Networks with nonordered partitioning of players: stability and efficiency with neighborhood-influenced cost topology

Abstract

This paper highlights the incentives of individuals to add or sever links in shaping stable and efficient networks when the society is partitioned into groups. In terms of the group partitioning, the players may unequally pay for the link connecting them. To be precise, the cost a player pays for her direct connection is determined by the composition of her neighborhood. In particular, the more members of a group the player has in her neighborhood, the less the average cost of a link is within this group. The main contributions of our paper lie in a detailed analysis of conditions under which particular network configurations—complete network, majority complete network, and complete bipartite network—achieve stability and unique efficiency. The paper examines the impact of the distribution of players across different groups on the stability and efficiency of these networks. We prove that majority complete networks can never be uniquely efficient when there is an equal number of players between two groups, but if they are efficient, the other two types of structures also attain efficiency. Moreover, under certain distributions of players, the unique stability of majority complete networks implies their unique efficiency.