Coordination Mechanisms with Partially Specified Probabilities
TLDR
This paper characterizes implementable outcomes in coordination mechanisms when players have only partially specified probabilities, using maximum-entropy inference.
Key contributions
- Analyzes implementable outcomes when only coarse data statistics, not full distributions, are known.
- Players form beliefs using maximum-entropy inference from partially specified probabilities.
- Shows implementable outcomes are "jointly coherent" with unrestricted messages, expanding correlated equilibria.
- Identifies a cross-entropy condition for implementability using canonical mechanisms.
Why it matters
This work is crucial for designing coordination mechanisms in real-world scenarios where full probability distributions are often unknown. It provides new theoretical characterizations, expanding the concept of correlated equilibria and offering practical tools for decision-making under uncertainty.
Original Abstract
We study which outcomes are implementable by disclosing coarse statistics of a data-generating process rather than its full distribution. Players observe data whose joint distribution is only partially known: they know the expectations of finitely many random variables and form beliefs by maximum-entropy inference. We obtain two characterizations. When message spaces are unrestricted, implementable outcomes coincide with jointly coherent outcomes, expanding the set of correlated equilibria. With canonical mechanisms, implementability reduces to a single cross-entropy condition: the target outcome must lie on the cross-entropy level set of some correlated equilibrium that passes through that equilibrium itself. Examples and several classes of games illustrate the reach of the framework.
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