Solving bargaining games by differential equations.

*(English)*Zbl 0719.90103Summary: “Solving games by differential equations” was the title of a paper by G. W. Brown and J. von Neumann [in: Contrib. Theory of Games, I, Ann. Math. Stud. 24, 73-79 (1950; Zbl 0041.255)]. The idea of solving bargaining games by differential equations goes back to H. Raiffa [in: Contrib. Theory of Games, II, Ann. Math. Stud. 28, 361-387 (1953; Zbl 0050.145)]. The present paper starts with a solution \(\phi\) of a bargaining game and constructs, by means of solving a set of differential equations, a new solution \(C\phi\), the continuation of \(\phi\). A property is called hereditary when it holds for \(C\phi\) whenever it holds for \(\phi\). Hereditary properties and properties of \(C\phi\) in relation to properties of \(\phi\) are studied. The paper includes a number of open problems.

##### MSC:

91A12 | Cooperative games |