Stochastic evolution of rules for playing normal form games

The evolution of boundedly rational rules for playing normal form games is studied within stationary environments of stochastically changing games. Rules are viewed as algorithms prescribing strategies for the different normal form games that arise. It is shown that many of the folk results of evolutionary game theory typically obtained with a fixed game and fixed strategies carry over to the present case. The results are also related to recent experiments on rules and games.Rules, evolutionary dynamics, stochastic dynamics, bounded rationality, learning, normal form games

On commercial media bias

Within the spokes model of Chen and Riordan (2007) that allows for non-localized competition among arbitrary numbers of media outlets, we quantify the effect of concentration of ownership on quality and bias of media content. A main result shows that too few commercial outlets, or better, too few separate owners of commercial outlets can lead to substantial bias in equilibrium. Increasing the number of outlets (commercial and non-commercial) tends to bring down this bias; but the strongest effect occurs when the number of owners is increased. Allowing for free entry provides lower bounds on fixed costs above which substantial commercial bias occurs in equilibrium.Commercial media, concentration and consolidation, media bias, self-censorship, ownership structure

Concentration and self-censorship in commercial media

Within a simple model of non-localized, Hotelling-type competition among arbitrary numbers of media outlets we characterize quality and content of media under different ownership structures. Assuming advertising-sponsored, profit-maximizing outlets, we show that (i) topics sensitive to advertisers can be underreported (self-censored) by all outlets in the market, (ii) self-censorship increases with the concentration of ownership, (iii) adding outlets, while keeping the number of owners fixed, may even increase self-censorship; the latter result relies on consumers' most preferred outlets being potentially owned by the same media companies. We argue that externalities resulting from self-censorship could be empirically large.Media economics; media consolidation; media markets; advertising and commercial media bias JEL Classification Numbers: L13; L82

What do the papers sell?

We model the market for news as a two-sided market where newspapers sell news to readers who value accuracy and sell space to advertisers who value advert-receptive readers. We show that monopolistic newspapers under-report or bias news that sufficiently reduces advertiser profits. Newspaper competition generally reduces the impact of advertising. In fact, as the size of advertising grows, newspapers may paradoxically reduce advertiser bias, due to increasing competition for readers. However, advertisers can counter this effect of competition by committing to news-sensitive cut-off strategies, potentially inducing as much under-reporting as in the monopoly case.Two-sided markets, advertising, media accuracy, media bias, media economics.

Quotient spaces of boundedly rational types

By identifying types whose low-order beliefs – up to level li – about the state of nature coincide, we obtain quotient type spaces that are typically smaller than the original ones, preserve basic topological properties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash (li; l-i)-equilibria capture players’ inability to distinguish types belonging to the same equivalence class. The case with uncertainty about the vector of levels (li; l-i) is also analyzed. Two examples illustrate the constructions.Incomplete-information games, high-order reasoning, type space, quotient space, hierarchies of beliefs, bounded rationality

Concentration and self-censorship in commercial media

Within a simple model of non-localized, Hotelling-type competition among arbitrary numbers of media outlets we characterize quality and content of media under different ownership structures. Assuming advertising-sponsored, profit-maximizing outlets, we show that (i) topics sensitive to advertisers can be underreported (self-censored) by all outlets in the market, (ii) self-censorship increases with the concentration of ownership, (iii) adding outlets, while keeping the number of owners fixed, may even increase self-censorship; the latter result relies on consumers' most preferred outlets being potentially owned by the same media companies. We argue that externalities resulting from self-censorship could be empirically large.Media economics; media consolidation; media markets; advertising and commercial media bias.

On some collusive and signaling equilibria in ascending auctions for multiple objects

We consider two ascending auctions for multiple objects: the SEAMO (simultaneous English auction for multiple objects) and the the JAMO (Japanese auction for multiple objects). We first derive a (competitive) Perfect Bayesian Equilibrium of the JAMO by exploiting the strategic equivalence between the JAMO and the Survival Auction which consists of a finite sequence of sealed-bid auctions. Then, we prove that many of the (unwanted) collusive or signaling equilibria studied in the literature in the framework of the SEAMO do not have a counterpart in the JAMO. However, it is shown that certain collusive equilibria based on retaliatory strategies do exist in both auctions.Multi-unit auctions; Ascending auctions; FCC auctions; Collusion; Retaliation

Approximate knowledge of rationality and correlated equilibria

We extend Aumann's [3] theorem deriving correlated equilibria as a consequence of common priors and common knowledge of rationality by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker notion, joint p-belief of rationality, where agents believe the other agents are rational with probabilities p = (pi)i2I or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p su ciently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's [4] theorem on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors.Spanish Ministry of Science and Technology (Grants SEJ2007-64340 and ECO2011-28965) Spanish Ministry of Science and Technology (Grant ECO2009-11213

On some geometry and equivalence classes of normal form games

Equivalence classes of normal form games are defined using the geometry of correspondences of standard equilibiurm concepts like correlated, Nash, and robust equilibrium or risk dominance and rationalizability. Resulting equivalence classes are fully characterized and compared across different equilibrium concepts for 2 x 2 games. It is argued that the procedure can lead to broad and game-theoretically meaningful distinctions of games as well as to alternative ways of viewing and testing equilibrium concepts. Larger games are also briefly considered.Non-cooperative games, classification and equivalence classes, experimental games, geometry of games