Theory and Application of Linear Supply Function Equilibrium in Electricity Markets

We consider a supply function equilibrium (SFE) model of interaction in an electricity market. We assume a linear demand function and consider a competitive fringe and several strategic players having capacity limits and affine marginal costs. The choice of SFE over Cournot equilibrium and other models and the choice of affine marginal costs is reviewed in the context of the existing literature. We assume that bid rules allow affine or piecewise affine non-decreasing supply functions by firms and extend results of Green and Rudkevitch concerning the linear SFE solution. An incentive compatibility result is proved. We also find that a piecewise affine SFE can be found easily for the case where there are non-negativity limits on generation. Upper capacity limits, however, pose problems and we propose an ad hoc approach. We apply the analysis to the England and Wales electricity market, considering the 1996 and 1999 divestitures. The piecewise affine SFE solutions generally provide better matches to the empirical data than previous analysis.     

Inducing liquidity in thin financial markets through combined-value trading mechanisms

Asset pricing theory hypothesizes that investors are only interested in portfolios; individual securities are evaluated only in terms of their contribution to portfolio risk and return. Yet, standard financial market design is that of parallel, unconnected markets, whereby investors cannot submit orders in one market conditional on events in others. When markets are thin, this exposes them to substantial execution risk. Fear of ending up with unbalanced portfolios after trading may even keep investors from submitting orders, further eroding liquidity and the ability of markets to equilibrate. The suggested solution is a portfolio trading mechanism referred to as combined-value trading (CVT). Investors are allowed to submit orders for packages of securities and the system matches trades and computes prices by optimally combining portfolio orders in an open book. We study the performance of the CVT mechanism experimentally and compare it to the performance of parallel, unconnected double auctions in experiments with similar parametrization and either a similar number of subjects or substantially thicker markets. We present evidence that our portfolio trading mechanism facilitates equilibration to the extent that the thicker markets do. Inspection of order submission and trade activity reveals that subjects manage to exploit the direct linkages between markets enabled by the CVT system.     

Supply function equilibria of pay-as-bid auctions

This paper characterizes the Nash equilibrium in a pay-as-bid (discriminatory), divisible-good, procurement auction. Demand by the auctioneer is uncertain as in the supply function equilibrium model. A closed form expression is derived for a one shot game. Existence of an equilibrium is ensured if the hazard rate of the demand distribution is monotonically decreasing with respect to the shock outcome and sellers have non-decreasing marginal costs. Multiple equilibria can be ruled out for markets, for which the auctioneer’s demand exceeds suppliers’ capacity with a positive probability. The derived equilibrium can be used to model strategic bidding behavior in pay-as-bid electricity auctions, such as the balancing mechanism of United Kingdom. Offer curves and mark-ups of the derived equilibrium are compared to results for the SFE of a uniform-price auction.      

Exchange in a general market with indivisible goods

We show how to restrict trades in exchange markets with heterogeneous indivisible goods so that the resulting restricted exchange markets, the fixed deal exchange markets, have a unique core allocation. Our results on fixed deal exchange markets generalize classical results on the Shapley-Scarf housing market, in which each agent owns one good only. Furthermore, we define the class of fixed deal exchange rules for general exchange markets, and prove that these are the only exchange rules that satisfy strategyproofness, individual rationality, and a weak form of efficiency.     

Matching through position auctions

Using a mechanism design framework, we characterize how a profit-maximizing intermediary can design matching markets when each agent is privately informed about his quality as a partner. Sufficient conditions are provided that ensure a version of positive assortative matching (what we call truncated positive assortative matching) maximizes profits. Under these conditions, all-pay position auctions always implement the profit-maximizing allocation. Winners-pay position auctions, however, only do so in sufficiently large markets.     

Altruism,Warm Glow and the Willingness-to-Donate for Green Electricity: An Artefactual Field Experiment

The ongoing liberalization of electricity markets in most western countries forms the background of our artefactual field experiment. Using a Cheap talk design [R.G. Cummings and L.O. Taylor. American Economic Review 89 (1999) 649–665] with supplementary monetary incentives, we test for presence of “warm glow” motivations [J. Andreoni. Journal of Political Economy 97 (1989) 1447–1458; Economic Journal 100 (1990) 464–477] in the willingness-to-donate for electricity generated from renewables. Our data from 200 participants supports impure altruism, that is, individuals benefit from both contributing to environmental quality and its current level when opting in favor of green electricity. Furthermore, we find evidence of crowding-out as well as crowding-in effects. Depending on the knowledge of people about electricity markets and the types of electricity contracts offered, “all-or-none” contracts are most likely to bring about crowding-out effects.     

Existence of equilibrium in large double auctions

We show the existence of a pure strategy, symmetric, increasing equilibrium in double auction markets with correlated, conditionally independent private values and many participants. The equilibrium we find is arbitrarily close to fully revealing as the market size grows. Our results provide strategic foundations for price-taking behavior in large markets.     

Star-shapedness of Richter-Aumann integral on a measure space with atoms: theory and economic applications

This paper provides sufficient (as well as necessary) conditions for the integral of a correspondence defined on a measure space with atoms to exhibit star-shaped values. This result is used to analyze the existence of a Nash equilibrium in games with a measure space of agents with atoms and of a competitive equilibrium in economies with mixed markets. In either case it is shown that an exact equilibrium exists whenever atoms are “small enough”.     

Tax and subsidy incidence equivalence theories: experimental evidence from competitive markets

A basic tenet in microeconomics is tax incidence equivalence, which holds that the burden of a unit tax on buyers and sellers is independent of who actually pays the tax. By contrast, policymakers and the public often mistake statutory incidence for economic incidence. Using competitive laboratory markets, I test both tax incidence equivalence and an analogous theorem for subsidies. For sufficiently large markets, the results show strong support for both theories; there is little to no evidence, even in the short run, of the popular misperception that statutory incidence equals economic incidence. In smaller markets in which competitive forces are weaker and relative bargaining strengths may play a role, the evidence for tax incidence equivalence is weaker as minor price discrepancies may persist between markets.     

Pitfalls in Restructuring the Electricity Industry

Abstract. This paper models some reductions in output that may follow the opening of electricity markets to competition. Specifically, we show that vertical separation of electricity generation, transmission and distribution could reduce welfare compared to the previous system of vertically integrated monopoly, if grid owners can act as monopolistic retailers or, alternatively, set access prices that maximize merchandizing surplus. Moreover, we show that a rule of non‐discriminatory pricing would not remedy any of these problems. Hence, to secure the efficiency gains of deregulation, the re‐regulation of the remaining monopolistic core – the electric grid – cannot rely on simple rules like cost‐based non‐discriminatory pricing.     

Liberalizing the energy markets of Western Europe – a computable equilibrium model approach

Using a computable equilibrium model, the short-run effects of a radical liberalization of the West European natural gas and electricity markets are examined. In each model country, oil, gas, coal and electricity are produced, traded and consumed. There are world markets for oil and coal, and well-integrated competitive markets for gas and electricity in Western Europe. Gas and electricity are transported and traded across markets under the assumption of ideal third-party access regimes for transportation and limited capacities in the transportation networks. It is found that relative to the data year 1996, radical liberalization reduces the average end-user price of natural gas by around 20%, and the average end-user price of electricity by around 50%. The supply of electricity increases by around 20%, mainly due to increased coal power production. After such liberalization, coal power emerges with the largest market share of electricity production in Western Europe.     

Intraday hedging with financial options: the case of electricity

As market intermediaries, electricity suppliers purchase electricity from the wholesale market or self-generate to deliver their customers. However, electricity suppliers are uncertain about how much electricity their residential customers will use at any hour of the day until they actually turn switches on. While demand uncertainty is a common feature of all commodity markets, suppliers generally rely on storage to manage it. Singularly, electricity suppliers are exposed to joint volumetric and price risk on an hourly basis given the physical attributes of electricity. In the literature on electricity markets, few articles compare the efficiency of forward contracts, options and physical assets (i.e. power plants) within intraday hourly hedging portfolios, whereas electricity markets are precisely hourly markets. We analyse portfolios made of forwards, options and/or power plants for specific hourly clusters (9 am, 12 pm, 18 pm, 9 pm) based on electricity market data from 2013 to 2015 from the integrated German–Austrian spot market. Through a VaR model, we prove that intraday hedging with forwards is structurally inefficient compared to financial options and physical assets, no matter the cluster hour. Moreover, our results demonstrate the contribution of ‘out of the money’ options for all hours within volatile spot markets.     

Competitive behavior in market games: Evidence and theory

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1973) [21]. Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market games.     

Market efficiency and continuous information arrival: evidence from prediction markets

Two regularities in financial economics are that prices underreact to news events and that they display short term momentum. This article tests for the presence of these regularities in prediction markets offered by the betting exchange Betfair on the 2008 Ryder Cup Golf Competition. Betfair offered in play prediction markets on the individual match play pairings and on the Cup result, with trading being virtually continuous in all markets. Modelled probabilities of the Cup result were updated continuously using trades in the individual match play pairings. These probabilities were then compared with the probabilities of the Cup result implied by odds in that market. The odds in the market for the Cup result underreact to both good and bad news that is provided by changes in the odds in the markets for the individual pairings. Further, these modelled probabilities Granger cause changes in the probabilities of the Cup result implied by odds in the market on that outcome. In addition, economically and statistically significant evidence of momentum is found in the odds in the market on the Cup result.     

Non-Walrasian equilibria and the law of one price

We present a market game which features multiple posts for each commodity. We use this framework to illustrate the idea that in non-Walrasian markets, where individual activities influence market clearing prices, there are equilibria where commodities are exchanged simultaneously in two posts at different prices, thus defying the ‘law of one price’. Such equilibria are compatible with an apparent arbitrage possibility, which dissipates whenever individuals try to take advantage of it.     

Constrained suboptimality in incomplete markets: a general approach and two applications

Summary. In this paper we re-examine generic constrained suboptimality of equilibrium allocations with incomplete numeraire asset markets. We provide a general framework which is capable of resolving some issues left open by the previous literature, and encompasses many kinds of intervention in partially controlled market economies. In particular, we establish generic constrained suboptimality, as studied by Geanakoplos and Polemarchakis, even without an upper bound on the number of households. Moreover, we consider the case where asset markets are left open, and the planner can make lump-sum transfers in a limited number of goods. We show that such a perfectly anticipated wealth redistribution policy, though consistent with the assumed incomplete financial structure, is typically effective. Received: August 14, 1995; revised version: April 11, 1997     

General equilibrium with nonconvexities and money

In a general-equilibrium economy with nonconvexities, there are sunspot equilibria with good welfare properties; sunspots can ameliorate the effects of the nonconvexities. For these economies, we show that agents act as if they have quasi-linear utility functions. We use this result to construct a new model of monetary exchange along the lines of Lagos and Wright, where trade occurs in both centralized and decentralized markets, but instead of quasi-linear preferences we assume general preferences but with indivisible labor. This suggests that modern monetary theory is more robust than one might have thought. It also constitutes progress on the classic problem of integrating monetary economics and general-equilibrium theory.     

Safe haven,hedge and diversification for G7 stock markets: Gold versus bitcoin

We compare gold and Bitcoin for the G7 stock markets, finding that gold and Bitcoin have distinct safe haven and hedging characteristics. Gold is an undisputable safe haven and hedge for several G7 stock indices, whereas Bitcoin takes these two functions in Canada. The out-of-sample hedging effectiveness of gold is much superior to that of Bitcoin. Furthermore, we find that the conditional diversification benefits offered by gold to equity investments in the G7 markets are comparatively much higher and more stable than those of Bitcoin, especially in the lower return quantiles, i.e., when both the stock and gold markets are in a bearish state. Implications are further discussed.     

Excess demand functions with incomplete markets—a global result

The purpose of this paper is to give a global characterization of excess demand functions in a two-period exchange economy with incomplete real asset markets. We show that continuity, homogeneity and Walras’ law characterize the aggregate excess demand functions on any compact price set which maintains the dimension of the budget set.     

What’s Causing Overreaction? An Experimental Investigation of Recency and the Hot‐hand Effect

A substantial body of empirical literature provides evidence of overreaction in markets. Past losers outperform past winners in stock markets as well as in sports markets. Two hypotheses are consistent with this observation. The recency hypothesis states that traders overweight recent information; they are too optimistic about winners and too pessimistic about losers. According to the hot‐hand hypothesis, traders try to discover trends in the past record of a firm or a team, and thereby overestimate the autocorrelation in the series. An experimental design allows us to distinguish between these hypotheses. The evidence is consistent with the hot‐hand hypothesis.