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Partial Altruism is Worse than Complete Selfishness in Nonatomic Congestion Games

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Document pages: 15 pages

Abstract: We seek to understand the fundamental mathematics governinginfrastructure-scale interactions between humans and machines, particularlywhen the machines intended purpose is to influence and optimize the behaviorof the humans. To that end, this paper investigates the worst-case congestionthat can arise in nonatomic network congestion games when a fraction of thetraffic is completely altruistic (e.g., benevolent self-driving cars) and theremainder is completely selfish (e.g., human commuters). We study theworst-case harm of altruism in such scenarios in terms of the perversity index,or the worst-case equilibrium congestion cost resulting from the presence ofaltruistic traffic, relative to the congestion cost which would result if alltraffic were selfish. We derive a tight bound on the perversity index for theclass of series-parallel network congestion games with convex latencyfunctions, and show three facts: First, the harm of altruism is maximized whenexactly half of the traffic is altruistic, but it gracefully vanishes when thefraction of altruistic traffic approaches either 0 or 1. Second, we show thatthe harm of altruism is linearly increasing in a natural measure of the "steepness " of network latency functions. Finally, we show that for anynontrivial fraction of altruistic traffic, the harm of altruism exceeds theprice of anarchy associated with all-selfish traffic: in a sense, partialaltruism is worse than complete selfishness.

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