Paulo Klinger Monteiro

Equilibrium without uniform conditions

Abstract We prove two general equilibrium existence theorems. In the first, we suppose pointwise properness of the preference on the Pareto optimal allocations. For example, to support a Pareto optimal allocation, we need to suppose properness only at the allocation itself. Our second theorem deals with the separable utilities case. With this assumption we prove the existence of equilibrium supposing properness only at the initial endownments.

Private provision of discrete public goods with incomplete information

We analyze the private provision of discrete public good games with incomplete information and continuous contributions. To use the terminology of [Admati and Perry, Review of Economic Studies 58 (1991) 259], we consider contribution and subscription games. In the former, contributions are not refunded if the project is not completed, while in the latter they are. We show that the contribution game has only the strong free riding equilibria if cost is high enough. Thus, in this range of cost, the subscription game is superior to the contribution game. We present several interesting equilibria of both types of games and give a new proof of the ex-post inefficiency of the contribution and the subscription games

Some results on the existence of utility functions on path connected spaces

Abstract This paper concerns the existence of utility representations for preferences defined on a path connected space X . This includes any convex set. A classical result of Eilenberg (1941) proves the existence of utility representations when the consumption set is connected and separable. In an infinite dimensional space the above result may not be useful, because we lack, in general, the separability of the space. The non-separable spaces L ∞ and ca ( K ) are typical examples in mathematical economics. In this paper we show that a continuous preference relation ≽, on X has a continuous utility representation if and only if it is countably bounded, i.e., there is some countable subset F of X such that for all x in X there exist y and z in F with y ≽ x ≽ z . An easy corollary states that any continuous preference which has a best and a worst point has a continuous representation. We also obtain a convex continuous preference on a Banach lattice that has not a utility representation, because it is not countably bounded.

Uniform payoff security and Nash equilibrium in compact games

We introduce a condition, uniform payoff security, for games with compact Hausdorff strategy spaces and payoffs bounded and measurable in players’ strategies. We show that if any such compact game G is uniformly payoff secure, then its mixed extension G¯ is payoff secure. We also establish that if a uniformly payoff secure compact game G has a mixed extension G¯ with reciprocally upper semicontinuous payoffs, then G has a Nash equilibrium in mixed strategies. We provide several economic examples of compact games satisfying uniform payoff security.

Inflation and income inequality: A shopping-time approach

Our work is based on a simplified heterogenous-agent shopping time economy in which economic agents present distinct productivities in the production of the consumption good, and differentiated access to transacting assets. The purpose of the model is to investigate whether, by focusing the analysis solely on endogenously determined shopping times, one can generate a positive correlation between inflation and income inequality. Our main result is to show that, provided the productivity of the interest-bearing asset in the transacting technology is high enough, it is true true that a positive link between inflation and income inequality is generated. Our next step is to show, through analysis of the steady-state equations, that our approach can be interpreted as a mirror image of the usual inflation-tax argument for income concentration. An example is offered to illustrate the mechanism.

First-Price Auction Symmetric Equilibria with a General Distribution

In this paper I obtain the mixed strategy symmetric equilibria of the independent private values, first-price auction for any distribution of valuations. The equilibrium strategy is a pure strategy at the continuity points of the distribution and bids a mixed strategy at the discontinuity points of the distribution.

Sequential asymmetric auctions with endogenous participation

In this paper we suggest a model of sequential auctions with endogenous participation where each bidder conjectures about the number of participants at each round. Then, after learning his value, each bidder decides whether or not to participate in the auction. In the calculation of his expected value, each bidder uses his conjectures about the number of participants for each possible subgroup. In equilibrium, the conjectured probability is compatible with the probability of staying in the auction. In our model, players face participation costs, bidders may buy as many objects as they wish and they are allowed to drop out at any round. Bidders can drop out at any time, but they cannot come back to the auction. In particular we can determine the number of participants and expected prices in equilibrium. We show that for any bidding strategy, there exists such a probability of staying in the auction. For the case of stochastically independent objects, we show that in equilibrium every bidder who decides to continue submits a bid that is equal to his value at each round. When objects are stochastically identical, we are able to show that expected prices are decreasing.

A new proof of the existence of equilibrium in incomplete market economies

In this paper I give a new proof of equilibrium existence in incomplete markets economies with a continuum of states.

Self-fulfilling equilibria: An existence theorem for a general state space

Abstract It is shown that under a weak regularity, a two-period incomplete market economy with a finite number of assets and general (e.g. uncountable) state spaces has an equilibrium. General state spaces are important in applications. The proof proceeds by establishing the existence of self-fulfilling spot price expectations possessing a strong continuity with respect to asset trades.

Non-marketed options, non-existence of equilibria, and non-linear prices

Abstract This paper presents a surprising example that shows that the lattice theoretic properties in Mas-Colells (1986) seminal work are relevant to the existence of equilibrium even when the commodity space is finite dimensional. The example is a two-period securities model with a three-dimensional portfolio space and two traders. The paper identifies a non-marketed call option that fails to have a minimum cost super-replicating portfolio. Using this option, we construct an economy that satisfies all of Mas-Colells assumptions, except that the three-dimensional commodity space is not a vector lattice. In this economy, there is no Walrasian equilibrium and the second theorem of welfare economics fails . Our example has important finite- as well as infinite-dimensional implications. It is also an example of a “well behaved” economy in which optimal allocations that are not supported by linear Walrasian prices are decentralized by the non-linear prices studied in Aliprantis–Tourky–Yannelis (2001).