property.However,for the consensus-startrespecting rule,the problem becomes polynomial-time solvable in this special case.We also study a dual restriction where the disqualifications of individuals fulfill the consecutive ones property,and show that under this restriction GCAI for both rules turn out to be polynomial-time solvable.Our reductions for showing W[2]-hardness also imply several algorithmic lowerbounds.

Rescuing the intracluster medium of NGC 5813

We use recent X-ray observations of the intracluster medium （ICM） of the galaxy group NGC 5813 to confront theoretical studies of ICM thermal evolution with the newly derived ICM prop- erties. We argue that the ICM of the cooling flow in the galaxy group NGC 5813 is more likely to be heated by mixing of post-shock gas from jets residing in hot bubbles with the ICM, than by shocks or turbulent- heating. Shocks thermalize only a small fraction of their energy in the inner regions of the cooling flow; in order to adequately heat the inner part of the ICM, they would overheat the outer regions by a large factor, leading to its ejection from the group. Heating by mixing, which was found to be much more efficient than turbulent-heating and shocks-heating, hence, rescues the outer ICM of NGC 5813 from its predestined fate according to cooling flow feedback scenarios that are based on heating by shocks.