Computing the Core-Center for the Following Game González-Díaz and Sánchez-Rodríguez introduced in 2007 the so-called Core-Center, a new and natural solution concept in Game Theory. It is basically defined as follows:

Core-Center: Let $(N,v)$ be a game with non-empty Core. The Core-Center of $(N,v)$ is defined as $\mathcal{K}(N,v)=\mathbb{E}[U(C)]$.

Where $\mathbb{E}[U(C)]$ is the result of endowing the Core with a uniform distribution and taking the expectation. In different words, $\mathbb{E}[U(C)]$ is the expected value of the core if all points in it are equally valuable. 
Consider the following game $(N,v)$ with $N=3$, $v(1,2)=0.75$, $v(1,3)=0.50$, $v(2,3)=0.25$, $v(N)=1$ and $0$ else. If I did it correctly, the Core-Center for this game should be: 
$\mathcal{K}(N,v)=\left(\frac{13}{24},\frac{7}{24},\frac{4}{24}\right)$.
I have two questions for this wonderful community:


*

*Could anyone prove or disprove my calculations for this example?

*Could anyone provide another $3$ or $4$ Player example and its Core-Center?
Please, show with detail how you made your computations!
Thank you all very much for your time.
EDIT: Just in case someone is interested, it turns out that the vector $\mathcal{K}(N,v)$ that I computed in my original question is not the Core Centre but the Alexia Value (Tijs, Borm, Lohmann and Quant, 2011), another Core-selector within the class of vectorial solution concepts in cooperative Game Theory.
 A: Thank you for being interested in the core-center topic. 
The core-center is the average of all the allocations in the core, so you can use integrals to have the solution. For three players it can
be done easily if you work with the projection and make the integrals in the two dimensional space. 
It is not true that it coincides with the average of the extreme points of the core for convex games. It coincides with
that average when there are some symmetries in the core. For special classes of games we have developed techniques to compute
the corecenter (airport and bankruptcy games). If you are interested you can revise, for instance, the paper González Díaz, J., Mirás Calvo, M.A.,
 Quinteiro Sandomingo, C., E. Sánchez (2016). Airport games: the core of an airport game and its center. Mathematical
Social Sciences, 82, 105-115. In that paper explicit formulae (with nice interpretations) are derived for the case of airport games.
In any case, if you want to compute the core-center of any 3 or 4 person balanced game you can use the interface web http://www.tuglabweb.co.nr/
 (after a free register). In your example, for game v(1,2)=0.75, v(1,3)=0.25, v(2,3)=0.5, v(N)=1, the core-center is (0.5556,0.3056,0.1389)
