arXiv subjects
Publications and source records attributed to Yi-Cheng Zhang.
Minority games where groups of agents remember, react or incorporate information with different timescales are investigated. We study how their respective gains depend on their timescales for standard models and games with no public information, and support our findings by analytical arguments whenever possible.
We analyze some voting models mimicking online evaluation systems intended to reduce the information overload. The minimum number of operations needed for a system to be effective is analytically estimated. When herding effects are present, linear preferential attachment marks a transition between trustful and biased reputations.
We analyze different methods of sorting and selecting a set of objects by their intrinsic value, via pairwise comparisons whose outcome is uncertain. After discussing the limits of repeated Round Robins, two new methods are presented: The {\it ran-fil} requires no previous knowledge on the set under consideration, yet displaying good performances even in the least favorable case. The {\it min-ent} method sets a benchmark for optimal dynamic tournaments design.
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. PACS: 02.50.Le; 89.65.Gh; 89.70.+c Keywords: Decision theory and game theory; Economics and financial markets; Information theory
We analyze different ways of pairing agents in a bipartite matching problem, with regard to its scaling properties and to the distribution of individual ``satisfactions''. Then we explore the role of partial information and bounded rationality in a generalized {\it Marriage Problem}, comparing the benefits obtained by self-searching and by a matchmaker. Finally we propose a modified matching game intended to mimic the way consumers' information makes firms to enhance the quality of their products in a competitive market.
The Interactive Minority Game (IMG) is an online version of the traditional Minority Game in which human players can enter into competition with the traditional computer-controlled agents. Through the rich (and, importantly, analytically understood) behaviour of the MG, we can explore humans' behaviour in different kinds of market--crowded, efficient, critical--with a high degree of control. To make the game easily understandable even to those who are encountering it for the first time, we have presented the game with a rather simplified interface; in this working paper we explain the underlying technical aspects for those who have experience with the traditional MG.
We propose a continuum model for the description of buyer and seller dynamics in an Internet market. The relevant variables are the research effort of buyers and the sellers' reputation building process. We show that, if a commercial web-site gives consumers the possibility to rate credibly sellers they bargained with, vendors are forced to be more honest. This leads to mutual beneficial symbiosis between buyers and sellers; the overall enhanced volume of transactions contributes ultimately to the web-site, which facilitates the matchmaking service.
We develop a method allowing us to reconstruct individual tastes of customers from a sparsely connected network of their opinions on products, services, or each other. Two distinct phase transitions occur as the density of edges in this network is increased: above the first - macroscopic prediction of tastes becomes possible, while above the second - all unknown opinions can be uniquely reconstructed. We illustrate our ideas using a simple Gaussian model, which we study using both field-theoretical methods and numerical simulations. We point out a potential relevance of our approach to the field of bioinformatics.
We provide the probability distribution function of matrix elements each of which is the inner product of two vectors. The vectors we are considering here are independently distributed but not necessarily Gaussian variables. When the number of components M of each vector is greater than the number of vectors N, one has a $N\times N$ symmetric matrix. When $M\ge N$ and the components of each vector are independent Gaussian variables, the distribution function of the $N(N+1)/2$ matrix elements was obtained by Wishart in 1928. When N > M, what we called the ``Anti-Wishart'' case, the matrix elements are no longer completely independent because the true degrees of freedom becomes smaller than the number of matrix elements. Due to this singular nature, analytical derivation of the probability distribution function is much more involved than the corresponding Wishart case. For a class of general random vectors, we obtain the analytical distribution function in a closed form, which is a product of various factors and delta function constraints, composed of various determinants. The distribution function of the matrix element for the $M\ge N$ case with the same class of random vectors is also obtained as a by-product. Our result is closely related to and should be valuable for the study of random magnet problem and information redundancy problem.
I summarize the recent work on market (in)efficiency, highlighting key elements why financial markets will never be made efficient. My approach is not by adding more empirical evidence, but giving plausible reasons as to where inefficiency arises and why it's not rational to arbitrage it away.
We explore the consequences of incomplete information in the stable marriage problem. When information capacity of the participants is increased, more favorable games are created and the quality of the matches are also better. The simple model serves as a metaphor for a world with ever more computing power that leads to more positive inter-personal interactions and of higher quality.
We study the role of active and passive investors in an investment market with uncertainties. Active investors concentrate on a single or a few stocks with a given probability of determining the quality of them. Passive investors spread their investment uniformly, resembling buying the market index. In this toy market stocks are introduced as good and bad. If a stock receives sufficient investment it will survive, otherwise die. Active players exert a selective pressure since they can determine to an extent the investment quality. We show that the active players provide the driving force whereas the passive ones act as free riders. While their gains do not differ too much, we show that the active players enjoy an edge. Their presence also provides better gains to the passive players and stocks themselves.
We present and study a Minority Game based model of a financial market where adaptive agents -- the speculators -- interact with deterministic agents -- called producers. Speculators trade only if they detect predictable patterns which grant them a positive gain. Indeed the average number of active speculators grows with the amount of information that producers inject into the market. Transitions between equilibrium and out of equilibrium behavior are observed when the relative number of speculators to the complexity of information or to the number of producers are changed. When the system is out of equilibrium, stylized facts arise, such as fat tailed distribution of returns and volatility clustering. Without speculators, the price follows a random walk; this implies that stylized facts arise because of the presence of speculators. Furthermore, if speculators abandon price taking behavior, stylized facts disappear.
We study the properties of the ``Rigid Laplacian'' operator, that is we consider solutions of the Laplacian equation in the presence of fixed truncation errors. The dynamics of convergence to the correct analytical solution displays the presence of a metastable set of numerical solutions, whose presence can be related to granularity. We provide some scaling analysis in order to determine the value of the exponents characterizing the process. We believe that this prototype model is also suitable to provide an explanation of the widespread presence of power-law in social and economic system where information and decision diffuse, with errors and delay from agent to agent.
We study a new evolutionary game, where players are tempted to take part by the premium, but compete for being the first who take a specific move. Those, who manage to escape the bulk of players, are the winners. While for large premium the game is very similar to the Minority Game studied earlier, significant new behavior, reminiscent of spin glasses is observed for premium below certain level.
We study investment strategy in different models of financial markets, where the investors cannot reach a perfect knowledge about available assets. The investor spends a certain effort to get information; this allows him to better choose the investment strategy, and puts a selective pressure upon assets. The best strategy is then a compromise between diversification and effort to get information.
Using the Minority Game model we study a broad spectrum of problems of market mechanism. We study the role of different types of agents: producers, speculators as well as noise traders. The central issue here is the information flow : producers feed in the information whereas speculators make it away. How well each agent fares in the common game depends on the market conditions, as well as their sophistication. Sometimes there is much to gain with little effort, sometimes great effort virtually brings no more incremental gain. Market impact is shown to play also an important role, a strategy should be judged when it is actually used in play for its quality. Though the Minority Game is an extremely simplified market model, it allows to ask, analyze and answer many questions which arise in real markets.
A model of open economics composed of producers and speculators is investigated by numerical simulations. The capital flows from the environment to the producers and from them to the speculators. The price fluctuations are suppressed by the speculators. When the aggressivity of the speculators grows, there is a transition from the regime with almost sure profit to a very risky regime in which very small fraction of speculators have stable gain. The minimum of price fluctuations occurs close to the transition.