José A. Rodrigues-Neto

Dress to impress: Brands as status symbols☆

We analyzed the market for indivisible, pure status goods. Firms produce and sell different brands of pure status goods to a population that is willing to signal individual abilities to potential matches in another population. Individual status is determined by the most expensive status good one has. There is a stratified equilibrium with a finite number of brands. Under constant tax rates, a monopoly sells different brands to social classes of equal measure, while in contestable markets, social classes have decreasing measures. Under optimal taxation, contestable markets have progressive tax rates, while a monopoly faces an adequate flat tax rate to all brands. In contrast with extant literature, subsidies may be socially optimal, depending on the parameters, in both market structures.

Representing roommates' preferences with symmetric utilities

In the context of the stable roommates problem, it is shown that acyclicity of preferences is equivalent to the existence of symmetric utility functions, i.e. the utility of agent i when matched with j is the same as js utility when matched with i.

Monotonic models and cycles

A partitional model of knowledge is monotonic if there exists a linear order on the state space such that, for every player, each element of her partition contains only a sequence of consecutive states. In monotonic models, the absence of alternating cycles is equivalent to the property that, for every pair of players, the join of their partitions contains only singletons. Under these equivalent conditions any set of posteriors for the players is consistent (i.e., there is a common prior). When checking for consistency in a monotonic model, it is not necessary to evaluate all cycle equations; if the cycle equations corresponding to cycles of length two hold, then there is a common prior.

Self-consistency, consistency and cycles in non-partitional knowledge models

This paper expands the correspondence model of knowledge to a framework where there is an objective and many subjective state spaces, one for each player. At every objective state, each player lists the subset of her subjective states that she considers possible. In this context, the question of “self-consistency” arises: given beliefs of a player, is it possible that all of these beliefs come from a common prior via Bayesian updating? This paper provides necessary and sufficient conditions for self-consistency. If all players are self-consistent, the question of consistency arises: is there a common prior that rationalizes the beliefs of all players? Is it possible that self-consistency or consistency holds regardless of the numerical values of beliefs of the players? This paper provides necessary and sufficient conditions for consistency of beliefs.

Competitive Equilibrium with Restricted Participation: The Case of Circular Trade

In a model of competitive equilibrium with restricted participation, we prove the existence of a circular competitive equilibrium (CCE). There is a unique CCE if all coefficients of relative risk aversion are bounded above by 1. The direction of trade is determined by the product of the marginal rates of substitution calculated at initial endowments. We also propose a measure for the trade volume (for each individual and for the entire market), prove a no-trade result, and calculate wealth and belief effects on the circular trade economy.

Monotonic Knowledge Models, Cycles, Linear Versions and Auctions with Differential, Finite Information

In games of incomplete information where each players information is represented by a partition of the state space, this paper presents a characterisation of monotonic models in terms of connected partitions and another in terms of versions . A model is monotonic if and only if there is a linear version, and this is true if and only if there is a real-valued function on the state space such that every partition of the model is connected with respect to this function. These results help us understand the strength of the connectedness assumption on common-value, second-price auctions with differential, finite information. We offer a simple sufficient condition for non-monotonicity to check if models are monotonic.