Equal Share Analysis for Location Games

Abstract

This is a solution concept for location games where the utility functions of the players are strictly decreasing with the Euclidean distance from their ideal positions: a player i is defined to be stronger than player j, iff more ideal positions of players are nearer to i than to j.

Solutions are characterized by dominance: A point y dominates a point x with respect to a coalition C, iff for any player j ∈ C who disimproves in y there is a player i ∈ C such that (1) i is not weaker than j; (2) j is nearer to x than i; (3) i prefers y to x. The basic idea of the concept is that a player i who is not weaker than another player j should be able to urge player j to deviate from a solution point which is nearer to j than to i as long as i and j are in coalition.

Experimental results show that the quality of the strength concept is comparable to that of the aspiration adjustment concept (ALBERS, ALBERS, 1983) which can be measured by a modification of the ‘measure of quality’ by SELTEN and KRISCHKER (1982). Other solution concepts like the competitive solution (McKELVEY, ORDESHOOK, WINER, 1978) lead to essentially worse predictions.