Equilibria of a two-stage market with chance outcome in the spot market

We address the problem of how to improve the efficiency of markets of similar goods (electric power, gas, and other resources). One way to undermine the market dominance of some companies is the possibility of forward contracts. Here a model of the spot and forward markets functioning as Curnout auctions is studied using the example of symmetrical oligopoly. Suppliers try to maximize their profit by this two-stage game’s strategies of traded subgame equilibrium (TSE). The conditions for equilibrium achieved by correlated mixed strategies are elucidated: either a “bull” or “bear” market is established according to a chance factor. The optimum strategies of rational bidders are found to depend on the reserve price and a risk-avoiding parameter. TSE is compared to the Nash equilibria for one-stage models.     

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.     

Cournot–Walras equilibrium as a subgame perfect equilibrium

In this paper, we investigate the problem of the strategic foundation of the Cournot–Walras equilibrium approach. To this end, we respecify à la Cournot–Walras the mixed version of a model of simultaneous, noncooperative exchange, originally proposed by Lloyd S. Shapley. We show, through an example, that the set of the Cournot–Walras equilibrium allocations of this respecification does not coincide with the set of the Cournot–Nash equilibrium allocations of the mixed version of the original Shapley’s model. As the nonequivalence, in a one-stage setting, can be explained by the intrinsic two-stage nature of the Cournot–Walras equilibrium concept, we are led to consider a further reformulation of the Shapley’s model as a two-stage game, where the atoms move in the first stage and the atomless sector moves in the second stage. Our main result shows that the set of the Cournot–Walras equilibrium allocations coincides with a specific set of subgame perfect equilibrium allocations of this two-stage game, which we call the set of the Pseudo–Markov perfect equilibrium allocations. We would like to thank Pierpaolo Battigalli, Marcellino Gaudenzi, and an anonymous referee for their comments and suggestions.     

Two-settlement electricity markets with price caps and Cournot generation firms

We compare two alternative mechanisms for capping prices in two-settlement electricity markets. With sufficient lead time, forward market prices are implicitly capped by competitive pressure of potential entry that will occur when forward prices rise above some backstop price. Another more direct approach is to cap spot prices through a regulatory intervention. In this paper we explore the implications of these two alternative mechanisms in a two-settlement Cournot equilibrium framework. We formulate the market equilibrium as a stochastic equilibrium problem with equilibrium constraints (EPEC) capturing congestion effects, probabilistic contingencies and horizontal market power. As an illustrative test case, we use the 53-bus Belgian electricity network with representative generator costs but hypothetical demand and ownership structure. Compared to a price-uncapped two-settlement system, a forward cap increases firms’ incentives for forward contracting, whereas a spot cap reduces such incentives. Moreover, in both cases, more forward contracts are committed as the generation resource ownership structure becomes more diversified.     

A study on the demand and response correspondences in the presence of indivisibilities

This paper attempts to study market and noncooperative game models in the presence of indivisibilities from a unified point of view. For market models we examine the sum of consumers’ demand correspondences mapping an integral price space to an integral commodity space, whereas for noncooperative game models we investigate the product of players’ response correspondences mapping a discrete strategy profile space to itself. We show that, in several typical models, the sum and the product correspondences share an important property that they are ‘locally gross direction preserving’, on the standard triangulation of the convex hull of the domain. Moreover, we prove the existence of a Walrasian equilibrium and a Nash equilibrium in respective models through a discrete multivariate mean value theorem.     

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.     

Term structure of interest rates and the expectation hypothesis: The euro area

This paper investigates the informational content of the yield curve in the European market using data on the Italian term structures. According to the expectation hypothesis theory (EHT) the current forward rate equals the future short rate plus a constant risk premium that is time invariant but maturity dependent. This theory has been widely tested in the empirical literature providing various findings according to the country where it has been applied and to the segment of the yield curve examined or the period under study. The standard approach to test the EHT uses the regression techniques assuming data on spot rates and their first differences to be stationary. Recently an increasing number of studies evidenced the non stationarity of interest rates time series and some tests of the EHT are formulated using term spread and forward-spot spread which are stationary. A new strand of literature suggests to investigate the EHT using a restricted VAR framework. In this paper, following [Jondeau, E., Ricart, R., 1999. The expectations hypothesis of the term structure: tests on us, german, french and uk euro-rates. Journal of International Money and Finance 18, 725–750, Ghazali, N.A. Low, S.W., 2002. The expectations hypothesis in emerging financial markets: the case of malaysia. Applied Economics 34, 1147–1156 and Seo, B., 2003. Non linear mean reversion in the term structure of interest rates. Journal of Economic Dynamics and Control 27, 2243–2265], we test if the expectation hypothesis holds using cointegration and error correction analysis. For the period under study results suggest that the long and short term interest rates are cointegrated and therefore subject to a long equilibrium path, providing evidence that the EHT holds for the Italian and the European market.     

Analysis of relationship between forward and spot markets in oligopolies under demand and cost uncertainties

In this paper, we consider interaction between spot and forward trading under demand and cost uncertainties, deriving the equilibrium of the multi-player dynamic games. The stochastic programming and worst-case analysis models based on discrete scenarios are developed to analyze the impact of demand uncertainty and risk aversion on oligopoly (forward and spot) markets’ structure in terms of the forwards and spot pricing, traded quantities and production. A real case of the Iberian electricity market is studied to illustrate performance of the models. The numerical experiments show that cost uncertainty impacts on the strategic decisions more than demand uncertainty.     

Non-additive anonymous games

This paper introduces a class of non-additive anonymous games where agents are assumed to be uncertain (in the sense of Knight) about opponents’ strategies and about the initial distribution over players’ characteristics in the game. We model uncertainty by non-additive measures or capacities and prove the Cournot–Nash equilibrium existence theorem for this class of games. Equilibrium distribution can be symmetrized under milder conditions than in the case of additive games. In particular, it is not required for the space characteristics to be atomless under capacities. The set-valued map of the Cournot–Nash equilibria is upper-semicontinuous as a function of initial beliefs of the players for non-additive anonymous games.     

具有偿付约束的衍生证券市场均衡存在性

本文通过一个简单的模型,证明了具有偿付约束的衍生证券市场均衡的存在性,由此解释了衍生证券市场的起因和衍生证券交易所的建立过程.这一结论很好地解释了市场摩擦对均衡存在性的影响,与无摩擦时均衡未必存在在形成了鲜明的对照.     

基于SV模型的国际现货贵金属市场收益波动的杠杆效应分析

针对国际现货贵金属市场收益波动中是否存在杠杆效应的问题,选取2008年至今的黄金、白银市场数据进行分析,运用具有杠杆效应的SV模型对其收益波动建模,并采取MCMC法—Gibbs法进行参数估计.结果表明:与股票市场的研究结论不同,国际现货黄金、白银市场在整个观察期内几乎不存在杠杆效应;但其震荡期内存在较弱的杠杆效应.     

On Nash–Cournot oligopolistic market equilibrium models with concave cost functions

We consider Nash–Cournot oligopolistic market equilibrium models with concave cost functions. Concavity implies, in general, that a local equilibrium point is not necessarily a global one. We give conditions for existence of global equilibrium points. We then propose an algorithm for finding a global equilibrium point or for detecting that the problem is unsolvable. Numerical experiments on some randomly generated data show efficiency of the proposed algorithm.     

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.     

Dynamic Walrasian price equilibrium problem: evolutionary variational approach with sensitivity analysis

Many authors have been devoted to the study of the static general economic equilibrium problem regulated to Walras’ law (see e.g. Arrow and Debreu in Econometrica 22:265–290, 1954; Arrow and Hahn in General competitive analysis, 1991; Arrow et al. in Econometrica 27:82–109, 1959; Border in Fixed point theorems with application to economics and game theory, Cambridge University Press, Cambridge, 1985; Dafermos in Math Programm 46:391–402, 1990; Dafermos and Zhao in Oper Res Lett 10:396–376, 1991; Donato et al. in J Glob Optim, 2007; Hahn in Stability, North Holland, Amsterdam, 1982; Jofré et al. in Math Oper Res, 2007; Nagurney in Network economics—a variational inequality approach, Kluwer, Dordrecht, 1999; Nagurney and Zhao in Network formalism for pure exchange economic equilibria, World Scientific Press, Singapore, 1993; Walker in J Polit Econ 94(4), 1987; Walras in Elements d’Economique Politique Pure, Corbaz, Lausanne, Switzerland, 1874; Zhao in Variational inequalities in general equilibrium: analysis and computation, PhD thesis, Brown University, 1988; and their bibliography). The aim of this paper is to provide a first approach to a particular dynamic general economic equilibrium problem: a Walrasian price equilibrium problem when the data are time-dependent. The equilibrium conditions that describe this pure exchange economic model are expressed in terms of an evolutionary variational inequality, for which existence and sensitivity results are given. Moreover, our problem can be expressed in a common way to many other equilibrium problems.     

Optimal Supply Functions in Electricity Markets with Option Contracts and Non-smooth Costs

In this paper we investigate the optimal supply function for a generator who sells electricity into a wholesale electricity spot market and whose profit function is not smooth. In previous work in this area, the generator’s profit function has usually been assumed to be continuously differentiable. However in some interesting instances, this assumption is not satisfied. These include the case when a generator signs a one-way hedge contract before bidding into the spot market, as well as a situation in which a generator owns several generation units with different marginal costs. To deal with the non-smooth problem, we use the model of Anderson and Philpott, in which the generator’s objective function is formulated as a Stieltjes integral of the generator’s profit function along his supply curve. We establish the form of the optimal supply function when there are one-way contracts and also when the marginal cost is piecewise smooth.We would like to thank two anonymous referees for careful reading of the paper and helpful comments which lead to a significant improvement of this paper.     

Supply Function Equilibrium in Electricity Spot Markets with Contracts and Price Caps

In electricity wholesale markets, generators often sign long term contracts with purchasers of power in order to hedge risks. In this paper, we consider a market where demand is uncertain, but can be represented as a function of price together with a random shock. Each generator offers a smooth supply function into the market and wishes to maximize his expected profit, allowing for his contract position. We investigate supply function equilibria in this setting, using a model introduced by Anderson and Philpott. We study first the existence of a unique monotonically increasing supply curve that maximizes the objective function under the constraint of limited generation capacity and a price cap, and discuss the influence of the generators contract on the optimal supply curve. We then investigate the existence of a symmetric Nash supply function equilibrium, where we do not have to assume that the demand is a concave function of price. Finally, we identify the Nash supply function equilibrium which gives rise to the generators maximal expected profit. This work was supported by the Australian Research Council Grant RMG1965The authors would like to thank three anonymous referees for their helpful comments     

Analysis of a Duopoly Supply Chain and its Application in Electricity Spot Markets

This paper studies a supply chain consisting of two suppliers and one retailer in a spot market, where the retailer uses the newsvendor solution as its purchase policy, and suppliers compete for the retailer’s purchase. Since each supplier’s bidding strategy affects the other’s profit, a game theory approach is used to identify optimal bidding strategies. We prove the existence and uniqueness of a Nash solution. It is also shown that the competition between the supplier leads to a lower market clearing price, and as a result, the retailer benefits from it. Finally, we demonstrate the applicability of the obtained results by deriving optimal bidding strategies for power generator plants in the deregulated California energy market. Supported in part by RGC (Hong Kong) Competitive Earmarked Research Grants (CUHK4167/04E and CUHK4239/03E), a Distinguished Young Investigator Grant from the National Natural Sciences Foundation of China, and a grant from Hundred Talents Program of the Chinese Academy of Sciences.     

Kalai-Smorodinsky Bargaining Solution Equilibria

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don’t have an a-priori opinion on the relative importance of all these criteria. Roemer (Econ. Bull. 3:1–13, 2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution (see Kalai and Smorodinsky in Econometrica 43:513–518, 1975). We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered by Roemer (Econ. Bull. 3:1–13, 2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations; in particular, we consider the extension to multicriteria games of the Selten’s trembling hand perfect equilibrium concept (see Selten in Int. J. Game Theory 4:25–55, 1975) and prove that perfect Kalai-Smorodinsky bargaining solution equilibria exist and properly refine both the perfect equilibria and the Kalai-Smorodinsky bargaining solution equilibria.     

中国棉花期货市场价格发现功能研究

期货市场和现货市场之间的价格发现功能一直是监管部门和投资者十分关心的问题。本文借助信息共享模型、脉冲响应函数和方差分解等方法，对中国棉花期货市场和现货市场的价格关系进行了实证研究。研究结果表明：棉花期货价格和现货价格之间存在显著的双向引导关系和长期均衡关系；期货市场和现货市场都扮演价格发现角色，且期货市场在价格发现中处于主导地位。     

Two-stage stochastic equilibrium problems with equilibrium constraints: modeling and numerical schemes

This article presents a two-stage stochastic equilibrium problem with equilibrium constraints (SEPEC) model. Some source problems which motivate the model are discussed. Monte Carlo sampling method is applied to solve the SEPEC. Convergence analysis on the statistical estimators of Nash equilibria and Nash stationary points are presented.