The core of endo-status games and one-to-one ordinal preference games (Q5932219)

In the paper the status games are considered. There are \(n\)-player ordinal preference cooperative games in which the outcomes are orders of the players within a hierarchy. Here each coalition \(S\) has an exogenously given set \(\Pi_S\) of allocations of positions to its members that it can enforce. For such games a condition of ``balance'' on the set \(\Pi^*=\{\Pi_S\}\) is defined. It is shown that if \(\Pi^*\) is balanced then the core of the associated status game is nonempty, and conversely, if \(\Pi^*\) is not balanced and the game is exchangeable then can be find an instance where the strict core is empty. In addition, a more general class of one-to-one ordinal preference games is defined, which include both exo-status and endo-status games, as well as the class of restricted houseswapping games with ordinal preferences. For these games a condition of balancedness is defined.