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

We consider status games [Quint, Thomas and Martin Shubik, 'Games of Status ', technical report, University of Nevada and Yale University (1999)]. Thes e are n-player ordinal preference cooperative games in which the outcomes a re orderings of the players within a hierarchy. In particular we study 'end o-status' games. Here each coalition S has an exogenously given set Pi (S) of allocations of positions to its members that it can enforce. For such ga mes, we define a condition of 'balance' on the set Pi* - {Pi (S)}(S subset of or equal toN). If Pi* is balanced, the core of the associated status gam e is nonempty. Conversely, if Pi* is not balanced, and the game is 'exchang eable', we can find an instance where the strict core is empty. Finally, we define a more general class of one-to-one ordinal preference (OOP) games, which include both 'exo-status' and 'endo-status' games [Quint, T., Shubik, M., 1999. Games of status. Technical report, University of Nevada and Yale University], as well as the class of restricted houseswapping games with o rdinal preferences (RHGOPs) [Quint, T., 1997. Restricted houseswapping game s. Journal of Mathematical Economics 27, 451-470]. We again define a condit ion of 'balancedness' for these games, which (a) guarantees core existence, (b) reduces to the above condition for status games, and (c) reduces to 'w eak balancedness' [Quint, T., 1997. Restricted houseswapping games. Journal of Mathematical Economics 27, 451-470] in the case of RHGOPs. (C) 2001 Els evier Science B.V. All rights reserved.