The stability and efficiency of direct and star networks in a loan game

• Network formation game is applied to analyze loans in a small group.
• Players first form a network and then trade according to the Myerson value.
• Star networks and direct networks are both efficient and internally stable.
• But they may be externally unstable.

We analyze a loan game where identical lenders and identical borrowers first form a loan network by creating bilateral links and then trade in this network. To predict the outcome of the loan game, we make two important assumptions: (i) players trade and split the surplus according to the Myerson value in any given loan network, and (ii) certain networks–networks that are pairwise stable and/or efficient under the Myerson value–are more likely to be formed. Two basic network structures, direct networks and star networks, are common in reality and sometimes coexist in a loan market. We explain these phenomena by showing that, if the link cost of each trade is small enough, these two networks are both efficient and internally stable, but they are not necessarily externally stable.