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AbstractWe introduce a new class of generalized measures of relative deprivation. The class takes the form of a power mean of order p . A characteristic of the class is that depending on the value of the proximity-sensitive parameter p , the class is capable of accommodating both a decreasing weight (the case of 1 p > ), and an increasing weight (the case of (0,1) p ∈ ) accorded to given changes in the incomes of the individuals who are wealthier than the reference individual, depending on their proximity in the income distribution to the reference individual.
Abstract:We consider the concept of generalized Kolmogorov-Sinai entropy, where instead of the Shannon entropy function, we consider an arbitrary concave function defined on the unit interval, vanishing in the origin. Under mild assumptions on this function, we show that this isomorphism invariant is linearly dependent on the Kolmogorov-Sinai entropy.
From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal, on which a two-parameter family of bimodal interval maps exhibits periodic orbits and chaos. While the fixed point b corresponding to a Nash equilibrium of such map f is usually repelling, it is globally Cesàro attracting on the diagonal, that is,for every x in the minimal invariant interval. This solves a known open question whether there exists a nontrivial smooth map other than x → axe −x with centers of mass of all periodic orbits coinciding. We also study the dependence of the dynamics on the two parameters.
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