{'fraction_non_alphanumeric': 0.016666666666666666, 'fraction_numerical': 0.0, 'mean_word_length': 5.908045977011494, '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}}
Manipulation of Preferences and Relative Utilitarianism

Given n agents with von Neumann-Morgenstern utility functions who wish to divide m commodities, consider the n-person noncooperative game with strategies consisting of concave, increasing von Neumann-Morgenstern utility functions, and whose outcomes are the relative utilitarian solution. It is shown that any constrained equal-income competitive equilibrium allocation for the true utilities is a Nash equilibrium outcome for the noncooperative game. Conditions are presented under which these are the only pure strategy equilibrium outcomes.