Abstract
A sharing game is a very simple device for partially reconciling an organization’s goal with the interests of its members. Each member chooses an action, bears its cost, and receives a share of the revenue which the members’ actions generate. A (pure-strategy) equilibrium of the game may be inefficient: surplus (revenue minus the sum of costs) may be less than maximal. In a previous paper, we found that for a wide class of reward functions, no one squanders at an inefficient equilibrium (spends more than at an efficient profile) if the revenue function has a complementarity property. In the present paper, we examine the “opposite” of the complementarity property (Substitutes) and we study a class of finite games where squandering equilibria indeed occur if Substitutes holds strongly enough. Squandering equilibria play a key role when one traces the effect of technological improvement on a sharing game’s surplus shortfall. We then turn to the question of choice among reward functions in a principal/agents setting. We find that if we again assume complementarity then strong conclusions can be reached about the reward functions preferred by “society”, by the players (agents), and by the principal.
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Acknowledgment
Courtney was partially supported by NSF VIGRE grant DMS-0602242 to the Department of Mathematics, University of Iowa.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Courtney, D., Marschak, T. Inefficiency and complementarity in sharing games. Rev Econ Design 13, 7–43 (2009). https://doi.org/10.1007/s10058-008-0065-4
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DOI: https://doi.org/10.1007/s10058-008-0065-4