By Richard Durrett
This publication may be of curiosity to scholars of arithmetic.
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Extra resources for Brownian motion and martingales in analysis
Prior to contract, each consumer solicits price quotations from each entrepreneur. Having compared the prices, D1 decides to buy from E1 and D2 from E2; this is illustrated by the pattern of thick lines representing the product flows. It should be noted that under competition the network of information flows is far more dense than the network of product flows. This is because product only flows when a contract has been agreed, while information flows every time a potential contact is investigated.
The leader may expect the individual to join his group, and possibly pay a membership fee, in return for receiving this service. In a private enterprise economy, entrepreneurs compete with each other for custom. Similarly, leaders of rival groups compete for members and also to gain influence for their views. As a result, both physical networks and social networks develop a multiplicity of competing hubs. Ordinary members use these hubs as gateways to the rest of the network. In effect, relationships between ordinary members of the network are mediated by the entrepreneurs from whom they buy, the leaders of the groups to which they belong and the hubs through which they travel and through which the goods they buy are consigned to their homes.
Outward-looking networks confer reputations on entrepreneurs (and others) which facilitate the intermediation of trade (and the advancement of the division of labour as a whole). These reputations create one-sided trust, which allows the entrepreneur to deal with other people who place themselves in his hands. Ordinary networks that promote shared interests also confer reputations on their members through emotional bonding, but these reputations are more localized, and in inwardlooking networks the obligations that members accept are limited to fellow members of the group.