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We develop a theory of news coverage in environments of information abundance that include both new and traditional news media, from online and print newspapers to radio and television. News consumers are time-constrained and browse through news items that are available across competing outlets, choosing which outlets to access and which stories to read or skip. Media firms are aware of consumers' preferences and constraints, and decide on rankings of news items that maximize their profits. We find that the news consumed in equilibrium is highly sensitive to the details of the environment. We show that even when readers and outlets are rational and unbiased, readers may consume more than they would like to, and the news items they consume may be significantly different from the ones they prefer. Important news items may be crowded out. Next, we derive implications on diverse aspects of current media, including a rationale for tabloid news, a rationale for why readers prefer like-minded news, and how advertising can contribute to crowding out news. We also analyze methods for restoring reader-efficient standards and discuss the political economy implications of the theory.

We study an interactive framework that explicitly allows for nonrational behavior. We do not place any restrictions on how players' behavior deviates from rationality, but rather, on players' higher-order beliefs about the frequency of such deviations. We assume that there exists a probability p such that all players believe, with at least probability p, that their opponents play rationally. This, together with the assumption of a common prior, leads to what we call the set of p-rational outcomes, which we define and characterize for arbitrary probability p. We then show that this set varies continuously in p and converges to the set of correlated equilibria as p approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The p-rational outcomes are easy to compute, also for games of incomplete information. Importantly, they can be applied to observed frequencies of play for arbitrary normal-form games to derive a measure of rationality p that bounds from below the probability with which any given player chooses actions consistent with payoff maximization and common knowledge of payoff maximization. ; Germano acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (Grant ECO2014-59225-P), as well as from the Barcelona GSE Research Network and the Generalitat de Catalunya. Zuazo-Garin acknowledges financial support from the Spanish Ministry of Science and Technology (Grant ECO2009-11213), from the Spanish Ministry of Economy and Competitiveness (Grant ECO2012-31326) and from the Basque Government (Grants IT568-13 and POS-2015-1-0022).

Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's (1989)Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with multiple rationalizable (ICR) actions, there exist similar types with unique rationalizable action. This paper studies how a wide class of departures from common belief in rationality impact Weinstein and Yildiz's discontinuity. We weaken ICR to ICRλ, where λ is a sequence whose term λn is the probability players attach to (n- 1)th-order belief in rationality. We find that Weinstein and Yildiz's discontinuity remains when λn is above an appropriate threshold for all n, but fails when λn converges to 0. That is, if players' confidence in mutual rationality persists at high orders, the discontinuity persists, but if confidence vanishes at high orders, the discontinuity vanishes. ; Germano acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (grant ECO2017-89240-P, AEI/FEDER, UE, and through the Severo Ochoa Program for Centers of Excellence in R&D, grant SEV-2015-0563). Zuazo-Garin acknowledges financial help from the Spanish Ministry of Economy and Competitiveness, from the Department of Language Policy and Culture of the Basque Government (grants ECO2012-31346 and POS-2015-1-0022 and IT568-13, respectively) and the ERC Starting Grant #759424, and thanks Northwestern University (both the Department of Economics and the Math Center at MEDS Department) for generous hospitality.