Exact stability and its applications to strong solvability
The author analyzes the core of a strategic game. He defines two new kinds of solutions, the exact core and biexact core. The \(n\)-person game is defined in normal form; the set of strategies of each player, the set of alternatives (finite set of real numbers), and a function mapping set of strategies onto the set of alternatives (the outcome function) are given. An alternative \(a\) is called \textit{exactly dominated} if some fixed coalition \(S\) is able to improve \(a\) in each case when \(a\) occurs. An alternative \(a\) is biexactly dominated when either \(S\) or \(S^C\) (complement of \(S\)) can improve \(a\). The exact core and biexact core are defined in the common manner. The game is said to be exact stable if it has a nonempty exact core, the same takes place for biexact stable games. The author applies the well-known definition of subadditivity and a less known one of tightness to derive conditions of exact and biexact stability. These notions may be examined to some specific games, for example, the author considers the ractangular game, that is a game for which the inverse image of every alternative \(a\) is a direct product. He proves that a nontrivial game is exact if and only if it is a one-player game. Various examples illustrate the results of the paper.
scientific article; zbMATH DE number 1452731
scientific article