# Tagged Questions

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### To what equal constant in the Gibbs lemma

The Gibbs lemma is broadly used in games theory and in mathematical economics (optimal distributions of resourses, Cournot competition e.t.c.). Here it is: Lemma (Gibbs). $f_1,f_2,\ldots,f_n$ be ...
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### Equitable division of a contiguous resource

I have come across the following result regarding equitable division of a resource, which is a simple and immediate consequence of linear programming complementarity (in the infinite-dimensional ...
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### Optimal tax Rate

Assume you have two countries A and B, with a tax rates $T_A$ and $T_B$. The tax is redistributed to each people equally. Hence if you live in A and you make $I$ as income then you will finally ...
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### Fairest way to choose gifts

Suppose that a parent brings home from a trip $2n$ gifts of roughly equal value for his/her two children. The children get to choose one at a time which gifts they want. What is the fairest way to do ...
I'm interested in the solution to the following problem: I have initial capital $C$ which I can invest into $M$ classes of resources, each unit of a class $m_i$ matures at time $t_i$, has a return of ...
The supermodularity means for every $x'>x$ and $y'>y$, $$f(x',y') + f(x,y) > f(x',y) + f(x,y').$$ Suppose $f$ and $g$ are supermodular, non-negative and increasing in both arguments. Is the ...