Open AccessIncomplete‐information games in large populations with anonymity
Author(s) -
Hellwig Martin F.
Publication year - 2022
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te4066
Subject(s) - macro , anonymity , component (thermodynamics) , probability distribution , computer science , mathematical economics , prior probability , function (biology) , econometrics , mathematics , artificial intelligence , statistics , bayesian probability , physics , computer security , evolutionary biology , biology , thermodynamics , programming language
The paper provides theoretical foundations for models of strategic interdependence under uncertainty that have a continuum of agents and a decomposition of uncertainty into a macro component and an agent‐specific micro component, with a law of large numbers for the latter. This macro–micro decomposition of uncertainty is implied by a condition of exchangeability of agents' types, which holds at the level of the prior if and only if it also holds at the level of agents' beliefs, i.e., posteriors. Under an additional condition of anonymity in payoffs, agents' behaviors are fully determined by their beliefs about the cross‐section distribution of types and other macro variables, and by their beliefs about the cross‐section distribution of other agents' strategies. Any probability distribution over cross‐section distributions of types and other macro variables is compatible with a fully specified belief system, but not every function from types to such probability distributions is compatible with a common prior. The paper gives necessary and sufficient conditions for compatibility of such a function with a common prior.