Any group of risk neutral agents who hold differing beliefs is vulnerable to money pumps (arbitrage). Thus, the agents may wish to reconcile their beliefs into a new joint belief. We propose a criterion for the choice of reconciled belief based on the notion of ``rate of arbitrage.''' It is...

Any group of risk neutral agents who hold differing beliefs is vulnerable to money pumps (arbitrage). Thus, the agents may wish to reconcile their beliefs into a new joint belief. We propose a criterion for the choice of reconciled belief based on the notion of ``rate of arbitrage.''' It is...

We propose a method to test a prediction of the distribution of a stochastic process. In a non-Bayesian, non-parametric setting, a predicted distribution is tested using a realization of the stochastic process. A test associates a set of realizations for each predicted distribution, on which the...

We study a one-sided offers bargaining game in which the buyer has private information about the value of the object and the seller has private infromation about his beliefs about the buyer. We show that this uncertainty about uncertainties dramatically changes the set of possible outcomes when...

We study the emergence and nature of long-run behavior of continuous state space dynamics that are subjected to random shocks. It is shown that the fine details of the underlying deterministic dynamics may be crucial in determining the evolution of the system. In particular, a risk dominated...

Prequential testing of a forecaster is known to be manipulable if the test must pass an informed forecaster for all possible true distributions. Stewart (2011) provides a non-manipulable prequential likelihood test that only fails an informed forecaster on a small, category I, set of...

We propose a method to test a prediction of the distribution of a stochastic process. In a non-Bayesian, non-parametric setting, a predicted distribution is tested using a realization of the stochastic process. A test associates a set of realizations for each predicted distribution, on which the...

The subjective framework for reasoning is extended to incorporate the representation of unawareness in games. Both unawareness of actions and decision makers are modeled as well as reasoning about others' unawareness. It is shown that a small grain of uncertainty about unawareness with rational...

We consider a cross-calibration test of predictions by multiple potential experts in a stochastic environment. This test checks whether each expert is calibrated conditional on the predictions made by other experts. We show that this test is good in the sense that a true expert--one informed of...