Dynamics of mergers, bifurcation and chaos: A new framework

Abstract

This paper is motivated by a gap in the existing literature on mergers since no attempt has been successfully made to consider endogenous multiple mergers that trigger reciprocal mergers, which in turn fuel further mergers and the process continues ad infinitum. The precise contribution of this paper is to model endogenous mergers such that groups of firms simultaneously decide whether to merge, or not, when their rivals decide to merge. We call this type of mergers endogenously-driven-reciprocal (EDR) mergers. We develop a framework to examine endogenously-driven-reciprocal mergers to establish that fluctuations in merger activities can be explained in a purely endogenous manner, without resorting to any ad hoc stochastic specifications. Our principal finding therefore is that complicated random looking sequences of mergers and merger waves might even prevail in deterministic models, under a reasonable condition. We then extend the model to include U-shaped cost functions and non-pecuniary goals of managers to establish the existence of multiple merger equilibria, which can cause a serious indeterminacy, historical lock-in and path dependency in the context of endogenously-driven-reciprocal mergers. We further show how multiplicity of merger equilibrium and bifurcations of these equilibria can lend fragility to the industrial system.