arXiv subjects

Sagar Chakraborty

Publications and source records attributed to Sagar Chakraborty.

At least 37 records · Page 2Linked to original sources

arXiv2024

Oscillatory equilibrium in asymmetric evolutionary games: Generalizing evolutionarily stable strategy

The concept of evolutionarily stability and its relation with the fixed points of the replicator equation are important aspects of evolutionary game dynamics. In the light of the fact that oscillating state of a population and individuals (or players) of different roles are quite natural occurrences, we ask the question how the concept of evolutionarily stability can be generalized so as to associate game-theoretic meaning to oscillatory behaviours of players asymmetrically interacting, i.e., if there are both intraspecific and interspecific interactions between two subpopulations in the population. We guide our scheme of generalization such that the evolutionary stability is related to the dynamic stability of the corresponding periodic orbits of a time-discrete replicator dynamics. We name the generalization of evolutionarily stable state as two-species heterogeneity stable orbit. Furthermore, we invoke the principle of decrease of relative entropy in order to associate the generalization of evolutionary stability with an information-theoretic meaning. This particular generalization is aptly termed as two-species information stable orbit.

q-bio.PE↗

arXiv2024

Eclectic Notes on Uncertainty, Information, and Classical Dynamics

Information is everywhere in nature which is very uncertain and unpredictable. But information, in itself, is a very ambiguous term. In this cursory write-up, we attempt to understand the formal meaning of information by quantifying uncertainty and discuss how it naturally appears in two core topics of classical physics -- classical mechanics and statistical mechanics. In the process, we witness how the concepts of the information theory render a unique viewpoint in physics. Except for the presentation of the material, the author claims no originality; however, the responsibility of every inadvertent error lies entirely with the author.

physics.class-ph↗

arXiv2024

Hypochaos prevents tragedy of the commons in discrete-time eco-evolutionary game dynamics

While quite a few recent papers have explored game-resource feedback using the framework of evolutionary game theory, almost all the studies are confined to using time-continuous dynamical equations. Moreover, in such literature, the effect of ubiquitous chaos in the resulting eco-evolutionary dynamics is rather missing. Here, we present a deterministic eco-evolutionary discrete-time dynamics in generation-wise non-overlapping population of two types of harvesters, one harvesting at a faster rate than the other, consuming a self-renewing resource capable of showing chaotic dynamics. In the light of our finding that sometimes chaos is confined exclusively to either the dynamics of the resource or that of the consumer fractions, an interesting scenario is realized: The resource state can keep oscillating chaotically, and hence, it does not vanish to result in the tragedy of the commons, extinction of the resource due to selfish indiscriminate exploitation, and yet the consumer population, whose dynamics depends directly on the state of the resource, may end up being composed exclusively of defectors, i.e., high harvesters. This appears non-intuitive because it is well known that prevention of tragedy of the commons usually requires substantial cooperation to be present.

q-bio.PE↗

arXiv2023

Repeated quantum game as a stochastic game: Effects of the shadow of the future and entanglement

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical randomness -- can be mapped to the paradigm of stochastic games. Subsequently, using the setup of two-player--two-action games, we explore the pure reactive strategies belonging to the set of reactive strategies, whose support in the quantum games is no longer countably finite but rather non-denumerably infinite. We find that how two pure strategies fare against each other is crucially dependent on the discount factor (the probability of occurrence of every subsequent round) and how much entangled the quantum states of the players are. We contrast the results obtained with the corresponding results in the classical setup and find fundamental differences between them: e.g, when the underlying game is the prisoner's dilemma, in the quantum game setup, always-defect strategy can be beaten by the tit-for-tat strategy for high enough discount factor.

quant-ph↗

arXiv2023

Replicator-mutator dynamics of Rock-Paper-Scissors game: Learning through mistakes

We generalize the Bush--Mosteller learning, the Roth--Erev learning, and the social learning to include mistakes such that the nonlinear replicator-mutator equation with either additive or multiplicative mutation is generated in an asymptotic limit. Subsequently, we exhaustively investigate the ubiquitous Rock-Paper-Scissors game for some analytically tractable motifs of mutation pattern. We consider both symmetric and asymmetric game interactions, and reveal that mistakes can some-times help the players learn. While the replicator-mutator flow exhibits rich dynamics that include limit cycles and chaotic orbits, it can control chaos as well to lead to rational Nash equilibrium outcome. Moreover, we also report an instance of hitherto unknown Hamiltonian structure of the replicator-mutator equation.

physics.soc-ph↗

arXiv2023

Inferring to C or not to C: Evolutionary games with Bayesian inferential strategies

Strategies for sustaining cooperation and preventing exploitation by selfish agents in repeated games have mostly been restricted to Markovian strategies where the response of an agent depends on the actions in the previous round. Such strategies are characterized by lack of learning. However, learning from accumulated evidence over time and using the evidence to dynamically update our response is a key feature of living organisms. Bayesian inference provides a framework for such evidence-based learning mechanisms. It is therefore imperative to understand how strategies based on Bayesian learning fare in repeated games with Markovian strategies. Here, we consider a scenario where the Bayesian player uses the accumulated evidence of the opponent's actions over several rounds to continuously update her belief about the reactive opponent's strategy. The Bayesian player can then act on her inferred belief in different ways. By studying repeated Prisoner's dilemma games with such Bayesian inferential strategies, both in infinite and finite populations, we identify the conditions under which such strategies can be evolutionarily stable. We find that a Bayesian strategy that is less altruistic than the inferred belief about the opponent's strategy can outperform a larger set of reactive strategies, whereas one that is more generous than the inferred belief is more successful when the benefit-to-cost ratio of mutual cooperation is high. Our analysis reveals how learning the opponent's strategy through Bayesian inference, as opposed to utility maximization, can be beneficial in the long run, in preventing exploitation and eventual invasion by reactive strategies.

q-bio.PE↗

arXiv2023

TransDocAnalyser: A Framework for Offline Semi-structured Handwritten Document Analysis in the Legal Domain

State-of-the-art offline Optical Character Recognition (OCR) frameworks perform poorly on semi-structured handwritten domain-specific documents due to their inability to localize and label form fields with domain-specific semantics. Existing techniques for semi-structured document analysis have primarily used datasets comprising invoices, purchase orders, receipts, and identity-card documents for benchmarking. In this work, we build the first semi-structured document analysis dataset in the legal domain by collecting a large number of First Information Report (FIR) documents from several police stations in India. This dataset, which we call the FIR dataset, is more challenging than most existing document analysis datasets, since it combines a wide variety of handwritten text with printed text. We also propose an end-to-end framework for offline processing of handwritten semi-structured documents, and benchmark it on our novel FIR dataset. Our framework used Encoder-Decoder architecture for localizing and labelling the form fields and for recognizing the handwritten content. The encoder consists of Faster-RCNN and Vision Transformers. Further the Transformer-based decoder architecture is trained with a domain-specific tokenizer. We also propose a post-correction method to handle recognition errors pertaining to the domain-specific terms. Our proposed framework achieves state-of-the-art results on the FIR dataset outperforming several existing models

cs.CV↗

arXiv2023

Periodic orbits in deterministic discrete-time evolutionary game dynamics: An information-theoretic perspective

Even though existence of non-convergent evolution of the states of populations in ecological and evolutionary contexts is an undeniable fact, insightful game-theoretic interpretations of such outcomes are scarce in the literature of evolutionary game theory. As a proof-of-concept, we tap into the information-theoretic concept of relative entropy in order to construct a game-theoretic interpretation for periodic orbits in a wide class of deterministic discrete-time evolutionary game dynamics, primarily investigating the two-player two-strategy case. Effectively, we present a consistent generalization of the evolutionarily stable strategy -- the cornerstone of the evolutionary game theory -- and aptly term the generalized concept: information stable orbit. The information stable orbit captures the essence of the evolutionarily stable strategy in that it compares the total payoff obtained against an evolving mutant with the total payoff that the mutant gets while playing against itself. Furthermore, we discuss the connection of the information stable orbit with the dynamical stability of the corresponding periodic orbit.

nlin.AO↗

arXiv2023

Selection-recombination-mutation dynamics: Gradient, limit cycle, and closed invariant curve

In this paper, the replicator dynamics of the two-locus two-allele system under weak mutation and weak selection is investigated in a generation-wise non-overlapping unstructured population of individuals mating at random. Our main finding is that the dynamics is gradient-like when the point mutations at the two loci are independent. This is in stark contrast to the case of one-locus multi-allele where the existence gradient behaviour is contingent on a specific relationship between the mutation rates. When the mutations are not independent in the two-locus two-allele system, there is the possibility of non-convergent outcomes, like asymptotically stable oscillations, through either the Hopf bifurcation or the Neimark--Sacker bifurcation depending on the strength of the weak selection. The results can be straightforwardly extended for multi-locus two-allele systems.

q-bio.PE↗

arXiv2022

Euler's Limit -- Revisited

The aim of this short note is that if $\{ a_{n}\}$ and $\{ b_{n}\}$ are two sequences of positive real numbers such that $a_{n}\to +\infty$ and $b_n$ satisfying the asymptotic formula $b_n\sim k\cdot a_{n}$, where $k>0$, then $\lim\limits_{n\to\infty}\left(1+\frac{1}{a_{n}}\right)^{b_{n}}= e^{k}$.

math.HO↗

arXiv2022

Dynamic Scaling in Rotating Turbulence: A Shell Model Study

We investigate the scaling form of appropriate time-scales extracted from time-dependent correlation functions in rotating, turbulent flows. In particular, we obtain precise estimates of the dynamic exponents $z_p$, associated with the time-scales, and their relation with the more commonly measured equal-time exponents $ζ_p$. These theoretical predictions, obtained by using the multifractal formalism, are validated through extensive numerical simulations of a shell model for such rotating flows.

physics.flu-dyn↗

arXiv2022

Geometric visualizations of $b^{e}<e^{b}$ when $e<b$

In connection to the two fascinating constants $e$ and $π$, there are many beautiful visual proofs to the inequality $π^{e}<e^π$. The aim of this classroom capsule is to give three visual proofs to the more general inequality $b^{e}<e^{b}$ where $e<b$.

math.HO↗

arXiv2022

Eco-evolutionary games for harvesting self-renewing common resource: Effect of growing harvester population

The tragedy of the commons (TOC) is a ubiquitous social dilemma witnessed in interactions between a population of living entities and shared resources available to them: The individuals in the population tend to selfishly overexploit a common resource as it is arguably the rational choice, or in case of non-human beings, it may be an evolutionarily uninvadable action. How to avert the TOC is a significant problem related to the conservation of resources. It is not hard to envisage situations where the resource could be self-renewing and the size of the population may be dependent on the state of the resource through the fractions of the population employing different exploitation rates. If the self-renewal rate of the resource lies between the maximum and the minimum exploitation rates, it is not a priori obvious under what conditions the TOC can be averted. In this paper, we address this question analytically and numerically using the setup of an evolutionary game theoretical replicator equation that models the Darwinian tenet of natural selection. Through the replicator equation, while we investigate how a population of replicators exploit the shared resource, the latter's dynamical feedback on the former is also not ignored. We also present a transparent bottom-up derivation of the game-resource feedback model to facilitate future studies on the stochastic effects on the findings presented herein.

q-bio.PE↗

arXiv2021

Subduing always defecting mutants by multiplayer reactive strategies: Non-reciprocity versus generosity

A completely non-generous and reciprocal population of players can create a robust cooperating state that cannot be invaded by always defecting free riders if the interactions among players are repeated for long enough. However, strict non-generosity and strict reciprocity are ideal concepts, and may not even be desirable sometimes. Therefore, to what extent generosity or non-reciprocity can be allowed while still not be swamped by the mutants, is a natural question. In this paper, we not only ask this question but furthermore ask how generosity comparatively fares against non-reciprocity in this context. For mathematical concreteness, we work within the framework of multiplayer repeated prisoner's dilemma game with reactive strategies in a finite and an infinite population; and explore the aforementioned questions through the effects of the benefit to cost ratio, the interaction group size, and the population size.

q-bio.PE↗

arXiv2021

Game-environment feedback dynamics in growing population: Effect of finite carrying capacity

The tragedy of the commons (TOC) is an unfortunate situation where a shared resource is exhausted due to uncontrolled exploitation by the selfish individuals of a population. Recently, the paradigmatic replicator equation has been used in conjunction with a phenomenological equation for the state of the shared resource to gain insight into the influence of the games on the TOC. The replicator equation, by construction, models a fixed infinite population undergoing microevolution. Thus, it is unable to capture any effect of the population growth and the carrying capacity of the population although the TOC is expected to be dependent on the size of the population. Therefore, in this paper, we present a mathematical framework that incorporates the density dependent payoffs and the logistic growth of the population in the eco-evolutionary dynamics modelling the game-resource feedback. We discover a bistability in the dynamics: a finite carrying capacity can either avert or cause the TOC depending on the initial states of the resource and the initial fraction of cooperators. In fact, depending on the type of strategic game-theoretic interaction, a finite carrying capacity can either avert or cause the TOC when it is exactly the opposite for the corresponding case with infinite carrying capacity.

nlin.AO↗

arXiv2021

Emergence of universality in the transmission dynamics of COVID-19

The complexities involved in modelling the transmission dynamics of COVID-19 has been a roadblock in achieving predictability in the spread and containment of the disease. In addition to understanding the modes of transmission, the effectiveness of the mitigation methods also needs to be built into any effective model for making such predictions. We show that such complexities can be circumvented by appealing to scaling principles which lead to the emergence of universality in the transmission dynamics of the disease. The ensuing data collapse renders the transmission dynamics largely independent of geopolitical variations, the effectiveness of various mitigation strategies, population demographics, etc. We propose a simple two-parameter model -- the Blue Sky model -- and show that one class of transmission dynamics can be explained by a solution that lives at the edge of a blue sky bifurcation. In addition, the data collapse leads to an enhanced degree of predictability in the disease spread for several geographical scales which can also be realized in a model-independent manner as we show using a deep neural network. The methodology adopted in this work can potentially be applied to the transmission of other infectious diseases and new universality classes may be found. The predictability in transmission dynamics and the simplicity of our methodology can help in building policies for exit strategies and mitigation methods during a pandemic.

physics.soc-ph↗

arXiv2021

Amplitude death in coupled replicator map lattice: averting migration dilemma

Populations composed of a collection of subpopulations (demes) with random migration between them are quite common occurrences. The emergence and sustenance of cooperation in such a population is a highly researched topic in the evolutionary game theory. If the individuals in every deme are considered to be either cooperators or defectors, the migration dilemma can be envisaged: The cooperators would not want to migrate to a defector-rich deme as they fear of facing exploitation; but without migration, cooperation can not be established throughout the network of demes. With a view to studying the aforementioned scenario, in this paper, we set up a theoretical model consisting of a coupled map lattice of replicator maps based on two-player--two-strategy games. The replicator map considered is capable of showing a variety of evolutionary outcomes, like convergent (fixed point) outcomes and nonconvergent (periodic and chaotic) outcomes. Furthermore, this coupled network of the replicator maps undergoes the phenomenon of amplitude death leading to non-oscillatory stable synchronized states. We specifically explore the effect of (i) the nature of coupling that models migration between the maps, (ii) the heterogenous demes (in the sense that not all the demes have same game being played by the individuals), (iii) the degree of the network, and (iv) the cost associated with the migration. In the course of investigation, we are intrigued by the effectiveness of the random migration in sustaining a uniform cooperator fraction across a population irrespective of the details of the replicator dynamics and the interaction among the demes.

physics.soc-ph↗

arXiv2021

Periodic Orbit can be Evolutionarily Stable: Case Study of Discrete Replicator Dynamics

In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or chaotic solution is many a time perceived as a shortcoming of the corresponding game dynamic because (Nash) equilibrium play is supposed to be robust and persistent behaviour, and any other behaviour in nature is deemed transient. Consequently, there is a lack of attempt to connect the non-fixed point solutions with the game theoretic concepts. Here we provide a way to render game theoretic meaning to periodic solutions. To this end, we consider a replicator map that models Darwinian selection mechanism in unstructured infinite-sized population whose individuals reproduce asexually forming non-overlapping generations. This is one of the simplest evolutionary game dynamic that exhibits periodic solutions giving way to chaotic solutions (as parameters related to reproductive fitness change) and also obeys the folk theorems connecting fixed point solutions with Nash equilibrium. Interestingly, we find that a modified Darwinian fitness -- termed heterogeneity payoff -- in the corresponding population game must be put forward as (conventional) fitness times the probability that two arbitrarily chosen individuals of the population adopt two different strategies. The evolutionary dynamics proceeds as if the individuals optimize the heterogeneity payoff to reach an evolutionarily stable orbit, should it exist. We rigorously prove that a locally asymptotically stable period orbit must be heterogeneity stable orbit -- a generalization of evolutionarily stable state.

q-bio.PE↗