Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Complexity of Agreement   A celebrated 1976 theorem of Aumann asserts that honest, rational Bayesian
agents with common priors will never "agree to disagree": if their opinions
about any topic are common knowledge, then those opinions must be equal.
Economists have written numerous papers examining the assumptions behind this
theorem. But two key questions went unaddressed: first, can the agents reach
agreement after a conversation of reasonable length? Second, can the
computations needed for that conversation be performed efficiently? This paper
answers both questions in the affirmative, thereby strengthening Aumann's
original conclusion.
  We first show that, for two agents with a common prior to agree within
epsilon about the expectation of a [0,1] variable with high probability over
their prior, it suffices for them to exchange order 1/epsilon^2 bits. This
bound is completely independent of the number of bits n of relevant knowledge
that the agents have. We then extend the bound to three or more agents; and we
give an example where the economists' "standard protocol" (which consists of
repeatedly announcing one's current expectation) nearly saturates the bound,
while a new "attenuated protocol" does better. Finally, we give a protocol that
would cause two Bayesians to agree within epsilon after exchanging order
1/epsilon^2 messages, and that can be simulated by agents with limited
computational resources. By this we mean that, after examining the agents'
knowledge and a transcript of their conversation, no one would be able to
distinguish the agents from perfect Bayesians. The time used by the simulation
procedure is exponential in 1/epsilon^6 but not in n.

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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin