%0 Journal Article
%T A Value for Games Defined on Graphs
%A N&#233
%A stor Bravo
%J Applied Mathematics
%P 331-348
%@ 2152-7393
%D 2024
%I Scientific Research Publishing
%R 10.4236/am.2024.155020
%X Given a graph <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>g</mi><mo>=</mo><mrow><mo>(</mo>
   <mrow>
    <mi>V</mi><mo>,</mo><mi>A</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>, we define a space of subgraphs <i>M</i> with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.
%K Graph Theory
%K Values for Graphs
%K Cooperation Games
%K Potential Function
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=133105