125 research outputs found
Strictly monotonic multidimensional sequences and stable sets in pillage games
Let have size . We show that
there are distinct points such that for
each , the coordinate sequence is strictly
increasing, strictly decreasing, or constant, and that this bound on is
best possible. This is analogous to the \erdos-Szekeres theorem on monotonic
sequences in . We apply these results to bound the size of a stable set
in a pillage game. We also prove a theorem of independent combinatorial
interest. Suppose is a set of points in
such that the set of pairs of points not sharing a coordinate is
precisely . We show that , and
that this bound is best possible
Asymmetric majority pillage games
This paper studies pillage games (Jordan in J Econ Theory 131.1:26-44, 2006, “Pillage and property”), which are well suited to modelling unstructured power contests. To enable empirical test of pillage games’ predictions, it relaxes a symmetry assumption that agents’ intrinsic contributions to a coalition’s power is identical. In the three-agent game studied: (i) only eight configurations are possible for the core, which contains at most six allocations; (ii) for each core configuration, the stable set is either unique or fails to exist; (iii) the linear power function creates a tension between a stable set’s existence and the interiority of its allocations, so that only special cases contain strictly interior allocations. Our analysis suggests that non-linear power functions may offer better empirical tests of pillage game theory
Sufficient conditions for unique stable sets in three agent pillage games
Pillage games (Jordan, 2006a) have two features that make them richer than cooperative games in either characteristic or partition function form: they allow power externalities between coalitions; they allow resources to contribute to coalitions’ power as well as to their utility. Extending von Neumann and Morgenstern’s analysis of three agent games in characteristic function form to anonymous pillage games, we characterise the core for any number of agents; for three agents, all anonymous pillage games with an empty core represent the same dominance relation. When a stable set exists, and the game also satisfies a continuity and a responsiveness axiom, it is unique and contains no more than 15 elements, a tight bound. By contrast, stable sets in three agent games in characteristic or partition function form may not be unique, and may contain continua. Finally, we provide an algorithm for computing the stable set, and can easily decide non-existence. Thus, in addition to offering attractive modelling possibilities, pillage games seem well behaved and analytically tractable, overcoming a difficulty that has long impeded use of cooperative game theory’s flexibility
Efficient sets are small
AbstractWe introduce efficient sets, a class of sets in Rp in which, in each set, no element is greater in all dimensions than any other. Neither differentiability nor continuity is required of such sets, which include: level sets of utility functions, quasi-indifference classes associated with a preference relation not given by a utility function, mean–variance frontiers, production possibility frontiers, and Pareto efficient sets. By Lebesgue’s density theorem, efficient sets have p-dimensional measure zero. As Lebesgue measure provides an imprecise description of small sets, we then prove the stronger result that each efficient set in Rp has Hausdorff dimension at most p−1. This may exceed its topological dimension, with the two notions becoming equivalent for smooth sets. We apply these results to stable sets in multi-good pillage games: for n agents and m goods, stable sets have dimension at most m(n−1)−1. This implies, and is much stronger than, the result that stable sets have m(n−1)-dimensional measure zero, as conjectured by Jordan
Sandspur, Vol 99 No 10, October 21, 1992
Rollins College student newspaper, written by the students and published at Rollins College. The Sandspur started as a literary journal.https://stars.library.ucf.edu/cfm-sandspur/2744/thumbnail.jp
Portland Daily Press: May 23,1885
https://digitalmaine.com/pdp_1885/1018/thumbnail.jp
The Advocate - Feb. 22, 1962
Original title (1951-1987)--The Advocate: official publication of the Archdiocese of Newark (N.J.)
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