F. K. Chow

Multiple choice minority game

Minority game is a model of heterogeneous players who think inductively. In this game, each player chooses one out of two alternatives every turn and those who end up in the minority side wins. It is instructive to extend the minority game by allowing players to choose one out of many alternatives. Nevertheless, such an extension is not straight-forward due to difficulties in finding a set of reasonable, unbiased and computationally feasible strategies. Here, we propose a variation of the minority game where every player has more than two options. Results of numerical simulations agree with the expectation that our multiple choices minority game exhibits similar behavior as the original two-choice minority game.

Minority game with peer pressure

To study the interplay between global market choice and local peer pressure, we construct a minority-game-like econophysical model. In this so-called networked minority game model, every selfish player uses both the historical minority choice of the population and the historical choice of ones neighbors in an unbiased manner to make decision. Results of numerical simulation show that the level of cooperation in the networked minority game differs remarkably from the original minority game as well as the prediction of the crowd–anticrowd theory. We argue that the deviation from the crowd–anticrowd theory is due to the negligence of the effect of a four point correlation function in the effective Hamiltonian of the system.

Social judgment theory based model on opinion formation, polarization and evolution

The dynamical origin of opinion polarization in the real world is an interesting topic that physical scientists may help to understand. To properly model the dynamics, the theory must be fully compatible with findings by social psychologists on microscopic opinion change. Here we introduce a generic model of opinion formation with homogeneous agents based on the well-known social judgment theory in social psychology by extending a similar model proposed by Jager and Amblard. The agents’ opinions will eventually cluster around extreme and/or moderate opinions forming three phases in a two-dimensional parameter space that describes the microscopic opinion response of the agents. The dynamics of this model can be qualitatively understood by mean-field analysis. More importantly, first-order phase transition in opinion distribution is observed by evolving the system under a slow change in the system parameters, showing that punctuated equilibria in public opinion can occur even in a fully connected social network.

Memory is relevant in the symmetric phase of the minority game

Minority game is a simple-mined econophysical model capturing the cooperative behavior among selfish players. Previous investigations, which were based on numerical simulations up to about 100 players for a certain parameter alpha in the range 0.1 < approximately alpha < approximately 1, suggested that memory is irrelevant to the cooperative behavior of the minority game in the so-called symmetric phase. Here using a large scale numerical simulation up to about 3000 players in the parameter range 0.01 < approximately alpha < approximately 1, we show that the mean variance of the attendance in the minority game actually depends on the memory in the symmetric phase. We explain such dependence in the framework of crowd-anticrowd theory. Our findings conclude that one should not overlook the feedback mechanism buried under the correlation in the history time series in the study of minority game.

How to attain maximum profit in minority game

What is the physical origin of player cooperation in minority game? And how to obtain maximum global wealth in minority game? We answer the above questions by studying a variant of minority game from which players choose among Nc alternatives according to strategies picked from a restricted set of strategy space. Our numerical experiment concludes that player cooperation is the result of a suitable size of sampling in the available strategy space. Hence, the overall performance of the game can be improved by suitably adjusting the strategy space size.

The relevance of memory in minority game

Minority Game (MG) has become a very commonly studied econophysical model in the past decade, after it was introduced in 1997. It is giving non-trivial cooperative behavior in multiple agent system, despite its simplicity. Since 1999, studies started focusing on whether the memory, which long seems believed to provide the feedback system, is essential in the game. Up till now, investigations concerning the memory in MG concluded that memory is relevant in the so-called asymmetric phase, but not the symmetric phase of the game. However, our recent study using large scale simulations (up to 3000 agents) shows that memory is actually also relevant in the symmetric phase. The fact that this was overlooked before might be due to the fact that small-scale simulations (around 100 agents ) were employed in previous investigations. This suggested that the memory of the game cannot be simply damped away in most of the parameter range.

Multiple choice minority game with different publicly known histories

In the standard minority game (MG), players use historical minority choices as the sole public information to pick one out of the two alternatives. However, publishing historical minority choices is not the only way to present global system information to players when more than two alternatives are available. Thus, it is instructive to study the dynamics and co-operative behaviours of this extended game as a function of the global information provided. We numerically find that, although the system dynamics depend on the kind of public information given to the players, the degree of co-operation follows the same trend as that of the standard MG. We also explain most of our findings by the crowd–anticrowd theory.

Playing the hypothesis testing minority game in the maximal reduced strategy space

Hypothesis Testing Minority Game (HMG) is a variant of the standard Minority Game (MG) that models the inertial behavior of agents in the market. In the earlier study of our group, we find that agents cooperate better in HMG than in the standard MG when strategies are picked from the full strategy space. Here we continue to study the behavior of HMG when strategies are chosen from the maximal reduced strategy space. Surprisingly, we find that, unlike the standard MG, the level of cooperation in HMG depends strongly on the strategy space used. In addition, a novel intermittency dynamics is also observed in the minority choice time series in a certain parameter range in which the orderly phases are characterized by a variety of periodic dynamics. Remarkably, all these findings can be explained by the crowd–anticrowd theory.