Games of Status Part I: Modeling Considerations

Many of the applications of game theory have been to economics where the individuals under study are assumed to be maximizing profits or “utility” or some other conventional economic goal of “status.” Loosely stated we think of status as one’s position in a society compared with others, often inferred via title such as “king,” “doctor,” or “number 1 heavy-weight contender.” Status, rank, or position in society may or may not be formally granted. Thus the status of a guru or wise man may be the outcome of a general (but not formal) growth of reputation and respect. In contrast, the status of a corporate president or admiral is primarily determined by a formal pecking order in the institution to which he or she belongs. The rank of a player or team within a sport is determined by a series of formal competitive interchanges, as is the standing of a student in an examination system which lays stress on prizes and position for those who emerge first. We believe that there is a distinction between status and wealth, with many instances in which one is traded for the other. History is replete with stories of rich men buying themselves knighthoods. In local and national politics, judgeships and ambassadorial appointments may be obtained by those who make the appropriate sidepayments in forms such as campaign contributions. The Austrian and Brazilian monarchies used the status attraction of minor titles as a source of revenue. Prior to the French Revolution, Schama (1989, 117) notes “If one had the funds it was possible to buy an entitling office, like the ‘secretaire du roi.’ No less than fifteen hundred nobles joined the order through the Paris Chamber in this way.” Soon after the revolution the value of previous status dropped in a drastic manner. Some years ago, one of us proposed the study of games of status where the payoff consisted only of the rank ordering of the players (Shubik, 1971). The paper written at that time suggested a way of going from a standard sidepayment game characteristic function to a “game of status.” On reconsidering the analysis of status, a more natural approach is to treat the definition of the characteristic function of an $n$-person game of a status as a primitive concept. Furthermore, it appears that there is a reasonably straightforward way to use sidepayment and no-sidepayment game theory to analyze tradeoffs between money (wealth) and status. In the two parts of this paper we divide difficulties. The first part is devoted to providing the motivation for the modeling and analysis of status games. We also present a discussion of the benefits to be derived from and the difficulties encountered in formulating mathematical models which depend on an intermix of social, political, and economic phenomena. In the second part we present our formal models and analysis. These include models in which only status is present, as well as constructs which include both wealth and status. There is a third related paper where we deal with the class of “general ordinal preferences” games, of which status games are a special class (Quint and Shubik, 1977).