Using a formal propositional language with operators "individual i assigns probability at least a" for countable many a, we devise an axiom system which is sound and complete with respect to the class of type spaces in the sense of Harsanyi (1967-68). A crucial axiom requires that degrees of...

The standard state-spaces of asymmetric information preclude non-trivial forms of unawareness (Modica and Rustichini, 1994, Dekel, Lipman and Rustichini, 1998). We introduce a generalized state-space model that allows for non-trivial unawareness among several individuals, and which satisfies...

The role of certifiers is to test products for quality, and to communicate the test results to the market. We construct a free-entry model of certification, where each certifier chooses a test standard and a price for certification. In equilibrium, certifiers differentiate their test standards,...

We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for many potential applications of asymmetric unawareness. We develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are...