Abstract:
A Lempel-Ziv complexity measure is introduced into the theory of a Minority Game (MG) in order to capture some features that volatility, one of the central quantities in this model of interacting agents, is not able to. Extracted solely from the binary string of outcomes of the game complexity offers new and valuable information on collective behavior of players. Also, we show that an expression for volatility may be included in the analytical expression for complexity.

Abstract:
In this paper, we study the algorithmic complexity of the Mastermind game, where results are single-color black pegs. This differs from the usual dual-color version of the game, but better corresponds to applications in genetics. We show that it is NP-complete to determine if a sequence of single-color Mastermind results have a satisfying vector. We also show how to devise efficient algorithms for discovering a hidden vector through single-color queries. Indeed, our algorithm improves a previous method of Chvatal by almost a factor of 2.

Abstract:
We provide some examples showing how game-theoretic arguments can be used in computability theory and algorithmic information theory: unique numbering theorem (Friedberg), the gap between conditional complexity and total conditional complexity, Epstein--Levin theorem and some (yet unpublished) result of Muchnik and Vyugin

Abstract:
In the standard minority game, each agent in the minority group receives the same payoff regardless of the size of the minority group. Of great interest for real social and biological systems are cases in which the payoffs to members of the minority group depend on the size of the minority group. This latter includes the fixed sum game. We find, remarkably, that the phase structure and general scaling behavior of the standard minority game persists when the payoff function depends on the size of the minority group. there is still a phase transition at the same value of z, the ratio of the dimension of the strategy space to the number of agents playing the game. We explain the persistence of the phase structure and argue that it is due to the absence of temporal cooperation in the dynamics of the minority game. We also discuss the behavior of average agent wealth and the wealth distribution in these variable payoff games.

Abstract:
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 the 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.

Abstract:
This paper gives a critical account of the minority game literature. The minority game is a simple congestion game: players need to choose between two options, and those who have selected the option chosen by the minority win. The learning model proposed in this literature seems to differ markedly from the learning models commonly used in economics. We relate the learning model from the minority game literature to standard game-theoretic learning models, and show that in fact it shares many features with these models. However, the predictions of the learning model differ considerably from the predictions of most other learning models. We discuss the main predictions of the learning model proposed in the minority game literature, and compare these to experimental findings on congestion games.

Abstract:
Ecologists and economists try to explain collective behavior in terms of competitive systems of selfish individuals with the ability to learn from the past. Statistical physicists have been investigating models which might contribute to the understanding of the underlying mechanisms of these systems. During the last three years one intuitive model, commonly referred to as the Minority Game, has attracted broad attention. Powerful yet simple, the minority game has produced encouraging results which can explain the temporal behaviour of competitive systems. Here we switch the interest to phenomena due to a distribution of the individuals in space. For analyzing these effects we modify the Minority Game and the Local Minority Game is introduced. We study the system both numerically and analytically, using the customary techniques already developped for the ordinary Minority Game.

Abstract:
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 one's 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.

Abstract:
We analyze the minority game for patients, and the results known from the minority game are applied to the patient problem consulted at the department of pediatric cardiology. We find numerically the standard deviation and the global efficiency, similar to the El Farol bar problem. After the score equation and the scaled utility are introduced, the dynamical behavior of our model is discussed for particular strategies. Our result presented will be compared with the well-known minority games.

Abstract:
It is known that the memory is relevant in the symmetric phase of the minority game. In our previous work we have successfully explained the quasi-periodic behavior of the game in the symmetric phase with the help of the probability theory. Based on this explanation, we are able to determine how the memory affects the variance of the system in this paper. By using some particular types of fake history such as periodic type and random type, we determine how efficient the memory has been used in the standard game. Furthermore, the analysis on the effective memory strongly supports the result we proposed previously that there are three distinct phases in the minority game.