A dynamic solution in \(N\)-person cooperative game theory (Q799596)

Given a superadditive side-payment game \(v:2^ N\backslash\{\Phi\}\to {\mathbb{R}}\) with a finite player set \(N\), a dynamic cooperative process of payoff allocation is constructed. At each step one player proposes his chosen coalition and a payoff allocation within the coalition. Players take turns in making such proposals over \(M\) steps. By working backward (à la dynamic programming) the proposal of each player can be found: Player \(j\) must, for a coalition \(C\) that contains \(j\), offer each \(i\in C\) at least as much as in any subsequent proposal made by \(i\), given the constraint of \(v(C)\). A dynamic solution is defined for a sequence of such processes as \(M\to\infty\). Several convergence results and experimental results are obtained.