{'fraction_non_alphanumeric': 0.018226002430133656, 'fraction_numerical': 0.002430133657351154, 'mean_word_length': 5.149253731343284, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Costs of Competition in General Networks

In this paper, we present an analysis of competition in congested networks. We consider the problem of routing flows across multiple paths controlled by serial and parallel service providers that charge prices for transmission. We study the efficiency properties of oligopoly equilibria. Our measure of efficiency is the difference between users’ willingness to pay and delay costs. Under the assumption that delay costs without transmission (latencies at zero) are equal to zero, we show that, irrespective of the number of serial and parallel providers, the efficiency of oligopoly equilibria in pure strategies is no worse than 1/2 times the efficiency of the social optimum. When latencies at zero can be positive, the efficiency of oligopoly equilibria can be arbitrarily low.