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Computational Complexity pp 1863–1879Cite as

Minority Games

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Article Outline

Glossary

Definition of the Subject

Introduction

The Minority Game

The Physical Properties of the Minority Game

Variants of the Minority Game

Analytic Approaches to the Minority Game

Minority Games and Financial Markets

Future Directions

Bibliography

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Abbreviations

Cumulated payoff:

It refers to the reward accumulation or the score counting for all the individual strategies being held by the agents in the game. Each strategy has itsown value of cumulated payoff.When a strategy gives a winning or losing prediction for the next round of the game (no matter whether the agents follow this prediction), scores are added to or deducted from this strategy respectively. It is also known as virtual point or virtual score of the strategies. The way of rewarding or penalizing is known as the payoff function.

Attendance:

In the contexts of the Minority Game, attendance refers to the collective sum of all agents’ actions at each round of the game. For the ordinary games, it is equal to the difference in the number of agents in choosing the two different choices or actions (in early formulation, it is equal to thenumber of agents in choosing one of the particular choice). The terminology “attendance” origins from the ancestor form of the Minority Game, the El Farol Bar problem by W.B. Arthur, in which agents choose whether to attend a bar at every round of the game.

Volatility:

Volatility in Minority Games is the time average variance of the attendance after each round of the game. It is an inverse measure of the efficiency of resource distribution in the game. A high volatility corresponds to large fluctuations in attendance and hence an inefficient game. A low volatility corresponds to smaller fluctuations in attendance and hence an efficient game.

Predictability:

It is an important macroscopic measurable in the game and also the order parameter which characterizes the major phase transition in the system. It is usually denoted by H which is a measure of non-uniform probabilistic outcome of the attendance given a certain information provided to the agents. A higher predictability refers to the case where attendance tends to be positive or negative for a certain piece of information, which makes the game outcome more predictable.

Symmetric and asymmetric phase:

The two important phases of the system. The symmetric phase is also known as crowded phase or the unpredictable phase. The asymmetric phase is also known as uncrowded phase, the dilute phase or the predictable phase. The system’s behaviors, dynamics and characteristics are different in these two phases. The two phases are characterized by the order parameter, called the predictability H.

Endogenous and exogenous games:

Endogenous games refer to games which utilize the past winning history to generate signals or information for agents to makedecisions in the next round. Endogenous games are also known as games with real history. Exogenous games refer to games which utilize random signals or information for agents to make decisions in the next round.Exogenous games are also known as games with random history, or external information.

On-line update and batch update:

On-line update refers to the evaluation of payoffs of strategies after each round of the game. Thus, the priority of strategies being employed by an agent may be altered after any round of the game. The exogenous game or random history game sometimes employ the batch update method which refers to the evaluation of payoffs on strategies only after a fixed number of rounds where all the possible signals or information have appeared. In games with ordinary batch update, all the possible signals appear once in each batch before the update of payoffs on strategies, the order of appearance of signals in each batch is thus irrelevant.

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  4. Minority Game’s website: http://www.unifr.ch/econophysics/minority/

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Author information

Authors and Affiliations

  1. Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China

    Chi Ho Yeung & Yi-Cheng Zhang

  2. Département de Physique, Université de Fribourg, Pérolles, Fribourg, Switzerland

    Chi Ho Yeung & Yi-Cheng Zhang

  3. School of Management, University of Electronic Science and Technology of China (UESTC), Chengdu, China

    Chi Ho Yeung & Yi-Cheng Zhang

Authors
  1. Chi Ho Yeung
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  2. Yi-Cheng Zhang
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Yeung, C., Zhang, YC. (2012). Minority Games. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_121

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