When Rationality Fails: Unstable exchange networks with empty cores

Power differences within networks can arise when some positions have many alternative transaction partners who themselves have few alternatives. Recent social psychological models developed to predict power in these situations have assumed that stable transaction patterns will emerge in these networks. These models depend on the assumption that stable exchange patterns will develop. Using the game theoretic concept of the core, we show that in some networks, stable patterns should not emerge. Who transacts with whom and terms of the transaction should never reach equilibrium. Three types of instability are distinguished in this article: unreliability, insecurity, and variety. These types of instability are affected by the existence and size of the core. Experiments and simulations comparing networks with and without core solutions and with different-sized cores show that the predicted differences exist.