Generalized strategies in the minority game

Effects of contrarians in the minority game

We study the effects of the presence of contrarians in an agent-based model of competing populations. Contrarians are common in societies. These contrarians are agents who deliberately prefer to hold an opinion that is contrary to the prevailing idea of the commons or normal agents. Contrarians are introduced within the context of the minority game (MG), which is a binary model for an evolving and adaptive population of agents competing for a limited resource. The average success rate among the agents is found to have a nonmonotonic dependence on the fraction a(c) of contrarians. For small a(c), the contrarians systematically outperform the normal agents by avoiding the crowd effect and enhance the overall success rate. For high a(c), the anti-persistent nature of the MG is disturbed and the few normal agents outperform the contrarians. Qualitative discussion and analytic results for the small a(c) and high a(c) regimes are presented, and the crossover behavior between the two regimes is discussed.

Theory of networked minority games based on strategy pattern dynamics

We formulate a theory of agent-based models in which agents compete to be in a winning group. The agents may be part of a network or not, and the winning group may be a minority group or not. An important feature of the present formalism is its focus on the dynamical pattern of strategy rankings, and its careful treatment of the strategy ties which arise during the system's temporal evolution. We apply it to the minority game with connected populations. Expressions for the mean success rate among the agents and for the mean success rate for agents with k neighbors are derived. We also use the theory to estimate the value of connectivity p above which the binary-agent-resource system with high resource levels makes the transition into the high-connectivity state.

Error-driven global transition in a competitive population on a network

We show, both analytically and numerically, that erroneous data transmission generates a global transition within a competitive population playing the "Minority Game" on a network. This transition, which resembles a phase transition, is driven by a "temporal symmetry breaking" in the global outcome series. The phase boundary, which is a function of the network connectivity p and the error probability q, is described quantitatively by the crowd-anticrowd theory.

Evolutionary minority game: the roles of response time and mutation threshold

In the evolutionary minority game, agents are allowed to evolve their strategies ("mutate") based on past experience. We explore the dependence of the system's global behavior on the response time and the mutation threshold of the agents. We find that the precise values of these parameters determine if the strategy distribution of the population has a U shape, inverse U shape, or W shape. It is shown that in a free society (market), highly adaptive agents (with short response times) perform best. In addition, "patient" agents (with high mutation thresholds) outperform "nervous" ones.

Enhanced winning in a competing population by random participation

We study a version of the minority game in which one agent is allowed to join the game in a random fashion. It is shown that in the crowded regime, i.e., for small values of the memory size m of the agents in the population, the agent performs significantly well if she decides to participate the game randomly with a probability q and she records the performance of her strategies only in the turns that she participates. The information, characterized by a quantity called the inefficiency, embedded in the agent's strategies performance turns out to be very different from that of the other agents. Detailed numerical studies reveal a relationship between the success rate of the agent and the inefficiency. The relationship can be understood analytically in terms of the dynamics in which the various possible histories are being visited as the game proceeds. For a finite fraction of randomly participating agents up to 60% of the population, it is found that the winning edge of these agents persists.

Strategy updating rules and strategy distributions in dynamical multiagent systems

In the evolutionary version of the minority game, agents update their strategies (gene value p) in order to improve their performance. Motivated by the recent intriguing results obtained for prize-to-fine ratios, which are smaller than unity, we explore the system's dynamics with a strategy updating rule of the form p-->p+/-delta(p) (0<or=p<or=1). We find that the strategy distribution depends strongly on the values of the prize-to-fine ratio R, the length scale delta(p), and the type of boundary condition used. We show that these parameters determine the amplitude and the frequency of the temporal oscillations observed in the gene space. These regular oscillations are shown to be the main factors which determine the strategy distribution of the population. In addition, we find that the agents characterized by p=1/2 (a coin-tossing strategy) have the best chances of survival at asymptotically long times, regardless of the value of delta(p) and the boundary conditions used.

Temporal oscillations and phase transitions in the evolutionary minority game

The study of societies of adaptive agents seeking minority status is an active area of research. Recently, it has been demonstrated that such systems display an intriguing phase transition: agents tend to self-segregate or to cluster according to the value of the prize-to-fine ratio R. We show that such systems do not establish a true stationary distribution. The winning probabilities of the agents display temporal oscillations. The amplitude and frequency of the oscillations depend on the value of R. The temporal oscillations that characterize the system explain the transition in the global behavior from self-segregation to clustering in the R<1 case.

Deterministic dynamics in the minority game

The minority game (MG) behaves as a stochastically disturbed deterministic system due to the coin toss invoked to resolve tied strategies. Averaging over this stochasticity yields a description of the MG's deterministic dynamics via mapping equations for the strategy score and global information. The strategy-score map contains both restoring-force and bias terms, whose magnitudes depend on the game's quenched disorder. Approximate analytical expressions are obtained and the effect of "market impact" is discussed. The global-information map represents a trajectory on a de Bruijn graph. For small quenched disorder, a Eulerian trail represents a stable attractor. It is shown analytically how antipersistence arises. The response to perturbations and different initial conditions is also discussed.

Dynamics of the batch minority game with inhomogeneous decision noise

We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques à la De Dominicis. The control parameters in this model are the ratio alpha=p/N of the number p of possible values for the external information over the number N of trading agents, and the statistical properties of the agents' decision noise parameters. The presence of decision noise is found to have the general effect of damping macroscopic oscillations, which explains why in certain parameter regions it can effectively reduce the market volatility, as observed in earlier studies. In the limit N-->infinity we (i) solve the first few time steps of the dynamics (for any alpha), (ii) calculate the location alpha(c) of the phase transition (signaling the onset of anomalous response), and (iii) solve the statics for alpha>alpha(c). We find that alpha(c) is not sensitive to additive decision noise, but we arrive at nontrivial phase diagrams in the case of multiplicative noise. Our theoretical results find excellent confirmation in numerical simulations.