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Register a new userDynamical instabilities in a simple minority game with discounting
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We explore the effect of discounting and experimentation in a simple model of interacting adaptive agents. Agents belong to either of two types and each has to decide whether to participate a game or not, the game being profitable when there is an excess of players of the other type. We find the emergence of large fluctuations as a result of the onset of a dynamical instability which may arise discontinuously (increasing the discount factor) or continuously (decreasing the experimentation rate). The phase diagram is characterized in detail and noise amplification close to a bifurcation point is identified as the physical mechanism behind the instability.
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We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which perception affects reality. By varying the `reality map, which relates the amount wagered to the probability of the outcome, it is possible to move continuously from a purely objective game in which probabilities have no dependence on wagers, to a purely subjective game in which probabilities equal the amount wagered. The reality map can reflect self-reinforcing strategies or self-defeating strategies. In self-reinforcing games, rational players can achieve increasing returns and manipulate the outcome probabilities to their advantage; consequently, an early lead in the game, whether acquired by chance or by strategy, typically gives a persistent advantage. We investigate the game both in and out of equilibrium and with and without rational players. We introduce a method of measuring the inefficiency of the game and show that in the large time limit the inefficiency decreases slowly in its approach to equilibrium as a power law with an exponent between zero and one, depending on the subjectivity of the game.
We introduce a version of the Minority Game where the total number of available choices is $D>2$, but the agents only have two available choices to switch. For all agents at an instant in any given choice, therefore, the other choice is distributed between the remaining $D-1$ options. This brings in the added complexity in reaching a state with the maximum resource utilization, in the sense that the game is essentially a set of MG that are coupled and played in parallel. We show that a stochastic strategy, used in the MG, works well here too. We discuss the limits in which the model reduces to other known models. Finally, we study an application of the model in the context of population movement between various states within a country during an ongoing epidemic. We show that the total infected population in the country could be as low as that achieved with a complete stoppage of inter-region movements for a prolonged period, provided that the agents instead follow the above mentioned stochastic strategy for their movement decisions between their two choices. The objective for an agent is to stay in the lower infected state between their two choices. We further show that it is the agents moving once between any two states, following the stochastic strategy, who are less likely to be infected than those not having (or not opting for) such a movement choice, when the risk of getting infected during the travel is not considered. This shows the incentive for the moving agents to follow the stochastic strategy.
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.
In this paper the extended model of Minority game (MG), incorporating variable number of agents and therefore called Grand Canonical, is used for prediction. We proved that the best MG-based predictor is constituted by a tremendously degenerated system, when only one agent is involved. The prediction is the most efficient if the agent is equipped with all strategies from the Full Strategy Space. Each of these filters is evaluated and, in each step, the best one is chosen. Despite the casual simplicity of the method its usefulness is invaluable in many cases including real problems. The significant power of the method lies in its ability to fast adaptation if lambda-GCMG modification is used. The success rate of prediction is sensitive to the properly set memory length. We considered the feasibility of prediction for the Minority and Majority games. These two games are driven by different dynamics when self-generated time series are considered. Both dynamics tend to be the same when a feedback effect is removed and an exogenous signal is applied.
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