Extremal Choice Equilibrium: Existence and Purification with Infinite-Dimensional Externalities

We prove existence and purification results for equilibria in which players choose extreme points of their feasible actions in a class of strategic environments exhibiting a product structure. We assume finite-dimensional action sets and allow for infinite-dimensional externalities. Applied to large games, we obtain existence of Nash equilibrium in pure strategies while allowing a continuum of groups and general dependence of payoffs on average actions across groups, without resorting to saturated measure spaces. Applied to games of incomplete information, we obtain a new purification result for Bayes-Nash equilibria that permits substantial correlation across types, without assuming conditional independence given the realization of a finite environmental state. We highlight our results in examples of industrial organization, auctions, and voting.

Admissibility and Event-Rationality

We develop an approach to providing epistemic conditions for admissible behavior in games. Instead of using lexicographic beliefs to capture infinitely less likely conjectures, we postulate that players use tie-breaking sets to help decide among strategies that are outcome-equivalent given their conjectures. A player is event-rational if she best responds to a conjecture and uses a list of subsets of the other players' strategies to break ties among outcome-equivalent strategies. Using type spaces to capture interactive beliefs, we show that common belief of event-rationality (RCBER) implies that players play strategies in S1W, that is, admissible strategies that also survive iterated elimination of dominated strategies (Dekel and Fudenberg (1990)). We strengthen standard belief to validated belief and we show that event-rationality and common validated belief of event-rationality (RCvBER) implies that players play iterated admissible strategies (IA). We show that in complete, continuous and compact type structures, RCBER and RCvBER are nonempty, and hence we obtain epistemic criteria for SinfW and IA.

Admissibility and event-rationality

Brandenburger et al. (2008) establish epistemic foundations for rationality and common assumption of rationality (RCAR), where rationality includes admissibility, using lexicographic type structures. Their negative result that RCAR is empty whenever the type structure is complete and continuous suggests that iterated admissibility (IA) requires players to have prior knowledge about each other, and therefore is a strong solution concept, not at the same level as iterated elimination of strongly dominated strategies (IEDS). We follow an alternative approach using standard type structures and show that IA can be generated in a complete and continuous type structure. A strategy is event-rational if it is a best response to a conjecture, as usual, and in addition it passes a “tie-breaking†test based on a set E of strategies of the other player. Event-rationality and common belief in event-rationality (RCBER) is characterized by a solution concept we call hypo-admissible sets and, in a complete structure, generates the strategies that are admissible and survive the iterated elimination of strongly dominated strategies (Dekel and Fudenberg (1990)). Extending event-rationality by adding what a player is certain about the other’s strategies as a tie-breaking set to each round of mutual belief we get common belief of extended event-rationality (RCBeER), which generates a more restrictive solution concept than the SAS (Brandenburger et al. (2008)) and in a complete structure produces the IA strategies. Contrary to the negative result in Brandenburger et al. (2008), we show that RCBER and RCBeER are nonempty in complete, continuous and compact type structures, therefore providing an epistemic criterion for IA <br><br> Keywords; epistemic game theory, admissibility, iterated weak dominance, common knowledge, rationality, completeness

The Inclusiveness of Exclusion

We extend Armstrong’s (1996) result on exclusion in multi-dimensional screening models in two key ways, providing support for the view that this result is quite generic and applicable to many different markets. First, we relax the strong technical assumptions he imposed on preferences and consumer types. Second, we extend the result beyond the monopolistic market structure to generalized oligopoly settings with entry. We also analyse applications to several quite different settings: credit markets, automobile industry, research grants, the regulation of a monopolist with unknown demand and cost functions, and involuntary unemployment in the labor market.Multidimensional screening; exclusion; regulation of amonopoly; involuntary unemployment

Diversidade genética em cultivares e linhagens de feijão comum (Phaseolus vulgaris L.) utilizando análises multivariadas

O objetivo deste trabalho foi avaliar a divergência genética entre cultivares/ linhagens de feijão comum e indicar genitores contratantes e superiores para produzir populações segregantes com alta variabilidade. Avaliou-se 25 cultivares/linhagens de feijão, em delineamento de blocos ao acaso com três repetições. Os caracteres agronômicos avaliados foram: Número de dias para o florescimento, Ciclo, Altura média final das plantas, Altura média da inserção primeira vagem, Comprimento médio longitudinal das vagens, Número médio de vagens por planta, Número médio de sementes por vagem, Número médio de sementes por planta, Peso médio de 100 sementes e Produtividade de grãos. Os dados obtidos foram submetidos à análise de variância, seguido do teste de agrupamento de Scott e Knott. Para a análise da divergência genética entre as cultivares/linhagens foi empregada análise multivariada com base na distância generalizada de Mahalanobis, realizando posteriormente os métodos aglomerativos de otimização de Tocher, método hierárquico “UPGMA” e projeção de distância no plano 2D. O grau de preservação das distâncias genéticas no dendrograma foi verificado a partir do Coeficiente de Correlação Cofenética. Utilizou-se, também, o critério de Singh (1981) para quantificar a contribuição relativa das características para a divergência genética. As cultivares/linhagens avaliadas apresentam dissimilaridade genética quanto às características agronômicas avaliadas. A característica comprimento médio longitudinal das vagens é a que mais contribuiu para estimar a diversidade genética entre as cultivares/linhagens. E híbridos com maior efeito heterótico podem ser obtidos dos cruzamentos entre Iraí × Goiano Precoce, Iraí × Pérola, Goiano Precoce × CNFC 10467 e IAPAR 81 × Pérola