Hierarchies of belief and interim rationalizability

In games with incomplete information, conventional hierarchies of belief are incomplete as descriptions of the players' information for the purposes of determining a player's behavior. We show by example that this is true for a variety of solution concepts. We then investigate what is essential about a player's information to identify behavior. We specialize to two player games and the solution concept of interim rationalizability. We construct the universal type space for rationalizability and characterize the types in terms of their beliefs. Infinite hierarchies of beliefs over conditional beliefs , which we call Delta-hierarchies, are what turn out to matter. We show that any two types in any two type spaces have the same rationalizable sets in all games if and only if they have the same Delta-hierarchies.Interim rationalizability, belief hierarchies

HIERARCHIES OF BELIEF AND INTERIM RATIONALIZABILITY

In games with incomplete information, conventional hierarchies of belief are incomplete as descriptions of the players’ information for the purposes of determining a player’s behavior. We show by example that this is true for a variety of solution concepts. We then investigate what is essential about a player’s information to identify rationalizable behavior in any game. We do this by constructing the universal type space for rationalizability and characterizing the types in terms of their beliefs. Infinite hierarchies of beliefs over conditional beliefs, what we call delta-hierarchies, are what turn out to matter. We show that any two types in any two type spaces have the same rationalizable sets in all games if and only if they have the same delta-hierarchies.

Carbon Monoxide Intensity Mapping at Moderate Redshifts

We present a study of the feasibility of an intensity-mapping survey targeting the 115 GHz CO(1-0) rotational transition at $z\sim3$. We consider four possible models and estimate the spatial and angular power spectra of CO fluctuations predicted by each of them. The frequency bandwidths of most proposed CO intensity mapping spectrographs are too small to use the Limber approximation to calculate the angular power spectrum, so we present an alternative method for calculating the angular power spectrum. The models we consider span two orders of magnitude in signal amplitude, so there is a significant amount of uncertainty in the theoretical predictions of this signal. We then consider a parameterized set of hypothetical spectrographs designed to measure this power spectrum and predict the signal-to-noise ratios expected under these models. With the spectrographs we consider we find that three of the four models give an SNR greater than 10 within one year of observation. We also study the effects on SNR of varying the parameters of the survey in order to demonstrate the importance of carefully considering survey parameters when planning such an experiment.Comment: 7 pages, 8 fgures, published in MNRA