Operations research games: A survey

Abstract

Optimization problems, allocation problems, cooperative games, 91-02, 91A12, 90B30, 90B35, 90B10, 90B05,

Insights into the Nucleolus of the Assignment Game

“…The interpretation of expression (3) is the following: the largest same amount that can be transferred from players in S to players in T with respect to the core 3 The lexicographic order ≥ lex on R d is defined in the following way: x ≥ lex y, where x, y ∈ R d , if x = y or if there exists 1 ≤ t ≤ d such that x k = y k for all 1 ≤ k < t and x t > y t .…”

“…Combinatorial optimization games, also known as OR-games (Curiel, 1997;Borm et al, 2001) analyze cooperative situations where the worth of a coalition of players is the optimal result of a well-known operations research problem. Among others we mention linear production games (Owen, 1975), minimum cost spanning tree games (Granot and Huberman, 1981) Matching in graphs are combinatorial optimization problems.…”

Minimum cost spanning tree games and spillover stability

“…When multiple players are involved in a particular OR problem, they do not only face the task of optimising some objective function, they also have to allocate the proceeds of cooperation in a fair way (see Borm et al 2001 for a survey). This article focuses on one such problem, the minimum cost spanning tree (mcst) problem as introduced by Claus and Kleitman (1973).…”

Production-inventory games: A new class of totally balanced combinatorial optimization games

“…Other operations research games are studied as well. For a clear and detailed presentation of operations research games (including inventory games) we refer to Borm et al (2001). We are not aware of any reference in the literature of centralization in inventory models that analyzes inventory models for which optimal operation is only defined implicitly as the optimal solution of a combinatorial problem (as it is the case in the discrete review model in this paper).…”