ABSTRACT. This paper surveys the nascent experimental research on the interaction between human and algorithmic traders in experimental markets. We first discuss studies in which algorithmic traders are in the researcher’s hands. Specifically, the researcher assigns computer agents as traders in the market. We then discuss the studies in which the researchers allow human traders to decide whether to employ algorithms for trading. The paper introduces the types and performances of algorithmic traders that interact with human subjects in the laboratory, including zero-intelligent traders, arbitragers, fundamentalists, adaptive algorithms, and manipulators. The potential impact of interactions with algorithms on the investor’s psychology is also discussed.

ABSTRACT. With the advent of the new era of Artificial Intelligence, we need to update our inferential methods in economics and the social sciences accordingly. The implementation of a slightly realistic considera- tion will easily reveal to us a very large domain. In this article, we employ the AI market simulation system called U-Mart to model the efficiency of a realistic futures market. In the actual market, participating agents send orders either randomly or non-intelligently, even though they de- pend on their own unambiguous strategies. It has been noted that purely random orders often result in the best performance in the market. Thus, the market system may have many redundancies. In the actual market, we cannot know an optimal solution in advance. Leaving aside from the efficiency of the market, however, we may be capable to build up/detect a winning strategy in the average, because the price behavior by itself will be characterized by the class properties such like constantly con- verging, periodic, chaotic, and complex. On the other hand, it is already known that these patterns are given rise by Fully Random, Rule-Based Interactive Cellular Automata (ICA), which is based on Alan Turing’s rule selection. In fact, a consecutive application of a different rule of CA randomly selected gives a various behavioral pattern represented by Class properties from fixed, periodic, chaotic and complex one (Carvalho 2011 [4]). Interactive randomness and heterogeneity must be essential for the pattern formations. Based on this hint, we suggested the idea of the length distribution of the FRICA’s cases. We then summarize the results on the log-log plot on the length distributions belonging to class 4: (i) The distributions will be long-tailed. (ii)They are similar to any power-law distribution. (iii)The slop e of each distribution may be different respectively in the same class 4. On the other hand, we have found not only the Nakajima- Mori agent configuration of the so-called traditional technical analytical agents (behavioral rules) to realize the future price time series similar to any given spot price time series in the AI market experiment, but also its minimal sized configuration 5. Thus we have applied the idea of the length distribution to the price movements generated by the U-Mart system. We employ the minimal sized composition as the default strategy composition, and then exam- ine the generated price movement in the minimal configuration. In the U-Mart acceleration experiment kit, it is prepared the 4 type patterns of price behavior of the referential spot price time series: ascending(up), descending(down), reversal(reverse), oscillating. As the experiment kit contains the time series to fulfill Class 1 to 4 argued in the above, we will have another identification procedure on the new set of additional agents. Thus we will have the experiments of identifying the effect of an additional agent strategy according to 4 types of price behavior of the referential time series.

ABSTRACT. The use of trading algorithms is proliferating in asset markets. In fragmented experimental laboratory markets, we examine the impact of different types of arbitrage seeking algorithms. These algorithms vary in their latency and whether they make or take market liquidity. We find the presence of algorithmic arbitrageurs generally enhances market quality. All arbitrage robot traders we examine lead to greater conformity to the law of one price across the fragmented markets. However, only the liquidity providing algorithm moves prices into closer alignment with fundamental values. The algorithmic arbitrageurs’ benefits in improved market quality incur varying associated costs, as measured by the wealth they extract from human traders. We identify factors, and their associated impacts, which drive differences in human trader performance. We also show the presence of an arbitrage robot trader does not affect these impacts. Hence these arbitrage robot traders do not discriminatorily prey on human traders based on individual characteristics or trading strategies they employ.

ABSTRACT. Simple risk parity asset allocation strategies combining stocks and bonds outperform the market portfolio on a risk-adjusted basis; this well-known anomaly---which I label the risk parity premium puzzle---cannot be explained by canonical asset pricing theory. In this paper, I provide a new resolution to this paradox using a model with minimal-intelligence traders. I argue that at the heart of the failure were the wrong microfoundations, which failed to incorporate crucial features of "the rules of the game" in real-world investing. Most importantly, asset pricing theory is built on the Arrow--Debreu time-state preference model, and thus, the theory assumes rational investors maximize expected utility by constructing preference orderings over investment choices using a subjective probability distribution of asset returns. Building on Herbert Simon's notion of bounded rationality, I incorporate real-world market institutions by positing a "Hayek hypothesis" of decentralized processes of competition between minimal-intelligence traders expressing their probability beliefs in terms prices. Market efficiency, in turn---rather than being defined by Fama's established joint hypothesis theorem---is viewed as a spontaneous order of collective rationality. To test this hypothesis, the model predicts how prices ought to behave if the market is collectively rational in this sense; in particular, returns follow a simple power law distribution as a function of macroeconomic shocks. Examining U.S. asset price data for the period 1926 to 2015, I find evidence that the model can explain the risk parity premium puzzle, and hence, provide support for a notion of bounded rationality adapted to the game of real-world investing.

ABSTRACT. I introduce PRZI (Parameterised-Response Zero Intelligence), a new form of zero-intelligence (ZI) trader intended for use in simulation studies of continuous double auction (CDA) markets. Like Gode & 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] that determines the _strategy_ for that trader. When s=0, a PRZI trader behaves identically to the ZIC strategy, with a rectangular PMF; but when s is approximately plus or minus one the PRZI trader's PMF becomes 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 SHVR strategy or the GVWY strategy, 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: (A) giving trader-agents plausibly useful ``market impact" responses to imbalances in a CDA-market's limit-order-book; (B) enabling the study of co-adaptive dynamics in continuous strategy-spaces rather than the discrete spaces that have traditionally been studied in the literature; and (C) giving _opinionated_ ZI traders that can be used to study issues arising from Shiller's notion of _narrative_economics_. Illustrative results from each of (A), (B), and (C) are given here. Python source-code for a PRZI trader has been made publicly available on GitHub.

ABSTRACT. We consider a model of a financial market a là Grossmann and Stiglitz, where three types of boundedly rational agents can either trade buying a costly normal signal $\theta_t$ on the future return, $D+\theta_t+\epsilon_t$; alternatively, they can trade assuming that some fake news $\zeta_t$ is informative when indeed it's not, see \cite{Black}, as $\zeta_t\perp\epsilon_t\perp\theta_t, \forall t$. Finally, agents can choose not to use any signal and stay uninformed. We denote the three strategies with the tags I(nformed), M(isinformed) and U(ninformed), respectively. The (local) equilibrium price is determined crossing demand and supply of the risky asset. Minimal learning capabilities are introduced in the model allowing agents to assess their performance every $T$ periods, when a fraction of the population is paired with another random peer and profits are compared. If agents $i$ and $j$ used strategies $S_i$ and $S_J\in S=\{I,M,U\}$, collecting profits $\pi_i^T< \pi_j^T$, respectively, then trader $i$-th switches to the information strategy used by $j$ in the following $T$ periods. Intuitively, agents change behaviour when they see that other strategies happen to have produced higher revenues. This copycat learning mechanism, with no optimization or forecasting attempt, is completed by tiny rates of random strategy mutations of a handful of agents who select randomly an element in $S$. A stochastic equilibrium in this market is a stationary distribution of the price $p_t$ as a function of the sequences $\theta_t,\zeta_t, \epsilon_t, t=1,2,...$, together with stationary fractions $\lambda_I,\lambda_M$ and $\lambda_U=1-\lambda_i-\almbda_M$ of the informed, misinformed and uninformed agents.

We retrieve some of the findings of the original Grossmann and Stiglitz model and, say, the relative share of informed to uninformed depends on the signal to noise ratio. However, despite the simplicity of the model, we obtain several novel and sharp results.

First, the fractions of agents at equilibrium are characterized by a condition among the probabilities to gain higher profits than other strategies. In detail, if we denote by $\pi_s$ the profit obtained by agents employing strategy $s\in S$ then we have that $$ P(\pi_i>\pi_j)=\frac{1}{2},\forall i\ne=j. $$ Hence, in equilibrium, the probability to gain more than other strategies is the same as the one of getting less, for all types. We named this peculiar situation, in which no agents has incentive "in probablity" to switch to another type, a "median equilibrium". In the special case with only two types, we provide a semi-analytical expression for the equilibrium fractions.

Second, through numerical simulations of an agent-based model, we show that the extinction of type-M agents is obtained only when $T\rightarrow\infty$ and mutation vanishes. In other words, the presence of misinformed traders is pervasive and robust and often they amounts to 10-20\% of the population in a variety of settings of practical interest. Under this respect, the model shows that the conventional conclusion that irrational agents are bound to disappear is at risk in an informationally rich situation, where the (true) signal cannot easily be distinguished from the (fake) info on returns, traders learn by imitation and the price is endogenously driven by the size of the three groups composing the population.

Third, even when the misinformed agents asymptotically fade away, their decay is extremely slow when $T$ takes low values, i.e., agents (quite) often revise their strategy regarding which information to consider (if at all). Hence, trading based on fake news is likely to be observed often. This nicely agrees with the informal observation that agents often are myopic and do not allow themselves a long span of time $T$ to gather data and critically gauge the quality of the available news, see \cite{arthur96}.

An interesting interpretation of the model is the one in which informed agents are the ones who take positions in the market using active mutual funds, therefore using the costly signals and skills of fund managers capable, to some extent, to exploit information through stock timing or picking. Uninformed agents would then be investors taking passive and nearly fees-free ETF or index funds. For low values of $T$, the resulting market exhibits a substantial part of ETF users (passive investing), coupled with some traders who acquires the services of costly professional managers, who partially reveal the signal they privately own to other market participants. An informationally efficient situation cannot be attained but, additionally, in our model the market is often populated by many misinformed traders who trade on irrelevant info at best (or pure noise), generating occasional trends, excess volume and leptokurtic price distribution that closely mimicks some common stylized facts of financial time-series.

Bibliography

Arthur, W. Brian and Holland, John H. and LeBaron, Blake D. and Palmer, Richard G. and Tayler, Paul (1996) Asset Pricing Under Endogenous Expectations in an Artificial Stock Market. Available at SSRN: https://ssrn.com/abstract=2252 or http://dx.doi.org/10.2139/ssrn.2252

Black, F. (1986), Noise. The Journal of Finance, 41: 528-543. https://doi.org/10.1111/j.1540-6261.1986.tb04513.x

ABSTRACT. How do alternative institutions perform in informational and allocative efficiency under different environments? What part does agent intelligence (or information like knowing your trader role, or not, pre-market) play in the price discovery process, convergence, and equilibrating tendencies in markets with decentralized information? Questions like these have motivated experimental economists since the dawn of the discipline. Initial studies were motivated by testing standard microeconomic models of short-run competitive equilibrium in markets, focused on market environments for non-tradeable (perishable) goods with induced private values/costs (Chamberlin 1948; Smith 1962). The experiments in this type of environment that relied on the continuous double auction (CDA) trading institution revealed high efficiency and strong convergence to equilibrium (Smith 1962, 1965). Pioneering work using simulations showed that even using near-zero intelligence automaton traders, the CDA achieved high levels of allocative efficiency (Gode and Sunder 1993). A more recent strand of experimental research has focused on environments where agents have private values but no predefined role as either buyers or sellers. Thus there is scope for efficiency gains (or losses), but participants must discover their role in the market (Goeree and Zhang 2013; Dickhaut et al. 2012; Kotani, Tanaka, and Managi 2018). This literature has found that the CDA has a subpar performance in terms of informational and allocative efficiency. We are only starting to understand the performance of market institutions for these types of markets in terms of informational and allocative efficiency. In this paper, we report about 200,000 trading markets using simulations in a 2×2×5 full factorial design. Our main goal in this research project is to understand the role of different types of traders under alternative institutions and environments for a market where each agent has no predefined role, starts with an endowment of one unit, and has a positive value for up to one more unit. We generate data using simulations with either Zero Intelligence Agents (ZIA) or Minimal Intelligence Agents–the first factor. The second factor involves two alternative institutions: the aforementioned CDA and the Uniform Price Double Auction (UPDA) first proposed by McCabe, Rassenti, and Smith (1993). Finally, the third factor involves 5 possible environments: a symmetric environment (where in equilibrium total surplus is split even between producers and consumers), two asymmetric environments –where 76% of the equilibrium surplus was for the consumers (producers) in the asymmetric demand (supply) treatment—, and two extreme swastika environments –a la Smith (1965), where the 100% of the surplus goes to one side of the market. Thus, we have over 5,000 trading periods for each institution (2), operating in each environment (5) populated by a particular type of agents (2). In addition, we complement the simulations with experimental data with human traders (using both institutions in the original symmetric environment). In terms of informational efficiency, we find that ZIA average period prices are close to the price tunnel consistently across trading institutions and environments, although with a large variance (the standard deviation in the average market price in ZIA UPDA is 2X under CDA). MIA on the other hand performs quite well in terms of informational efficiency in the symmetric environment (and especially under the UPDA). But MIA performs poorly in the other environments with prices that deviate systematically from the competitive equilibrium price tunnel. As for allocative efficiency, we find that in these complex markets with no predefined roles, ZIA is unable to generate efficiency gains. Independent of trading institutions or environments, efficiency gains hover around zero (with a very large variance) and are as often positive as negative. Even in this complex environment, MIA can realize efficiency gains in every environment and every institution. However, in terms of allocative efficiency gains, MIA has a higher mean (92.8%) and lower standard deviation (13.8) under the UPDA institution relative to the CDA (mean 60.2%, SD 24.2). Furthermore, in the symmetric environment, they outperform humans in the UPDA treatment.

ABSTRACT. Trader behavior and market convergence are studied in a general equilibrium two good setting through the use of the continuous double auction. The transaction history varies across session in its accessibility. Congruently, the orderbook, which houses the traders' bids and asks, differs across sessions in the visual and interactive availability of active orders. The set of active bids and asks shown to traders in a session is either (1) only the best bid and ask in the market or (2) the full set of active orders; similarly, the set of visible transactions spans the full history of the trading period to only a trader's own transactions. I leverage this variation to identify the impacts of differing levels of market transparency on outcomes such as price and allocation efficiency, order volume and timing, and learning. As a set of benchmarks, I run simulations using variations of zero-intelligence (Gode and Sunder, 1993) and belief-based (Gjerstad and Dickhaut, 1998) trader behavior models adjusted for a pure exchange setting.Trader behavior and market convergence are studied in a general equilibrium two good setting through the use of the continuous double auction. The transaction history varies across session in its accessibility. Congruently, the orderbook, which houses the traders' bids and asks, differs across sessions in the visual and interactive availability of active orders. The set of active bids and asks shown to traders in a session is either (1) only the best bid and ask in the market or (2) the full set of active orders; similarly, the set of visible transactions spans the full history of the trading period to only a trader's own transactions. I leverage this variation to identify the impacts of differing levels of market transparency on outcomes such as price and allocation efficiency, order volume and timing, and learning. As a set of benchmarks, I run simulations using variations of zero-intelligence (Gode and Sunder, 1993) and belief-based (Gjerstad and Dickhaut, 1998) trader behavior models adjusted for a pure exchange setting.