# Games of Status and Wealth and Status Part II: A Game Theoretic Approach

*Tom Quint* and
*Martin Shubik*

Research in Economics from Santa Fe Institute

**Abstract:**
In Part I we provide a heuristic discussion of the motivation for the investigation of games of status. Here we confine our remarks to several alternative formulations of games of status and to exploring the relationship between these games and the class of simple games, in part using the results from Quint and Shubik (1997). A Game of Status is an $n$-player cooperative game in which the outcomes are orderings of the players. Notationally, suppose the player set is $N = \{1,...,n\}$. Then, outcomes are represented by permutations of $N$, where if $I$ occurs at position $j$ in the permutation, this is taken to mean that player $I$ attains the $j$th best position. For example, if $n=4$, the outcome in which player 3 comes in ``first place,'' player 1 comes in ``second place,'' player 4 comes in ``third place,'' and player 2 is ``last'' is represented by the permutation [3 1 4 2].$^1$ Let $r_{ij}$ denote the payoff that player $I$ obtains if he ends up in the $j$th position. We assume that $j \greaterthan k$ implies $r_{ij} \greaterthanor= r_{ik}$ for all $I$, i.e. players always desire to be placed as far ``up'' in the hierarchy as possible. Alternatively, a {\bf Game of Status with Ties} is a variant in which outcomes are allowed in which players ``tie'' for positions. For example, an outcome in the $n=4$ case could now be [3 1$T$4 2], which represents the situation in which player 3 again comes in ``first place'' and 2 again comes in ``last,'' but now players 1 and 4 come in tied for second place. In our current analysis, we consider only Games of Status without Ties, as we feel these should be eaiser to analyze. $^1$For now, we use the ``vector notation'' for the permutation. Later on, when we formalize the model, we will write this using a permutation matrix.

**Keywords:** Game theory; economics (search for similar items in EconPapers)

**Date:** 1997-12

**References:** Add references at CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

http://www.santafe.edu/sfi/publications/Working-Papers/97-12-092E.html (text/html)

**Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://www.santafe.edu/sfi/publications/Working-Papers/97-12-092E.html [301 Moved Permanently]--> https://www.santafe.edu/sfi/publications/Working-Papers/97-12-092E.html)**

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:wop:safire:97-12-092e

Access Statistics for this paper

More papers in Research in Economics from Santa Fe Institute Contact information at EDIRC.

Bibliographic data for series maintained by Thomas Krichel ().