I explore the competitive effects of on-net/off-net differentiation in a market with two asymmetric networks by combining the literature on on-net/off-net differentiation with research on costly consumer search in an agent-based simulation model. All consumers in the market are subscribed to one of two networks, whereby, initially, clusters of subscribers to network B exist. A priori, consumers lack information on the market shares of both network and, hence, have to engage in costly fixed-sample search. With respect to the extent of search costs, I distinguish between three types of consumers: (1) fully informed consumers (FICs) have non-positive search costs and, accordingly, are always perfectly informed about networks' market shares; (2) partly informed consumers (PICs) have moderate search costs, which allow them to observe market shares within a circular sensing field; and (3) locally informed consumers (LICs) have high search costs and, hence, only observe market shares among their immediate eight neighbours. Irrespective of their type, consumers maximize their expected utility by subscribing to the network offering the lowest expected cost for a call to a random consumer. The results of a systematic variation of the key parameters of the model show that the larger network's probability to increase its market share or to corner the market is negatively affected by the fraction of PICs and LICs, whereas it is positively affected by PICs's sensing radius, the larger network's initial market share, and the number of clusters. The introduction of calling clubs reveals that the probability of calling a friend inflicts a negative effect while the size of the calling clubs has a positive effect. These findings highlight the pivotal role of the amount of information available to consumers for the distribution of market shares.