arXiv subjects

Vikash Kumar Dubey

Publications and source records attributed to Vikash Kumar Dubey.

5 recordsLinked to original sources

arXiv2026

Upstream reciprocity versus downstream reciprocity: Catalyzing cooperation

Why would anyone help a stranger, knowing they may never meet again? Indirect reciprocity offers one of the most compelling evolutionary answers, yet its two canonical forms -- upstream reciprocity (experience-based), and downstream reciprocity (reputation-based) -- have been studied mostly in isolation. Their joint dynamics in finite and structured populations remain largely unexplored. Here, we fill this gap using agent-based simulations in which an agent is behaviourally either defector, upstream reciprocator, or downstream reciprocator, and the agents' population state is temporally updated using different evolutionary update mechanisms. We show that update mechanism plays a surprisingly decisive role in shaping the fate of downstream and especially upstream reciprocators. Whether agents' experiences and reputations are updated globally or locally can shift outcomes from rich behavioural coexistence to the dominance of downstream reciprocators alone. Intriguingly, we uncover a robust structural feature that persists across all the explored update rules and population sizes: an optimal network degree at which upstream reciprocity is maximized, reflecting a fundamental tug-of-war between cooperative clustering and exposure to defectors. Our results highlight that while downstream reciprocity can either foster or inhibit upstream reciprocity depending on the update mechanism, its net effect on cooperation remains largely positive.

q-bio.PE↗

arXiv2026

Oscillatory evolutionarily stable state and limit cycle in replicator dynamics

The idea of evolutionarily stable state (ESS) of a population is a cornerstone of evolutionary game theory; moreover, it coincides with the game-theoretic concept of Nash equilibrium. Such a state corresponds to a strategy adopted by the population such that a rare mutant strategy cannot invade the population. In parallel, the dynamical formulation of evolutionary game theory -- particularly through replicator dynamics embodying the tenet of survival of the fittest -- provides a framework for modelling frequency-dependent selection over time. While it is well known that an ESS corresponds to stable fixed point in replicator dynamics, the evolutionary game-theoretic characterization of limit cycles is unknown. Here we fill this lacuna by defining oscillatory ESS (OESS) which we prove to be a stable limit cycle. We also show when an OESS is unique and if there are multiple OESSes, then what their locations are in the phase space.

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arXiv2025

Evolutionarily stable strategy in asymmetric games: Dynamical and information-theoretical perspectives

Evolutionarily stable strategy (ESS) is the defining concept of evolutionary game theory. It has a fairly unanimously accepted definition for the case of symmetric games which are played in a homogeneous population where all individuals are in same role. However, in asymmetric games, which are played in a population with multiple subpopulations (each of which has individuals in one particular role), situation is not as clear. Various generalizations of ESS defined for such cases differ in how they correspond to fixed points of replicator equation which models evolutionary dynamics of frequencies of strategies in the population. Moreover, some of the definitions may even be equivalent, and hence, redundant in the scheme of things. Along with reporting some new results, this paper is partly indented as a contextual mini-review of some of the most important definitions of ESS in asymmetric games. We present the definitions coherently and scrutinize them closely while establishing equivalences -- some of them hitherto unreported -- between them wherever possible. Since it is desirable that a definition of ESS should correspond to asymptotically stable fixed points of replicator dynamics, we bring forward the connections between various definitions and their dynamical stabilities. Furthermore, we find the use of principle of relative entropy to gain information-theoretic insights into the concept of ESS in asymmetric games, thereby establishing a three-fold connection between game theory, dynamical system theory, and information theory in this context. We discuss our conclusions also in the backdrop of asymmetric hypermatrix games where more than two individuals interact simultaneously in the course of getting payoffs.

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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.

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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.

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