Understanding di usion processes is key to market strategies as well as innovation and sustainability policies. In promoting new products and technologies, firms and governments need to understand the conditions favouring successful spread of these products. We propose a generic di usion model based on percolation theory. Our reference is a new product di usion in a social network through word-of-mouth. Given that consumers di er in their reservation prices, a critical price exists that defines

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... a phase transition from a no-di usion to a di usion regime. As consumer surplus is maximised just below a product's critical price, one can systematically compare the economic e iciency of network structures by investigating their critical price. Networks with low clustering were the most e icient, because clustering leads to redundant information flows hampering e ective product di usion. We further showed that the more equal a society, the more e icient the di usion process. percolation process (Solomon et al. ). The acceptance threshold of a node in the percolation model describes the idea of consumers' reservation price well. Starting from the generic assumption that consumers di er in their reservation prices, we showed that network structures supporting the speed of di usion are not necessarily those that lead to a greater extent of di usion and vice versa. In particular, we showed that smallworld networks, which exhibit short path lengths and high clustering (Watts & Strogatz ), lead to fast but o en only limited di usion compared to fully random networks, which exhibit short path lengths and low clustering. The reason for limited di usion in small-world networks is the redundancy in information spreading due to clustering. Accordingly, consumer welfare is much lower in small-world networks than in random networks for a wide ranges of prices. . Our main contributions are threefold. First, we introduce the standard percolation theory as it has already been applied before to the topic of innovation di usion in social networks (Solomon et al. ; Hohnisch et al. ; Cantono & Silverberg ), and translate the percolation model into an explicit welfare-theoretical framework in which the ine iciency of networks can be expressed by unfulfilled consumer surplus. In this framework, the network e iciency is indicated by the critical price below which di usion becomes complete. Second, we show that for a standard linear demand curve with uniformly distributed reservation prices, the ine iciency of social networks is a function of its clustering: i.e., the higher the degree of clustering ("friends-of-friendsbeing-friends"), the less e icient a social network is in di using an innovation. Our finding that low clustering supports a wide di usion therefore supplements the insight that a short average path length supports a fast di usion (Watts & Strogatz ; Cowan & Jonard ). Third, the detrimental welfare e ects of clustering, in turn, decline for less dispersed distributions of consumers' preferences: as preferences become more alike, so does the critical price below which full di usion occurs, for di erent network topologies.