Zero Intelligence Research Articles

Comparative analysis of bidding strategies for auction-based local energy markets

In view of the ongoing integration of distributed energy resources (DERs) and energy storage into the energy system, conventional consumers are transitioning into prosumers and flexumers. Local energy markets (LEMs) enables these end users to trade electricity directly with each other in order to obtain lower energy prices and to increase the local self-consumption. Since bidding strategies have a decisive impact on efficient trading in auction-based LEMs, the comparison and consistent evaluation of bidding strategies is an important research area. As novelty we propose an uniform evaluation methodology keeping all market features equal except the used bidding strategy. For the first time we evaluate a device-oriented (DO) strategy including an incentive price signal with a zero-intelligence (ZI) strategy, a learning-intelligence (LI) strategy employing the modified Roth–Erev learning algorithm. As evaluation we analyze the resulting market trading with various key performance indicators (KPIs), which consider both cost savings and local energy supply. Our findings reveal that the chosen bidding strategy has a decisive impact on cost savings and the distribution of gains between the buyer and seller side. In a photovoltaic (PV) and combined heat and power (CHP) scenario with different technology penetrations, the end users’ gains attain the highest values for the DO bidding strategy with 7909 € and 16454 €. Also the average market clearing prices are for the DO bidding strategy the highest with 0.269 €/kWh for the and 0.3032 €/kWh, which implies that the seller side predominantly obtains the gains.

Role of Market Microstructure in Price Convergence: A Meta Analysis

This study aims to revisit the assumptions of economic theory that lead to the predictions of competitive equilibrium theory. Extensive work has already been done to answer how well these assumptions of microeconomic theory approximate the real-world market. In this context, two kinds of tools can be found in the literature that tries to answer this question. One is experimental economics (EE) where individuals are involved in a simplified market that mirrors the real-world markets. Human behavior is observed here under an alternating set of rules. The second tool is agent-based Modeling (ABM) which approximates the real-world markets with artificial agents where every agent possesses unique characteristics and the market comprises a diverse set of decision rules. In ABM, computer simulations imitate human behavior. Our results, however, state that with Zero Intelligence agents, the market is not even closer to the level of prediction of a theoretical competitive market. It also makes sense as random number generations should not lead the market to a level of efficiency higher than human agents and we cannot rule out the importance of rationality possessed by humans to bring more efficient results than ZI agents with no rationality.

Role of Market Microstructure in Price Convergence: A Historic Meta-Review

This study aims to revisit the assumptions of economic theory that lead to the predictions of competitive equilibrium theory. Extensive work has already been done to answer how well these assumptions of microeconomic theory approximate the real-world market. In this context, two kinds of tools can be found in the literature that tries to answer this question. One is experimental economics (EE) where individuals are involved in a simplified market that mirrors the real-world markets. Human behavior is observed here under an alternating set of rules. The second tool is agent-based Modeling (ABM) which approximates the real-world markets with artificial agents where every agent possesses unique characteristics and the market comprises a diverse set of decision rules. In ABM, computer simulations imitate human behavior. Our results, however, state that with Zero Intelligence agents, the market is not even closer to the level of prediction of a theoretical competitive market. It also makes sense as random number generations should not lead the market to a level of efficiency higher than human agents and we cannot rule out the importance of rationality possessed by humans to bring more efficient results than ZI agents with no rationality.

Parameterised response zero intelligence traders

I introduce parameterised response zero intelligence (PRZI), a new form of zero intelligence (ZI) trader intended for use in simulation studies of the dynamics of continuous double auction markets. Like Gode and Sunder’s classic ZIC trader, PRZI generates quote prices from a random distribution over some specified domain of discretely valued allowable quote prices. Unlike ZIC, which uses a uniform distribution to generate prices, the probability distribution in a PRZI trader is parameterised in such a way that its probability mass function (PMF) is determined by a real-valued control variable s in the range [-1.0,+1.0]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[-1.0, +1.0]$$\\end{document} that determines the strategy for that trader. When s=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s=0$$\\end{document}, a PRZI trader behaves identically to the ZIC strategy, with a uniform PMF; but when s≈±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s \\approx \\pm 1$$\\end{document} the PRZI trader’s PMF becomes maximally skewed to one extreme or the other of the price range, thereby making it more or less “urgent” in the prices that it generates, biasing the quote price distribution towards or away from the trader’s limit price. To explore the co-evolutionary dynamics of populations of PRZI traders that dynamically adapt their strategies, I show initial results from long-term market experiments in which each trader uses a simple stochastic hill-climber algorithm to repeatedly evaluate alternative s-values and choose the most profitable at any given time. In these experiments the profitability of any particular s-value may be non-stationary because the profitability of one trader’s strategy at any one time can depend on the mix of strategies being played by the other traders at that time, which are each themselves continuously adapting. Results from these market experiments demonstrate that the population of traders’ strategies can exhibit rich dynamics, with periods of stability lasting over hundreds of thousands of trader interactions interspersed by occasional periods of change. Python source code for PRZI traders, and for the stochastic hill-climber, have been made publicly available on GitHub.

Spoofing the Limit Order Book: A Strategic Agent-Based Analysis

We present an agent-based model of manipulating prices in financial markets through spoofing: submitting spurious orders to mislead traders who learn from the order book. Our model captures a complex market environment for a single security, whose common value is given by a dynamic fundamental time series. Agents trade through a limit-order book, based on their private values and noisy observations of the fundamental. We consider background agents following two types of trading strategies: the non-spoofable zero intelligence (ZI) that ignores the order book and the manipulable heuristic belief learning (HBL) that exploits the order book to predict price outcomes. We conduct empirical game-theoretic analysis upon simulated agent payoffs across parametrically different environments and measure the effect of spoofing on market performance in approximate strategic equilibria. We demonstrate that HBL traders can benefit price discovery and social welfare, but their existence in equilibrium renders a market vulnerable to manipulation: simple spoofing strategies can effectively mislead traders, distort prices and reduce total surplus. Based on this model, we propose to mitigate spoofing from two aspects: (1) mechanism design to disincentivize manipulation; and (2) trading strategy variations to improve the robustness of learning from market information. We evaluate the proposed approaches, taking into account potential strategic responses of agents, and characterize the conditions under which these approaches may deter manipulation and benefit market welfare. Our model provides a way to quantify the effect of spoofing on trading behavior and market efficiency, and thus it can help to evaluate the effectiveness of various market designs and trading strategies in mitigating an important form of market manipulation.

Technical Note: Parameterised-Response Zero-Intelligence (PRZI) Traders

This brief technical note introduces PRZI (Parameterised-Response Zero Intelligence), a new form of zero-intelligence trader intended for use in simulation studies of auction markets. Like Gode & Sunder's classic Zero-Intelligence Constrained (ZIC) trader, PRZI generates quote-prices from a random distribution over some specified domain of discretely-valued allowable quote-prices. Unlike ZIC, which uses a uniform distribution to generate prices, the probability distribution in a PRZI trader is parameterised in such a way that its probability mass function (PMF) is determined by a real-valued control variable s in the range [-1.0, +1.0] that determines the strategy for that trader. When s is zero, a PRZI trader behaves identically to the ZIC strategy, with a flat/rectangular PMF; but when s is close to plus or minus one the PRZI trader's PMF becomes asymptotically maximally skewed to one extreme or the other of the price-range, thereby enabling the PRZI trader to act in the same way as the Shaver strategy (SHVR) or the Giveaway strategy (GVWY), both of which have recently been demonstrated to be surprisingly dominant over more sophisticated, and supposedly more profitable, trader-strategies that incorporate adaptive mechanisms and machine learning. Depending on the value of s, a PRZI trader will behave either as a ZIC, or as a SHVR, or as a GVWY, or as some hybrid strategy part-way between two of these three previously-reported strategies. The novel smoothly-varying strategy in PRZI has value in giving trader-agents plausibly useful market impact responses to imbalances in an auction-market's limit-order-book, and also allows for the study of co-adaptive dynamics in continuous strategy-spaces rather than the discrete spaces that have traditionally been studied in the literature.

Profitability, efficiency, and inequality in double auction markets with snipers

This research builds upon two early efforts to explore robot trading strategies within the double auction market: (1) Gode and Sunder's Zero Intelligence robots, a simple, loss-avoiding, random, persistent, liquidity-providing strategy that produced, in double auction markets, high efficiency of allocation and market price convergence (within-period) towards the predictions of competitive theory; and (2) an entirely parasitic version of Todd Kaplan's Snipers, a simple, loss-avoiding, deterministic, liquidity-removing strategy. The original version of Kaplan's Snipers achieved the highest profit in an early tournament (the Santa Fe Double Auction Tournament) in part by accepting others’ orders when there was an excellent price, a low bid-ask spread, or time was running out. As we increase the proportion of snipers in a market, we find that sniping is not generally superior to the ZI strategy and that the snipers’ parasitic and end-of-period behaviors eventually cause extreme price variance and divergence from competitive equilibrium, lower market efficiencies, and rising Gini coefficients of inequality. Our results contrast with earlier claims by Gode and Sunder and others that double auction market efficiency and convergence to competitive equilibria are market properties relatively insensitive to agent strategies. Instead, we find a need to consider agent strategy in explaining how our market outcomes differ from those previously obtained either by Gode and Sunder or by Kaplan's successful tournament entry. Specifically, the interaction of parasitic sniper strategies creates a trading constraint: snipers will never trade with each other. These strategy-induced trading constraints force the standard market efficiency metric lower as the sniper population rises.

Estimation of zero-intelligence models by L1 data

A unit volume zero-intelligence (ZI) model is defined and the distribution of its L1 process is recursively described. Further, a generalized ZI model allowing non-unit market orders, shifts of quotes and general in-spread events is proposed and a formula for the conditional distribution of its quotes is given, together with a formula for price impact. For both the models, MLE estimators are formulated and shown to be consistent and asymptotically normal. Consequently, the estimators are applied to data of six US stocks from nine electronic markets. It is found that more complex variants of the models, despite being significant, do not give considerably better predictions than their simple versions with constant intensities.

A Behaviorally Informed Survey-Powered Market Agent

We introduce a new method for converting individual probability estimates (obtained through surveys) into market orders for use in a Continuous Double Auction prediction market. Our Survey-Powered Market Agent (SPMA) algorithm is based on actual forecaster behavior, and offers notable advantages over existing market agent algorithms such as Zero Intelligence Plus (ZIP) agents: SPMAs only require probability estimates (and not bid direction nor quantity), are more behaviorally realistic, and work well when probabilities change over time. We validate SPMA using prediction market data and probability estimates elicited through surveys from a large set of forecasters on 88 individual forecasting problems over the course of a year. SPMA outperforms simple averages of the same probability forecasts and is competitive with sophisticated opinion poll aggregation methods and prediction markets. We use a rich set of market and poll data to empirically test the assumptions behind SPMA’s operation. In addition to aggregation efficiency, SPMA provides a framework for studying how forecasters convert probability estimates into trading orders, and offers a foundation for building hybrid markets which mix market traders and individuals producing independent probability estimates.

Supply, Demand and Zero-Intelligence: Shape Matters

This paper applies a simple sequential bargaining (SB) as a proxy for the continuous double auction (CDA) to study how the shape of supply and demand curves makes similar outcomes between the two markets populated by zero-intelligence (ZI) agents. At first, we derive analytical expressions for transaction probabilities of ZI pairs in the SB, as well as the three expected outcomes. Those are the allocative efficiency (AE), the average trading price, and the trading volume. Then, we conduct simulations by transferring the identical supply and demand functions from the SB to the CDA because of the complexity of its period. They produce similar statistical results as in the SB although the AE in the CDA is a little higher than that in the SB, while the trading volume is a little smaller than that in the SB. Statistical properties still hold for special shapes that make the long-run outcomes of CDA and the expected outcomes of SB deviate a lot from their corresponding competitive equilibriums. It is concluded that transaction probabilities or frequencies of ZI pairs help to explain how the principle of statistics determines both expected outcomes of a SB and long-run outcomes of a CDA populated by ZI agents.

Can Prospect Theory Explain Market Calendar Effects?

The purpose of this project is to determine if calendar effects observed in stock markets can be explained by prospect theory. In order to answer this question, I have created an agent based model simulating a stock market. There was no sign of any calendar effect in any of the configurations tested to a very high degree of confidence. In addition, there was no obvious difference in the market results generated between optimizing traders following multiple complex strategies and simple zero intelligence traders constrained only by their respective liquidity.

A Generic Framework for a Combined Agent-based Market and Production Model

Agent-based market models are in general based on a-priori defined supply and demand schemes. Likewise, production models assume that prices are known a-priori. In reality prices depend on variable demands and supplies, while demand and supply depend on variable prices, and these two processes are interconnected. This paper describes a model that for the first time simulates a combined agent-based double auction market and production model. The model is built around von Neumann technology matrices (von Neumann, Rev Econ Stud 13(1):1–9, 1946) which provide the links between products. Agents possess one or more technologies to produce products from other products. They trade in order to acquire the inputs and sell in order to generate revenue, and the price is determined by a process of negotiation between buyers and sellers. The algorithm of negotiation is based on Cliff’s Zero Intelligence Plus approach (Cliff, Minimal-intelligence agents for bargaining behaviors in market-based environments. Technical report, School of Cognitive and Computing Sciences, University of Sussex, 1997), but instead of a single commodity with fixed limit prices the agents change their limit prices for multiple products based on the simulated economic situation. The combination of production and market provides a simple but complete bottom-up model framework for microeconomics. As the results show, the model employs a price mechanism that results in an appropriate allocation of resources without a central command.

Zero intelligence in economics and finance

AbstractThis paper reviews the Zero Intelligence (ZI) methodology for investigating markets. This approach models individual traders, operating within a market mechanism, who behave without strategy, in order to determine the impact of the market mechanism and consequently the effect of trader behaviour. The paper considers the major contributions and models within this area from both the economics and finance communities before examining the strengths and weaknesses of this methodology.

Qualitative One-to-Many Multi-Issue Negotiation: Approximating the QVA

When there is one buyer interested in obtaining a service from one of a set of sellers, multi-attribute or multi-issue auctions can ensure an allocation that is efficient. Even when there is no transferable utility (e.g., money), a recent qualitative version of the Vickrey auction may be used, the QVA, to obtain a Pareto-efficient outcome where the best seller wins. However, auctions generally require that the preferences of at least one party participating in the auction are publicly known, while often making this information public is costly, undesirable, or even impossible. It would therefore be useful to have a method that does not impose such a requirement, but is still able to approximate the outcome of such an auction. The main question addressed here is whether the Pareto-efficient best-seller outcome in multi-issue settings without transferable utility (such as determined by the QVA) can be reasonably approximated by multi-bilateral closed negotiation between a buyer and multiple sellers. In these closed negotiations parties do not reveal their preferences explicitly, but make alternating offers. The main idea is to have multiple rounds of such negotiations. We study three different variants of such a protocol: one that restricts the set of allowed offers for both the buyer and the seller, one where the winning offer is announced after every round, and one where the sellers are only told whether they have won or not after every round. It is shown experimentally that this protocol enables agents that can learn preferences to obtain agreements that approximate the Pareto-efficient best-seller outcome as defined by the auction mechanism. We also show that the strategy that exploits such a learning capability in negotiation is robust against and dominates a Zero Intelligence strategy. It thus follows that the requirement to publicly announce preferences can be removed when negotiating parties are equipped with the proper learning capabilities and negotiate using the proposed multi-round multi-bilateral negotiation protocol.

Statistical properties of agent-based models in markets with continuous double auction mechanism

Real world markets display power-law features in variables such as price fluctuations in stocks. To further understand market behavior, we have conducted a series of market experiments on our web-based prediction market platform which allows us to reconstruct transaction networks among traders. From these networks, we are able to record the degree of a trader, the size of a community of traders, the transaction time interval among traders and other variables that are of interest. The distributions of all these variables show power-law behavior. On the other hand, agent-based models have been proposed to study the properties of real financial markets. We here study the statistical properties of these agent-based models and compare them with the results from our web-based market experiments. In this work, three agent-based models are studied, namely, zero-intelligence (ZI), zero-intelligence-plus (ZIP) and Gjerstad–Dickhaut (GD). Computer simulations of variables based on these three agent-based models were carried out. We found that although being the most naive agent-based model, ZI indeed best describes the properties observed in real markets. Our study suggests that the basic ingredient to produce the observed properties from real world markets could in fact be the result of a continuously evolving dynamical system with basic features similar to the ZI model.

The Retailer Needs to Be Paid for Sophisticated Decisions: Modelling Promotional Interactions between Consumers, Retailers and Brand Managers

Competition among brands that sell through a supermarket chain is a repeated moderated oligopoly, where the retailer moderates brand competition by choosing the store promotions that consumers see each week. The interactions between consumers, retailers and brand managers are complex, with each having different goals and constraints. Here we use regression and Genetic Algorithm techniques to model these interactions. Our goal is to address an important question in the literature; specifically whether the retailer gains positive returns through more sophisticated moderation. In doing so, we draw on work in economics showing that unsophisticated or Zero-Intelligence (ZI) agents can often replicate real-world outcomes. Hence we posit and test three levels of retailer sophistication - ZI, naive and sophisticated - bringing a novel perspective to this important topic.We find that, although the behavior of brand managers is more realistic with the sophisticated retailer, on average the category volumes are lower than with either of the naive or ZI retailer. The dominant brand, however, does benefit with the sophisticated retailer, by preserving its profits and reducing those of its competitors. We speculate that the retailer either receives adequate side-payments from the dominant brand or there are sufficient spin-off benefits in other categories to compensate the retailer for the loss of volume in the focal category.

Asset price bubbles and crashes with near-zero-intelligence traders

We examine whether a simple agent-based model can generate asset price bubbles and crashes of the type observed in a series of laboratory asset market experiments beginning with the work of Smith, Suchanek and Williams (1988). We follow the methodology of Gode and Sunder (1993, 1997) and examine the outcomes that obtain when populations of zero-intelligence (ZI) budget constrained, artificial agents are placed in the various laboratory market environments that have given rise to price bubbles. We have to put more structure on the behavior of the ZI-agents in order to address features of the laboratory asset bubble environment. We show that our model of “near-zero-intelligence” traders, operating in the same double auction environments used in several different laboratory studies, generates asset price bubbles and crashes comparable to those observed in laboratory experiments and can also match other, more subtle features of the experimental data.

Statistical Properties of Stock Order Books: Empirical Results and Models

We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most interesting features concern (i) the statistics of incoming limit order prices, which follows a power-law around the current price with a diverging mean; and (ii) the humped shape of the average order book, which can be quantitatively reproduced using a 'zero intelligence' numerical model, and qualitatively predicted using a simple approximation.

The Predictive Power of Zero Intelligence in Financial Markets

Standard models in economics stress the role of intelligent agents who maximize utility. However, there may be situations where, for some purposes, constraints imposed by market institutions dominate intelligent agent behavior. We use data from the London Stock Exchange to test a simple model in which zero intelligence agents place orders to trade at random. The model treats the statistical mechanics of order placement, price formation, and the accumulation of revealed supply and demand within the context of the continuous double auction, and yields simple laws relating order arrival rates to statistical properties of the market. We test the validity of these laws in explaining the cross-sectional variation for eleven stocks. The model explains 96% of the variance of the bid-ask spread, and 76% of the variance of the price diffusion rate, with only one free parameter. We also study the market impact function, describing the response of quoted prices to the arrival of new orders. The non-dimensional coordinates dictated by the model approximately collapse data from different stocks onto a single curve. This work is important from a practical point of view because it demonstrates the existence of simple laws relating prices to order flows, and in a broader context, because it suggests that there are circumstances where institutions are more important than strategic considerations.

Statistical theory of the continuous double auction

Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyse it using simulation, dimensional analysis, and theoretical tools based on mean field approximations. The model makes testable predictions for basic properties of markets, such as price volatility, the depth of stored supply and demand versus price, the bid–ask spread, the price impact function, and the time and probability of filling orders. These predictions are based on properties of order flow and the limit order book, such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly there are no free parameters. We show that the order size, which can be cast as a non-dimensional granularity parameter, is in most cases a more significant determinant of market behaviour than tick size. We also provide an explanation for the observed highly concave nature of the price impact function. On a broader level, this work suggests how stochastic models based on zero intelligence agents may be useful to probe the structure of market institutions. Like the model of perfect rationality, a stochastic zero intelligence model can be used to make strong predictions based on a compact set of assumptions, even if these assumptions are not fully believable.