Circumventing the Price of Anarchy
SIAM Journal on Computing(2013)
摘要
Many natural games have a dramatic difference between the
quality of their best and worst Nash equilibria, even in pure
strategies. Yet, nearly all results to date on dynamics in games show only
convergence to some equilibrium, especially within a
polynomial number of steps. In this work we initiate a theory of how
well-motivated multiagent dynamics can make use of global
information about the game---which might be common knowledge or
injected into the system by a helpful central agency---and show that
in a wide range of interesting games this can allow the dynamics to
quickly reach (within a polynomial number of steps) states of cost
comparable to the best Nash equilibrium.
We present several natural models for dynamics that can use such
additional information and analyze their ability to reach low-cost
states for two important and widely studied classes of
potential games: network design with fair cost-sharing and
party affiliation games (which include consensus and cut games). From
the perspective of a central agency, our work can be viewed as
analyzing how a public service advertising campaign can help “nudge” behavior into a good state, when players cannot be expected to all
blindly follow along but instead view the information as an additional
input into their dynamics. We show that in many cases, this
additional information is sufficient for natural dynamics to quickly
reach states of cost comparable to the best Nash equilibrium of the game.
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关键词
game theory,dynamics in games,potential games,quality of equilibria,68Q25,68T05,91A06,91A40
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