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“When is fair sharing optimal?”

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We consider revenue division problems in iterative settings. In our model, a group of agents has some initial resources, used in order to generate revenue. At every time-step, the revenue shares received at time t are agent resources at time t+1, and the game is repeated. The key issue here is that the way resources are shared has a dramatic effect on long-term social welfare, so in order to maximize individual long-term revenue one must consider the welfare of others, a behaviour not captured by other models of cooperation among economic agents. Our work focuses on a setting where agents must agree on a single revenue sharing contract at time 0, and continue using that contract indefinitely. We identify conditions that ensure that no agent regrets choosing the initial agreement, namely that the utility function is concave and homogeneous of degree greater or equal to 1. We apply our results to some families of utility functions, and discuss their implication in these domains. Finally, we contrast our proposed revenue sharing scheme with the well-known core revenue sharing scheme for network flow games. We show that our proposed method better rewards agents with larger initial edge capacities; this is rather unlike the canonical core revenue sharing scheme, which pays only the edges in the minimum cut of the graph.

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