Schrödinger’s Ants: A Continuous Description of Kirman’s Recruitment Model

Moran, José; Fosset, Antoine; Benzaquen, Michael; Bouchaud, Jean‐Philippe

doi:10.2139/ssrn.3575759

Cited by 7 publications

(36 citation statements)

References 30 publications

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“…2 reveals that the empirical distributions of n A and n P are remarkably well fitted by a Beta distribution. This is exactly what one obtains in Kirman and Föllmer's ant recruitment model [8,9], in which the Beta distribution emerges as the stationary distribution describing a colony of ants preying on two distinct food sources. Such a distribution also emerges as the stationary distribution describing genetic populations between two competing alleles [10,11].…”

Section: Stylized Factssupporting

confidence: 72%

“…In the model, at each time step a given ant may either (i) encounter another ant from the other inexhaustible food source and decide to switch to her peer's source (be recruited), or (ii) spontaneously decide to switch food sources without interacting. The driving mechanism of the dynamics results from the trade-off between the intensity of the noise-term (spontaneous switching), and that of the interaction term µ, see also [9].…”

Section: A Simple Modelmentioning

confidence: 99%

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From Ants to Fishing Vessels: A Simple Model for Herding and Exploitation of Finite Resources

Morán¹,

Fosset²,

Kirman³

et al. 2020

Preprint

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We analyse the dynamics of fishing vessels with different home ports in an area where these vessels, in choosing where to fish, are influenced by their own experience in the past and by their current observation of the locations of other vessels in the fleet. Empirical data from the boats near Ancona and Pescara shows stylized statistical properties that are reminiscent of Kirman and Föllmer's ant recruitment model, although with two ant colonies represented by the two ports. From the point of view of a fisherman, the two fishing areas are not equally attractive, and he tends to prefer the one closer to where he is based. This piece of evidence led us to extend the original ants model to a situation with two asymmetric zones and finite resources. We show that, in the mean-field regime, our model exhibits the same properties as the empirical data. We obtain a phase diagram that separates high and low herding regimes, but also fish population extinction. Our analysis may have interesting policy implications for the ecology of fishing areas.

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Section: Stylized Factssupporting

confidence: 72%

Section: A Simple Modelmentioning

confidence: 99%

From Ants to Fishing Vessels: A Simple Model for Herding and Exploitation of Finite Resources

Morán¹,

Fosset²,

Kirman³

et al. 2020

Preprint

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“…In fact, this time can be rather accurately computed by changing variables from P to φ where P = (1 + sin φ)/2, which allows one to get rid of the factor P(1 − P) in front of the Wiener noise, see e.g. Moran et al (2020a). Using a standard approach (e.g.…”

Section: Discussionmentioning

confidence: 99%

“…When δ → 0, the distribution of P becomes highly peaked around 0 and 1. This model is studied in detail inMoran et al (2020a) who show that the time spent by Pt in the vicinity of 0 or 1 is equal to δ −1 and is independent of λ. This switching time also corresponds to the ergodic time defined as the time required for P to approach the stationary distribution P 0 .…”

mentioning

confidence: 99%

Self-Fulfilling Prophecies, Quasi Non-Ergodicity and Wealth Inequality

Bouchaud¹,

Farmer²

2020

Preprint

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We construct a model where people trade assets contingent on an observable signal that reflects public opinion. The agents in our model are replaced occasionally and each person updates beliefs in response to observed outcomes. We show that the distribution of the observed signal is described by a quasi non-ergodic process and that people continue to disagree with each other forever. Our model generates large wealth inequalities that arise from the multiplicative nature of wealth dynamics which makes successful bold bets highly profitable. The flip side of this statement is that unsuccessful bold bets are ruinous and lead the person who makes such bets into poverty. People who agree with the market belief have a low expected subjective gain from trading. People who disagree may either become spectacularly rich, or spectacularly poor.

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“…This is connected to more recent research, where analogous classes of behaviour, under different types of memory kernels, govern whether an agent freely explores the space of choices or becomes trapped by "force of habit" [7]. Other examples of trapping, for at least long periods of time, can be found in the behavioural economics literature; for instance, a revisited version of Kirman's classic ant toy model [8] showcases how a single ant choosing to look for different food supplies can set off a torrent of ants following it, leading eventually to the colony switching to that food supply [9]. Additionally, trapping effects appear in the field of opinion dynamics where they relate to the tendency of a population to segregate into different viewpoints.…”

Section: Introductionmentioning

confidence: 99%

Decision-making with distorted memory: Escaping the trap of past experience

Mitsokapas,

Harris

2021

Preprint

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Snapshots of "best" (or "worst") experience are known to dominate human memory and may thus also have a significant effect on future behaviour. We consider here a model of repeated decision-making where, at every time step, an agent takes one of two choices with probabilities which are functions of the maximum utilities previously experienced. Depending on the utility distributions and the level of noise in the decision process, it is possible for an agent to become "trapped" in one of the choices on the basis of their early experiences. If the utility distributions for the two choices are different, then the agent may even become trapped in the choice which is objectively worse in the sense of expected long-term returns; crucially we extend earlier work to address this case. Using tools from statistical physics and extreme-value theory, we show that for exponential utilities there is an optimal value of noise which maximizes the expected returns in the long run. We also briefly discuss the behaviour for other utility distributions.

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Schrödinger’s Ants: A Continuous Description of Kirman’s Recruitment Model

Cited by 7 publications

References 30 publications

From Ants to Fishing Vessels: A Simple Model for Herding and Exploitation of Finite Resources

From Ants to Fishing Vessels: A Simple Model for Herding and Exploitation of Finite Resources

Self-Fulfilling Prophecies, Quasi Non-Ergodicity and Wealth Inequality

Decision-making with distorted memory: Escaping the trap of past experience

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