My bibliography  Save this paper

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

## Author

Listed:
• Tom Quint
• Martin Shubik

## 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.

## Suggested Citation

• Tom Quint & Martin Shubik, 1997. "Games of Status and Wealth and Status Part II: A Game Theoretic Approach," Research in Economics 97-12-092e, Santa Fe Institute.
• Handle: RePEc:wop:safire:97-12-092e
as

File URL: http://www.santafe.edu/sfi/publications/Working-Papers/97-12-092E.html

## References listed on IDEAS

as
1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
3. Avner Shaked & Larry Samuelson & George J. Mailath, 1997. "Correlated equilibria and local interactions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 551-556.
4. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-157, January.
5. Stephen Morris, "undated". "Co-operation and Timing," Penn CARESS Working Papers b8d506ba7aa15345b602bb4eb, Penn Economics Department.
6. Sugden, Robert, 1995. "The coexistence of conventions," Journal of Economic Behavior & Organization, Elsevier, vol. 28(2), pages 241-256, October.
Full references (including those not matched with items on IDEAS)

### Keywords

Game theory; economics;

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wop:safire:97-12-092e. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel). General contact details of provider: http://edirc.repec.org/data/epstfus.html .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

We have no references for this item. You can help adding them by using this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.