Index of authors and papers to Volume 360

Payoffs which depend on the scores of the strategies are introduced into the standard Minority Game (MG). The double-periodicity behavior of the standard model is consequently removed, and stylized facts arise, such as long-range volatility correlations and “fat-tails” of the probability distribution of the returns. Furthermore, the score-dependent payoffs could coexist with the inactive strategy in the grand canonical MG, and play an important role in the thermal MG.     

Emergence of trend trading and its effects in minority game

In this paper, we extended Minority Game (MG) by equipping agents with both value and trend strategies. In the new model, agents (we call them strong-adaptation agents) can autonomically select to act as trend trader or value trader when they game and learn in system. So the new model not only can reproduce stylized factors but also has the potential to investigate into the process of some problems of securities market. We investigated the dynamics of trend trading and its impacts on securities market based on the new model. Our research found that trend trading is inevitable when strong-adaptation agents make decisions by inductive reasoning. Trend trading (of strong-adaptation agents) is not irrational behavior but shows agent's strong-adaptation intelligence, because strong-adaptation agents can take advantage of the pure value agents when they game together in hybrid system. We also found that strong-adaptation agents do better in real environment. The results of our research are different with those of behavior finance researches.     

Crowd-anticrowd theory of multi-agent market games

We present a dynamical theory of a multi-agent market game, the so-called Minority Game (MG), based on crowds and anticrowds. The time-averaged version of the dynamical equations provides a quantitatively accurate, yet intuitively simple, explanation for the variation of the standard deviation (`volatility') in MG-like games. We demonstrate this for the basic MG, and the MG with stochastic strategies. The time-dependent equations themselves reproduce the essential dynamics of the MG. Received 28 August 2000 and Received in final form 23 September 2000     

Incomplete strategy effect in Minority Game

We perform simulations with the extended Incomplete Minority Game model, and find that limited incompleteness in strategies can improve the system efficiency greatly. There is a critical p_Ic such that agents in a system can get the best cooperation. The critical strategy density value α_c decreases monotonously with the increase of p_I. We also mix incomplete strategy agents with standard strategy agents to study the effect of incompleteness distribution on system properties and group average profit. Concentration of incompleteness weakens its effect. When p_I is close to zero, agents using incomplete strategies averagely have better profits than those using standard strategies.     

The $-game

We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In contrast with previous MG, the best strategies are not always targeting the minority but are shifting opportunistically between the minority and the majority. The emergent properties of the price dynamics and of the wealth of agents are strikingly different from those found in MG. As the memory of agents is increased, we find a phase transition between a self-sustained speculative phase in which a “stubborn majority” of agents effectively collaborate to arbitrage a market-maker for their mutual benefit and a phase where the market-maker always arbitrages the agents. A subset of agents exhibit a sustained non-equilibrium risk-return profile. Received 5 June 2002 / Received in final form 21 November 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: sornette@unice.fr RID="b" ID="b"CNRS UMR7536 RID="c" ID="c"CNRS UMR6622     

Analytical model for minority games with evolutionary learning

In a recent work [D. Campos, J.E. Llebot, V. Méndez, Theor. Popul. Biol. 74 (2009) 16] we have introduced a biological version of the Evolutionary Minority Game that tries to reproduce the intraspecific competition for limited resources in an ecosystem. In comparison with the complex decision-making mechanisms used in standard Minority Games, only two extremely simple strategies (juveniles and adults) are accessible to the agents. Complexity is introduced instead through an evolutionary learning rule that allows younger agents to learn taking better decisions. We find that this game shows many of the typical properties found for Evolutionary Minority Games, like self-segregation behavior or the existence of an oscillation phase for a certain range of the parameter values. However, an analytical treatment becomes much easier in our case, taking advantage of the simple strategies considered. Using a model consisting of a simple dynamical system, the phase diagram of the game (which differentiates three phases: adults crowd, juveniles crowd and oscillations) is reproduced.     

Illusory versus genuine control in agent-based games

In the Minority, Majority and Dollar Games (MG, MAJG, $G) agents compete for rewards, acting in accord with the previously best-performing of their strategies. Different aspects/kinds of real-world markets are modelled by these games. In the MG, agents compete for scarce resources; in the MAJG agents imitate the group to exploit a trend; in the $G agents attempt to predict and benefit both from trends and changes in the direction of a market. It has been previously shown that in the MG for a reasonable number of preliminary time steps preceding equilibrium (Time Horizon MG, THMG), agents’ attempt to optimize their gains by active strategy selection is “illusory”: the hypothetical gains of their strategies is greater on average than agents’ actual average gains. Furthermore, if a small proportion of agents deliberately choose and act in accord with their seemingly worst performing strategy, these outperform all other agents on average, and even attain mean positive gain, otherwise rare for agents in the MG. This latter phenomenon raises the question as to how well the optimization procedure works in the THMAJG and TH$G. We demonstrate that the illusion of control is absent in THMAJG and TH$G. This provides further clarification of the kinds of situations subject to genuine control, and those not, in set-ups a priori defined to emphasize the importance of optimization.     

Strategy correlations and timing of adaptation in Minority Games

We study the role of strategy correlations and timing of adaptation for the dynamics of Minority Games, both simulationally and analytically. Using the exact generating functional approach à la De Dominicis we compute the phase diagram and the behaviour of batch and on-line games with correlated strategies, complementing exisiting replica studies of their statics. It is shown that the timing of adaptation can be relevant; while conventional games with uncorrelated strategies are nearly insensitive to the choice of on-line versus batch learning, we find qualitative differences when anti-correlations are present in the strategy assignments. The available standard approximations for the volatility in terms of persistent order parameters in the stationary ergodic states become unreliable in batch games under such circumstances. We then comment on the role of oscillations and the relation to the breakdown of ergodicity. Finally, it is discussed how the generating functional formalism can be used to study mixed populations of so-called ‘producers’ and ‘speculators’ in the context of the batch Minority Games.     

Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

We discuss a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game. As in markets, agents interact through a collective aggregate variable — which plays a role similar to price — whose value is fixed by all of them. Agents follow a simple reinforcement-learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy. We derive the exact solution of the model in the “thermodynamic” limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the market price plays a key role: even though price has a weak dependence on the behavior of each individual agent, the collective behavior crucially depends on whether agents account for such dependence or not. Remarkably, if the adaptive behavior of agents accounts even “infinitesimally” for this dependence they can, in a whole range of parameters, reduce global fluctuations by a finite amount. Both global efficiency and individual utility improve with respect to a “price taker” behavior if agents account for their market impact.     

The minority game with incomplete strategies

This paper proposes a new model of Incomplete Minority Game (IMG), which features a default hierarchy of rules. This model introduces random bits into players’ individual strategies and is capable of applying the exception rules in the absence of the default one. Analysis of the numerical experiment results indicates that, in comparison with the standard Minority Game (SMG) model, this IMG model expands the maximum ensemble of uncorrelated strategies (MEUS) and excels in the effective strategy set and dynamic evolution of individual strategies, which enhance the overall performance by reaching an approximate ideal status in a shorter time with less memory steps and more stable combination of strategies. This paper also discusses the practical implication of the new IMG model.     

The Interactive Minority Game: a Web-based investigation of human market interactions

The unprecedented access offered by the World Wide Web brings with it the potential to gather huge amounts of data on human activities. Here we exploit this by using a toy model of financial markets, the Minority Game (MG), to investigate human speculative trading behaviour and information capacity. Hundreds of individuals have played a total of tens of thousands of game turns against computer-controlled agents in the Web-based Interactive Minority Game. The analytical understanding of the MG permits fine-tuning of the market situations encountered, allowing for investigation of human behaviour in a variety of controlled environments. In particular, our results indicate a transition in players’ decision-making, as the markets become more difficult, between deductive behaviour making use of short-term trends in the market, and highly repetitive behaviour that ignores entirely the market history, yet outperforms random decision-making.     

A tractable evolutionary model for the Minority Game with asymmetric payoffs

We set up a simple behavioral model for a large population of agents who are repeatedly playing the Minority Game and whose interaction is modeled by means of the so-called replicator dynamics. This allows us to specify the dynamics of the aggregate variables, the number of agents choosing each side, in terms of a low-dimensional dynamical system that gives qualitatively the same results of the existing computational approaches. As an extension we introduce asymmetric payoffs, i.e., we analyze the case where the minority and majority payoffs are side dependent. In this case the fluctuations out of the equilibrium are qualitatively different. In particular, contrary to the previous case, they are associated with a difference in the average payoff gained by each side. Furthermore, a parameter region exists where the dynamics does not converge to any isolated periodic attractor.     

”Illusion of control” in Time-Horizon Minority and Parrondo Games

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive [J.D. Taylor, S.E. Brown, Psych. Bull. 103, 193 (1988); A. Bandura, Self-efficacy: the exercise of control (WH Freeman, New York, 1997)]. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate [E. Langer, J. Pers. Soc. Psych. 7, 185 (1975)] or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Time-Horizon Minority Game [M.L. Hart, P. Jefferies, N.F. Johnson, Phys. A 311, 275 (2002)] and the Parrondo Game [J.M.R. Parrondo, G.P. Harmer, D. Abbott, Phys. Rev. Lett. 85, 5226 (2000); J.M.R. Parrondo, How to cheat a bad mathematician (ISI, Italy, 1996)], that agents who optimize their strategy based on past information may actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the “illusion of control” in certain set-ups a priori defined to emphasize the importance of optimization. An erratum to this article is available at .     

Evolutionary games on scale-free networks with a preferential selection mechanism

Considering the heterogeneity of individuals’ influence in the real world, we introduce a preferential selection mechanism to evolutionary games (the Prisoner’s Dilemma Game and the Snowdrift Game) on scale-free networks and focus on the cooperative behavior of the system. In every step, each agent chooses an individual from all its neighbors with a probability proportional to k^α indicating the influence of the neighbor, where k is the degree. Simulation results show that the cooperation level has a non-trivial dependence on α. To understand the effect of preferential selection mechanism on the evolution of the system, we investigate the time series of the cooperator frequency in detail. It is found that the cooperator frequency is greatly influenced by the initial strategy of hub nodes when α>0. This observation is confirmed by investigating the system behavior when some hub nodes’ strategies are fixed.     

The effects of behavioral and structural assumptions in artificial stock market

Recent literature has developed the conjecture that important statistical features of stock price series, such as the fat tails phenomenon, may depend mainly on the market microstructure. This conjecture motivated us to investigate the roles of both the market microstructure and agent behavior with respect to high-frequency returns and daily returns. We developed two simple models to investigate this issue. The first one is a stochastic model with a clearing house microstructure and a population of zero-intelligence agents. The second one has more behavioral assumptions based on Minority Game and also has a clearing house microstructure. With the first model we found that a characteristic of the clearing house microstructure, namely the clearing frequency, can explain fat tail, excess volatility and autocorrelation phenomena of high-frequency returns. However, this feature does not cause the same phenomena in daily returns. So the Stylized Facts of daily returns depend mainly on the agents’ behavior. With the second model we investigated the effects of behavioral assumptions on daily returns. Our study implicates that the aspects which are responsible for generating the stylized facts of high-frequency returns and daily returns are different.     

Bubbles,crashes and intermittency in agent based market models

We define and study a rather complex market model, inspired from the Santa Fe artificial market and the Minority Game. Agents have different strategies among which they can choose, according to their relative profitability, with the possibility of not participating to the market. The price is updated according to the excess demand, and the wealth of the agents is properly accounted for. Only two parameters play a significant role: one describes the impact of trading on the price, and the other describes the propensity of agents to be trend following or contrarian. We observe three different regimes, depending on the value of these two parameters: an oscillating phase with bubbles and crashes, an intermittent phase and a stable `rational' market phase. The statistics of price changes in the intermittent phase resembles that of real price changes, with small linear correlations, fat tails and long range volatility clustering. We discuss how the time dependence of these two parameters spontaneously drives the system in the intermittent region. We analyze quantitatively the temporal correlation of activity in the intermittent phase, and show that the `random time strategy shift' mechanism that we proposed earlier allows one to understand the observed long ranged correlations. Other mechanisms leading to long ranged correlations are also reviewed. We discuss several other issues, such as the formation of bubbles and crashes, the influence of transaction costs and the distribution of agents wealth. Received 5 July 2002 / Received in final form 9 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: irene.giardina@roma1.infn.it     

Study on system dynamics of evolutionary mix-game models

Mix-game model is ameliorated from an agent-based MG model, which is used to simulate the real financial market. Different from MG, there are two groups of agents in Mix-game: Group 1 plays a majority game and Group 2 plays a minority game. These two groups of agents have different bounded abilities to deal with historical information and to count their own performance. In this paper, we modify Mix-game model by assigning the evolution abilities to agents: if the winning rates of agents are smaller than a threshold, they will copy the best strategies the other agent has; and agents will repeat such evolution at certain time intervals. Through simulations this paper finds: (1) the average winning rates of agents in Group 1 and the mean volatilities increase with the increases of the thresholds of Group 1; (2) the average winning rates of both groups decrease but the mean volatilities of system increase with the increase of the thresholds of Group 2; (3) the thresholds of Group 2 have greater impact on system dynamics than the thresholds of Group 1; (4) the characteristics of system dynamics under different time intervals of strategy change are similar to each other qualitatively, but they are different quantitatively; (5) As the time interval of strategy change increases from 1 to 20, the system behaves more and more stable and the performances of agents in both groups become better also.     

Diversity of scales makes an advantage: The case of the Minority Game

We use the Minority Game as a testing frame for the problem of the emergence of diversity in socio-economic systems. For the MG with heterogeneous impacts, we show that the direct generalisation of the usual agents’ profit does not fit some real-world situations. As a typical example we use the traffic formulation of the MG. Taking into account vehicles of various lengths it can easily happen that one of the roads is crowded by a few long trucks and the other contains more drivers but still is less covered by vehicles. Most drivers are in the shorter queue, so the majority win. To describe such situations, we generalised the formula for agents’ profit by explicitly introducing a utility function depending on an agent’s impact. Then, the overall profit of the system may become positive depending on the actual choice of the utility function. We investigated several choices of the utility function and showed that this variant of the MG may turn into a positive sum game.     

Evolutionary ultimatum game on complex networks under incomplete information

This paper studies the evolutionary ultimatum game on networks when agents have incomplete information about the strategies of their neighborhood agents. Our model assumes that agents may initially display low fairness behavior, and therefore, may have to learn and develop their own strategies in this unknown environment. The Genetic Algorithm Learning Classifier System (GALCS) is used in the model as the agent strategy learning rule. Aside from the Watts-Strogatz (WS) small-world network and its variations, the present paper also extends the spatial ultimatum game to the Barabási-Albert (BA) scale-free network. Simulation results show that the fairness level achieved is lower than in situations where agents have complete information about other agents’ strategies. The research results display that fairness behavior will always emerge regardless of the distribution of the initial strategies. If the strategies are randomly distributed on the network, then the long-term agent fairness levels achieved are very close given unchanged learning parameters. Neighborhood size also has little effect on the fairness level attained. The simulation results also imply that WS small-world and BA scale-free networks have different effects on the spatial ultimatum game. In ultimatum game on networks with incomplete information, the WS small-world network and its variations favor the emergence of fairness behavior slightly more than the BA network where agents are heterogeneously structured.     

In search for the optimal strategy in population dynamics

A unification of recently proposed models describing population dynamics is presented. We study the effect of different factors, like environmental conditions, concentration of individuals in a given area and migration strategies, on population dynamics. Moreover, we show that a population occupying a smaller area is more susceptible to extinction, which is a well known biological fact. We solve the model using Monte Carlo simulations and the mean-field approach. Constructing flow diagrams we find the optimal strategy in population dynamics. Received 10 June 2001 and Received in final form 22 November 2001