Robert Aumann

Robert Aumann is a German-born Israeli-American mathematician and game theorist, long at the Hebrew University of Jerusalem, who shared the 2005 Nobel Memorial Prize in Economic Sciences. His 1976 paper "Agreeing to Disagree" gave a precise model of common knowledge and proved that two agents with a common prior whose posterior beliefs are common knowledge cannot hold different posteriors. The result became a reference point in epistemic logic and in philosophical debates about peer disagreement.

Key ideas

• Something is common knowledge when everyone knows it, everyone knows that everyone knows it, and so on without end.
• Rational agents with a common prior cannot agree to disagree once their posteriors are common knowledge.
• Repeated interaction can sustain cooperation that one-shot games cannot.
• Correlated equilibrium generalises Nash equilibrium by allowing shared random signals.

Major works

• "Subjectivity and Correlation in Randomized Strategies" (1974)
• Values of Non-Atomic Games (1974, with Lloyd Shapley)
• "Agreeing to Disagree" (1976)

In the conversation

• Debate Truth as ‘what inquiry converges on’ breaks down exactly where we most need it: ethics Ethan Mercer · 6 replies
• Question Why does the muddy children puzzle need the parent’s announcement if every child already knew? Huang Wei-ting · 3 replies