Endogenous Mechanisms and Nash Equilibrium in Competitive Contracting

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm's catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism - and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.common agency with adverse selection, endogenous contracting mechanisms, discontinuous games, catalog games, existence of Nash equilibrium, competitive contracting

Equilibrium Selection and the Rate of Convergence in Coordination Games with Simultaneous Play

We apply the dynamic stochastic framework proposed in the recent evolutionary literature to a class of coordination games played simultaneously by the entire population. In these games, payoffs whence best replies are determined by a summary statistic of the population strategy profile. We demonstrate that with simultaneous play, the equilibrium selection depends crucially on how best responses to the summary statistic remain piece-wise constant. In fact, all the strict Nash equilibria in the underlying stage game can be declared stochastically stable depending on how the best response mapping generates piece-wise constant best responses. Furthermore, we show that if the best response mapping is sufficiently asymmetric, the expected waiting time until the unique stochastically stable state is reached is of the same order as the mutation rate, even in the limit as the population size grows to infinity.equilibrium selection; stochastic stability; waiting time; rate of convergence

Discrete Public Goods with Incomplete Information

We investigate a simultaneous discrete public good provision game with incomplete information. To use the terminology of Admati and Perry (1991), we consider both contribution and subscription games. In the former, contributions are not refunded if the project is not completed, while in the latter they are. In the presence of complete information about individuals' valuations for the public good, the difference between the equilibrium outcomes of a subscription game and a contribution game is not significant. However, there is both casual evidence from the fund-raising literature and experimental evidence that subscription games are ``superior '', i.e., a refund increases the chance of providing the good given that it is efficient to do so. Our analysis shows that this is indeed the case in the presence of incomplete information. We compute a symmetric equilibrium for the subscription game and show that it is not necessarily efficient. This inefficiency stems from the difficulties arising in coordinating to overcome the free-rider problem in the presence of incomplete information. Although it is well known that informational disparities impose limits on the efficiency of outcomes, the novel feature of our analysis is to explicitly model the resulting trade-off --- when deciding how much to contribute towards the public good --- between increasing the likelihood of provision and creating incentives for free-riding by the other player. Moreover, we show that for the contribution game, ``contributing zero'' is the only equilibrium for a given range of the fixed cost of provision and for a family of distributions.public goods; incomplete information; continuous distribution

Corruption and Auctions

We investigate the outcome of an auction where the auctioneer approaches one of the two existing bidders and offers an opportunity for him to match his opponent's bid in exchange for a bribe. In particular, we examine two types of corruption arrangements. In the first case, the auctioneer approaches the winner to offer the possibility of a reduction in his bid to match the loser's bid in exchange for a bribe. In the second arrangement, the auctioneer approaches the loser and offers him the possibility of matching the winner's bid in exchange for a bribe. While oral auctions are corruption free under the two arrangements, corruption affects both bidding behavior, efficiency and the seller's expected revenue in a first­price auction

Equilibria in reflexive Banach lattices with a continuum of agents.

We consider exchange economies with a measure space of agents and for which the commodity space is a separable and reflexive Banach lattice. Under assumptions imposing uniform bounds on marginal rates of substitution, positive results on core-Walras equivalence were established in Rustichini-Yannelis [27] and Podczeck [25]. In this paper we prove that under similar assumptions on marginal rates of substitution, the set of competitive equilibria (and thus the core) is non-empty.Competitive equilibria; Continuum of agents; Reflexive Banach lattice commodity spaces; Uniform properness;

Three principles of competitive nonlinear pricing

We make three contributions to the theory of contracting under asymmetric information. First , we establish a competitive analog to the revelation principle which we call the implementation principle. This principle provides a complete characterization of all incentive compatible, indirect contracting mechanisms in terms of contract catalogs (or menus), and allows us to conclude that in competitive contracting situations, firms in choosing their contracting strategies can restrict attention, without loss of generality, to contract catalogs. Second, we establish a competitive taxation principle. This principle, a refinement of the implementation principle, provides a complete characterization of all implementable nonlinear pricing schedules in terms of product-price catalogs and allows us to reduce any game played over nonlinear pricing schedules to a strategically equivalent game played over product-price catalogs. Third, applying the notion of payoff security (Reny (1999)) and the competitive taxation principle, we demonstrate the existence of a Nash equilibrium for the mixed extension of the nonlinear pricing game. Moreover, we identify a large class of competitive nonlinear pricing games whose mixed extensions satisfy payoff security. This paper extends earlier work by the first author (see Page 1992, 1999))

Endogenous Mechanisms and Nash Equilibrium in Competitive Contracting

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm's catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism - and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria

Selection of materials for blast furnace injection using quality indicators.

The injection of pulverized materials is a technique used in most of the blast furnaces in the world to reduce coke and charcoal consumption. In addition, injection is one of the main variables of the blast furnace heat control. Coal is the most used material for the injection, but some industries have been attempting to use other materials, usually mixtures, in order to reduce the total dependence on it. The quality of the injected material influences some operational parameters, such as the permeability, the heat control, and also the quality of the hot metal produced. Due to these factors, the strategy and quality of these materials should be planned and evaluated using quality indicators to achieve good production, with low cost and environmental impact. In this context, there is a large number of researches on different materials, especially waste from iron and steelmaking processes, among others. Herein, some quality indicators of different materials tested on industrial and laboratory scales were analyzed compared, and the feasibility of using new materials injected into the blast furnace was discussed

A generative-oriented model-driven design environment for customizable video surveillance systems

To tackle the growing complexity and huge demand for tailored domestic video surveillance systems along with a high demanding time-to-market expectation, engineers at IVV Automação, LDAa are exploiting video surveillance domain as families of systems that can be developed following a pay-as-you-go fashion rather than developing an ex-nihilo new product. Several and different new functionalities are required for each new product’s hardware platforms (e.g., ranging from mobile phone, PDA to desktop PC) and operating systems (e.g., flavors of Linux, Windows and MAC OS X). Some of these functionalities have special economical constraints of development time and memory footprint. To better accommodate all the above listing requirements, a model-driven generative software development paradigm supported by mainstream tools is proposed to offer a significant leverage in hiding commonalities and configuring variabilities across families of video surveillance products while maintaining the new product quality.This work was funded through the Competitive Factors Operational Program COMPETE and through national funds though the Science and Technology Foundation - FCT, within the project: FCOMP-01-0124-FEDER-022674. This work was developed in cooperation with IVV Automation; all support and means provided by the company is acknowledged