Profitability of a merger on networks

In this paper, we examine the profitability of a merger when agents interact on a network. We assume that the value function is size-dependent, i.e. the value of a coalition does not depend on the identities of the coalition but only on each size of its components. Under the assumption that the third difference of the value function with respect to the size of each component is nonnegative, which is a weaker condition of increasing complementarity by Segal in 2003, we show that a merger of any subset of agents cannot be profitable if the underlying network is cycle-complete.