Monotonicity in asymmetric first-price auctions with affiliation

I study monotonicity of equilibrium strategies in first-price auctions with asymmetric bidders, risk aversion, affiliated types, and interdependent values. Every mixed-strategy equilibrium is shown to be outcome-equivalent to a monotone pure-strategy equilibrium under the “priority rule” for breaking ties. This provides a missing link to establish uniqueness in the “general symmetric model” of Milgrom and Weber (Econometrica 50:1089–1122, 1982). Non-monotone equilibria can exist under the “coin-flip rule” but they are distinguishable: all non-monotone equilibria have positive probability of ties whereas all monotone equilibria have zero probability of ties. This provides a justification for the standard empirical practice of restricting attention to monotone strategies. Hendricks et al. (2003) provide an overview of recent empirical work. For a survey of experimental work, see Kagel and Levin (2002).     

Application of a dynamic market inverse elasticity law with linear and log-linear demand models

In this paper we will evaluate the significance of the inclusion of “dynamics” in profit maximization for widely used demand functions. Specifically we will consider both linear and log-linear demand models. Using these demand functions we will obtain closed form solutions for optimum prices (dynamic market inverse elasticity laws). The optimum price in a market governed by dynamic demand response is different from the one within a static response framework; we will relate the differences to specific characteristics of the demand function. One focus of this work will be to develop intuitive explanations for our conclusion regarding the relative size of the optimum price in static and dynamic markets. This work was completed when the author was with Bell Laboratories, USA.     

Nash implementation of competitive equilibria in the job-matching market

This paper studies Nash implementation in the job-matching market where each worker works for only one firm and a firm hires as many workers as it wishes. We show that the competitive equilibrium correspondence (CEC) is the smallest Nash implementable correspondence satisfying individual rationality and Pareto indifference. Furthermore, the CEC is the minimal monotonic extension of the worker-optimal and firm-optimal subcorrespondences. We offer two “good” mechanisms that implement this correspondence in Nash equilibrium.     

Stochastic measures of arbitrage

Empirical research has provided evidence supporting the existence of arbitrage opportunities in real financial markets although market imperfections are often the main reason to explain these empirical deviations. Consequently, recent literature has turned the attention to imperfect markets in order to extend the most significant results on asset pricing. This paper develops several stochastic measures providing relative arbitrage earnings available in a financial market. The measures allow us to take into account different type of frictions. They are introduced by means of several dual pairs of vector optimization problems. Primal problems permit us to characterize the arbitrage absence even in an imperfect market and they also provide optimal arbitrage portfolios if the arbitrage absence fails. Dual ones allow us to extend the risk-neutral valuation methodology for imperfect and noarbitrage free markets and provide new interpretations for the measures in terms of “frictions effect” or “committed errors” in the valuation process. Partially funded by Comunidad Autónoma de Madrid (ref: CAM 07T/0027/2000) and Spanish Ministry of Science and Technology (ref: BEC2000-1388-C04)     

A two stage stochastic equilibrium model for electricity markets with two way contracts

This paper investigates generators’ strategic behaviors in contract signing in the forward market and power transaction in the electricity spot market. A stochastic equilibrium program with equilibrium constraints (SEPEC) model is proposed to characterize the interaction of generators’ competition in the two markets. The model is an extension of a similar model proposed by Gans et al. (Aust J Manage 23:83–96, 1998) for a duopoly market to an oligopoly market. The main results of the paper concern the structure of a Nash–Cournot equilibrium in the forward-spot market: first, we develop a result on the existence and uniqueness of the equilibrium in the spot market for every demand scenario. Then, we show the monotonicity and convexity of each generator’s dispatch quantity in the spot equilibrium by taking it as a function of the forward contracts. Finally, we establish some sufficient conditions for the existence of a local and global Nash equilibrium in the forward-spot markets. Numerical experiments are carried out to illustrate how the proposed SEPEC model can be used to analyze interactions of the markets.     

Almost sure Nash equilibrium strategies in evolutionary models of asset markets

We consider a stochastic model of a financial market with long-lived dividend-paying assets and endogenous asset prices. The model was initially developed and analyzed in the context of evolutionary finance, with the main focus on questions of “survival and extinction” of investment strategies. In this paper we view the model from a different, game-theoretic, perspective and examine Nash equilibrium strategies, satisfying equilibrium conditions with probability one.     

Evolutionary finance and dynamic games

The paper examines a game-theoretic evolutionary model of an asset market with endogenous equilibrium asset prices. Assets pay dividends that are partially consumed and partially reinvested. The investors use general, adaptive strategies (portfolio rules), distributing their wealth between assets, depending on the exogenous states of the world and the observed history of the game. The main objective of the work is to identify strategies, allowing an investor to “survive”, i.e. to possess a positive, bounded away from zero, share of market wealth over the whole infinite time horizon. This work brings together recent studies on evolutionary finance with the classical topic of non-cooperative market games.     

On equilibrium in pure strategies in games with many players

We demonstrate that, if there are sufficiently many players, any Bayesian equilibrium of an incomplete information game can be “ε-purified” . That is, close to any Bayesian equilibrium there is an approximate Bayesian equilibrium in pure strategies. Our main contribution is obtaining this result for games with a countable set of pure strategies. In order to do so we derive a mathematical result, in the spirit of the Shapley–Folkman Theorem, permitting countable strategy sets. Our main assumption is a “large game property,” dictating that the actions of relatively small subsets of players cannot have large affects on the payoffs of other players. E. Cartwright and M. Wooders are indebted to Phillip Reny, Frank Page and two anonymous referees for helpful comments.     

Stochastic models for bidding strategies on oligopoly electricity market

In this paper we consider the forward/futures contracts and Asian-type call options for power delivery as important components of the bidding strategies of the players’ profits on the electricity market. We show how these derivatives can affect their profit. We use linear asymmetric supply function equilibrium (SFE) and Cournot models to develop firms’ optimal bidding strategies by including forward/futures contracts and Asian-type options. We extend the methodology proposed by Niu et al. (IEEE Trans Power Syst 20(4):1859–1867, 2005), where only forward contracts for power delivery were considered in the SFE model.     

Stochastic programming: Potential hazards when random variables reflect market interaction

There are two types of random phenomena modeled in stochastic programs. One type is what we may term “external” or “natural” random variables, such as temperature or the roll of a dice. But in many other cases, random variables are used to reflect the behavior of other market participants. This is the case for such as price and demand of a product. Using simple game theoretic models, we demonstrate that stochastic programming may not be appropriate in these cases, as there may be no feasible way to replace the decisions of others by a random variable, and arrive at the correct decision. Hence, this simple note is a warning against certain types of stochastic programming models. Stochastic programming is unproblematic in pure forms of monopoly and perfect competition, and also with respect to external random phenomena. But if market power is involved, such as in oligopolies, the modeling may not be appropriate.     

Existence of general equilibrium for stochastic economy with infinite-dimensional commondity space and incomplete financial markets

This paper analyses the general equilibrium existence problem in a (finite) discretetime economy with infinite-dimensional commodity space and inComplete financial markets. It isassumed that the trading takes place in the sequence of spot markets and futures markets for sccurities payable in units of account. Unlimited short-selling in securities is allowed. The existence of such an equilibrium is proved under the following conditions: Mackey continuous,weakly convex ,strictly monotone,complete preferences and strictly positive endowments.     

Estimating conjectural variations for electricity market models

Agents’ behavior in oligopolistic markets has traditionally been represented by equilibrium models. Recently, several approaches based on conjectural variations equilibrium models have been proposed for representing agents’ behavior in electrical power markets. These models provide insight of market equilibrium sensitivity to agents’ strategies and external variables, and therefore, they are widely applied. Unfortunately, not enough analysis has been done in how these user-supplied parameters, the conjectural variations, should be estimated. This paper proposes a parameter inference procedure based on two stages. The first stage infers historical values of the parameter by fitting the models’ results to historical market data. The second stage is based on a statistical time-series model whose objective is to forecast parameter values in future scenarios. Additionally, results of this procedure’s application to a real-size case are presented.     

Proper rationalizability and backward induction

This paper introduces a new normal form rationalizability concept, which in reduced normal form games corresponding to generic finite extensive games of perfect information yields the unique backward induction outcome. The basic assumption is that every player trembles “more or less rationally” as in the definition of a ε-proper equilibrium by Myerson (1978). In the same way that proper equilibrium refines Nash and perfect equilibrium, our model strengthens the normal form rationalizability concepts by Bernheim (1984), B?rgers (1994) and Pearce (1984). Common knowledge of trembling implies the iterated elimination of strategies that are strictly dominated at an information set. The elimination process starts at the end of the game tree and goes backwards to the beginning. Received: October 1996/Final version: May 1999     

Supply chain organization and e-commerce: a model to analyze store-picking, warehouse-picking and drop-shipping

Across many industries, e-commerce generates substantial modifications in supply chain structures. The aim of this article is to assess different forms of existing organizations when a store-based sales network coexists with a web site order network. Three main organizational models can be detected: “store-picking”, “dedicated warehouse-picking” and “drop-shipping”. We use a “newsboy” order policy model to compare the advantages of these different models and to note the impact of some parameters on inventory and flow management policies throughout the supply chain. Several effects are presented, particularly those linked to the size of the Internet market in relation to traditional market size and market demand hazards.      

Conditional Viability for Impulse Differential Games

We introduce in this paper the concept of “impulse evolutionary game”. Examples of evolutionary games are usual differential games, differentiable games with history (path-dependent differential games), mutational differential games, etc. Impulse evolutionary systems and games cover in particular “hybrid systems” as well as “qualitative systems”. The conditional viability kernel of a constrained set (with a target) is the set of initial states such that for all strategies (regarded as continuous feedbacks) played by the second player, there exists a strategy of the first player such that the associated run starting from this initial state satisfies the constraints until it hits the target. This paper characterizes the concept of conditional viability kernel for “qualitative games” and of conditional valuation function for “qualitative games” maximinimizing an intertemporal criterion. The theorems obtained so far about viability/capturability issues for evolutionary systems, conditional viability for differential games and about impulse and hybrid systems are used to provide characterizations of conditional viability under impulse evolutionary games.     

An analytical study of the sensitivity of a discrete stochastic model for sales dynamics

We consider a discrete model for sales dynamics in the case of a stochastic model of the market. The model includes “fast” and “slow” components of the market situation described by a stochastic process of “white noise” type and the correlated stochastic process. By using an integral representation of the main characteristics of the Kalman filter, we obtain expressions for stochastic parameters of additional errors of the estimate that arise in the case where the characteristics of noises are inexact. We make an asymptotical analysis of these expressions and give recommendations for the price-forming strategy in the case of uncertainty of the market situation. Bibliography: 2 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 110–116.     

Pricing swing options with regime switching

Gasoline price is highly volatile and exhibits Markov regime-switching process. In the electricity and the natural gas markets, “swing” options, which can provide some protection against day-to-day price fluctuations, are used to incorporate flexibility in delivering acquired energy. We propose a framework for pricing swing options for an underlying variable that follows a regime-switching process. We study the proposed framework in the gasoline industry for pricing swing options under price uncertainty by extracting the gasoline market information, estimating the parameters of the regime-switching process, and then presenting different numerical examples.     

Randomized stopping games and Markov market games

We study nonzero-sum stopping games with randomized stopping strategies. The existence of Nash equilibrium and ɛ-equilibrium strategies are discussed under various assumptions on players random payoffs and utility functions dependent on the observed discrete time Markov process. Then we will present a model of a market game in which randomized stopping times are involved. The model is a mixture of a stochastic game and stopping game. Research supported by grant PBZ-KBN-016/P03/99.     

Generalized correlated equilibrium for two-person games in extensive form with perfect information

A correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is applied for two-person finite games in extensive form with perfect information. Randomization by an umpire takes place over the leaves of the game tree. At every decision point players have the choice either to follow the recommendation of the umpire blindly or freely choose any other action except the one suggested. This scheme can lead to Pareto-improved outcomes of other correlated equilibria. Computational issues of maximizing a linear function over the set of soft correlated equilibria are considered and a linear-time algorithm in terms of the number of edges in the game tree is given for a special procedure called “subgame perfect optimization”.     

Analysis on the forward market equilibrium model

We establish the existence results for the Allaz-Vila [B. Allaz, J.-L. Vila, Cournot competition, forward markets and efficiency, J. Econ. Theory 59 (1993) 1-16] forward market equilibrium model when the M producers have different linear cost functions. We also consider an example with three asymmetric producers. The computational results supplement the conclusion in that the forward trading would increase market efficiency.