arXiv subjects

Andrew Belmonte

Publications and source records attributed to Andrew Belmonte.

18 recordsLinked to original sources

arXiv2023

Stability of Dining Clubs in the Kolkata Paise Problem with and without Cheating

We introduce the idea of a dining club to the Kolkata Paise Restaurant Problem. In this problem, $N$ agents choose (randomly) among $N$ restaurants, but if multiple agents choose the same restaurant, only one will eat. Agents in the dining club will coordinate their restaurant choice to avoid choice collision and increase their probability of eating. We model the problem of deciding whether to join the dining club as an evolutionary game and show that the strategy of joining the dining club is evolutionarily stable. We then introduce an optimized member tax to those individuals in the dining club, which is used to provide a safety net for those group members who don't eat because of collision with a non-dining club member. When non-dining club members are allowed to cheat and share communal food within the dining club, we show that a new unstable fixed point emerges in the dynamics. A bifurcation analysis is performed in this case. To conclude our theoretical study, we then introduce evolutionary dynamics for the cheater population and study these dynamics. Numerical experiments illustrate the behaviour of the system with more than one dining club and show several potential areas for future research.

physics.soc-ph↗

arXiv2022

Community Formation in Wealth-Mediated Thermodynamic Strategy Evolution

We study a dynamical system defined by a repeated game on a 1D lattice, in which the players keep track of their gross payoffs over time in a bank. Strategy updates are governed by a Boltzmann distribution which depends on the neighborhood bank values associated with each strategy, relative to a temperature scale which defines the random fluctuations. Players with higher bank values are thus less likely to change strategy than players with lower bank value. For a parameterized rock-paper-scissors game, we derive a condition under which communities of a given strategy form with either fixed or drifting boundaries. We show the effect of temperature increase on the underlying system, and identify surprising properties of this model through numerical simulations.

nlin.AO↗

arXiv2020

Imitation of Success Leads to Cost of Living Mediated Fairness in the Ultimatum Game

The mechanism behind the emergence of cooperation in both biological and social systems is currently not understood. In particular, human behavior in the Ultimatum game is almost always irrational, preferring mutualistic sharing strategies, while chimpanzees act rationally and selfishly. However, human behavior varies with geographic and cultural differences leading to distinct behaviors. In this paper, we analyze a social imitation model that incorporates internal energy caches (e.g., food/money savings), cost of living, death, and reproduction. We show that when imitation (and death) occurs, a natural correlation between selfishness and cost of living emerges. However, in all societies that do not collapse, non-Nash sharing strategies emerge as the de facto result of imitation. We explain these results by constructing a mean-field approximation of the internal energy cache informed by time-varying distributions extracted from experimental data. Results from a meta-analysis on geographically diverse ultimatum game studies in humans, show the proposed model captures some of the qualitative aspects of the real-world data and suggests further experimentation.

physics.soc-ph↗

arXiv2020

Fixation in the stochastic Lotka-Volterra model with small fitness trade-offs

We study the probability of fixation in a stochastic two-species competition model. By identifying a naturally occurring fast timescale, we derive an approximation to the associated backward Kolmogorov equation that allows us to obtain an explicit closed form solution for the probability of fixation of either species. We use our result to study fitness tradeoff strategies and show that, despite some tradeoffs having nearly negligible effects on the corresponding deterministic dynamics, they can have large implications for the outcome of the stochastic system.

q-bio.PE↗

arXiv2020

Generalized Hamiltonian Dynamics and Chaos in Evolutionary Games on Networks

We study the network replicator equation and characterize its fixed points on arbitrary graph structures for $2 \times 2$ symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of an independent vertex set in the graph and also show that complex behavior cannot emerge in $2 \times 2$ games. This links a property of the dynamical system with a combinatorial graph property. We contrast this by showing that ordinary rock-paper-scissors (RPS) exhibits chaos on the 3-cycle and that on general graphs with $\geq 3$ vertices the network replicator with RPS is a generalized Hamiltonian system. This stands in stark contrast to the established fact that RPS does not exhibit chaos in the standard replicator dynamics or the bimatrix replicator dynamics, which is equivalent to the network replicator on a graph with one edge and two vertices ($K_2$).

nlin.CD↗

arXiv2020

Simultaneous games with purchase of randomly supplied perfect information: Oracle Games

We study the role of costly information in non-cooperative two-player games when an extrinsic third party information broker is introduced asymmetrically, allowing one player to obtain information about the other player's action. This broker or "oracle" is defined by a probability of response, supplying correct information randomly; the informed player can pay more for a higher probability of response. We determine the necessary and sufficient conditions for strategy profiles to be equilibria, in terms of how both players change their strategies in response to the existence of the oracle, as determined by its cost of information function. For mixed strategy equilibria, there is a continuous change as information becomes cheaper, with clear transitions occuring at critical {\it nodes} at which pure strategies become dominated (or undominated). These nodes separate distinct responses to the information for sale, alternating between regions where the paying player increases the amount of information purchased, and regions where the other player moves away from riskier strategies, in favor of safer bets that minimize losses. We derive conditions for these responses by defining a value of information.

cs.GT↗

arXiv2019

Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies

We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus. Two conjectures on general convergence are also discussed. We then consider the case where players not only may choose their strategies, but also affect their local topology. We show that for prisoner's dilemma, the graph structure converges to a set of disconnected cliques and strategic consensus occurs in each clique. Several examples from various matrix games are provided. A variation of the model is then used to create a simple model for the spreading of trends, or information cascades in (e.g., social) networks. We provide theoretical and empirical results on the trend-spreading model.

math.DS↗

arXiv2018

A game-theoretic mechanism for aggregation and dispersal of interacting populations

We adapt a fitness function from evolutionary game theory as a mechanism for aggregation and dispersal in a partial differential equation (PDE) model of two interacting populations, described by density functions $u$ and $v$. We consider a spatial model where individuals migrate up local fitness gradients, seeking out locations where their given traits are more advantageous. The resulting system of fitness gradient equations is a degenerate system having spatially structured, smooth, steady state solutions characterized by constant fitness throughout the domain. When populations are viewed as predator and prey, our model captures prey aggregation behavior consistent with Hamilton's selfish herd hypothesis. We also present weak steady state solutions in 1d that are continuous but in general not smooth everywhere, with an associated fitness that is discontinuous, piecewise constant. We give numerical examples of solutions that evolve toward such weak steady states. We also give an example of a spatial Lotka--Volterra model, where a fitness gradient flux creates instabilities that lead to spatially structured steady states. Our results also suggest that when fitness has some dependence on local interactions, a fitness-based dispersal mechanism may act to create spatial variation across a habitat.

q-bio.PE↗

arXiv2017

Fast cheater migration stabilizes coexistence in a public goods dilemma on networks

Through the lens of game theory, cooperation is frequently considered an unsustainable strategy: if an entire population is cooperating, each indi- vidual can increase its overall fitness by choosing not to cooperate, thereby still receiving all the benefit of its cooperating neighbors while no longer expending its own energy. Observable cooperation in naturally-occurring public goods games is consequently of great interest, as such systems offer insight into both the emergence and sustainability of cooperation. Here we consider a population that obeys a public goods game on a network of discrete regions (that we call nests), between any two of which individuals are free to migrate. We construct a system of piecewise-smooth ordinary differential equations that couple the within-nest population dynamics and the between-nest migratory dynamics. Through a combination of analytical and numerical methods, we show that if the workers within the population migrate sufficiently fast relative to the cheaters, the network loses stability first through a Hopf bifurcation, then a torus bifurcation, after which one or more nests collapse. Our results indicate that fast moving cheaters can act to stabilize worker-cheater coexistence within network that would otherwise collapse. We end with a comparison of our results with the dynamics observed in colonies of the ant species Pristomyrmex punctatus and in those of the Cape honeybee Apis mellifera capensis, and argue that they qualitatively agree.

q-bio.PE↗

arXiv2012

Spatial Pattern Dynamics due to the Fitness Gradient Flux in Evolutionary Games

We introduce a non-diffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in 1D for two-strategy games including the coordination game and the prisoner's dilemma, and in 2D for the rock-paper-scissors game. In 1D we observe modified travelling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

nlin.PS↗

arXiv2010

Hydraulic jumps on an incline

When a fluid jet strikes an inclined solid surface at normal incidence, gravity creates a flow pattern with a thick outer rim resembling a parabola and reminiscent of a hydraulic jump. There appears to be little theory or experiments describing simple aspects of this phenomenon, such as the maximum rise height of the fluid above the impact point, and its dependence on jet velocity and inclination angle. We address this with experiments, and present a simple theory based on horizontal hydraulic jumps which accounts for the rise height and its scaling, though without describing the shape of the parabolic envelope.

physics.flu-dyn↗

arXiv2009

Superheated water drops in hot oil

Drops of water at room temperature were released in hot oil, which had a temperature higher than that of the boiling point of water. Initially, the drop temperature increases slowly mainly due to heat transfer diffusion; convective heat transfer is small because the motion takes place at a small Reynolds number. Once the drop reaches the bottom of the container, it sticks to the surface with a certain contact angle. Then, a part of the drop vaporizes: the nucleation point may appear at the wall, the interface or the bulk of the drop. The vapor expands inside the drop and deforms its interface. The way in which the vapor expands, either smooth or violent, depends on the location of the nucleation point and oil temperature. Furthermore, for temperatures close to the boiling point of water, the drops are stable (overheated); the vaporization does not occur spontaneously but it may be triggered with an external perturbation. In this case the growth of the vapor bubble is rather violent. Many visualization for different conditions will be shown and predictions of the growth rate will be discussed.

physics.flu-dyn↗

arXiv2008

Surface texture and pulsation due to balloon bursting in different liquids

We study the instabilities occurring during the burst of an air balloon in a liquid. These instabilities are typical for the deformation of an interface between two fluids of different densities, similar to fingering in Rayleigh-Taylor instability (see e.g. Sharp, 1984). In the Video a series of bursts are shown for air balloons in different liquids. When the balloon tears it tracks the surface, generating wrinkles and releasing the pressure inside. Apparently, the texture of the surface during the burst becomes smoother as the viscosity increases. During the burst the surface breaks and generates several small bubbles. Furthermore, the pressure inside the balloon is higher than the external pressure before the burst; once the balloon tears the pressure is released and the generated bubbles pulsate several times (see e.g. Brennen, 1995). Such oscillations are more evident for higher internal pressures.

physics.flu-dyn↗

arXiv2007

Fingering instabilities of a reactive micellar interface

We present an experimental study of the fingering patterns in a Hele-Shaw cell, occurring when a gel-like material forms at the interface between aqueous solutions of a cationic surfactant cetyltrimethylammonium bromide) and an organic salt (salicylic acid), two solutions known to form a highly elastic wormlike micellar fluid when mixed homogeneously. A variety of fingering instabilities are observed, depending on the velocity of the front (the injection rate), and on which fluid is injected into which. We have found a regime of non-confined stationary or wavy fingers for which width selection seems to occur without the presence of bounding walls, unlike the Saffman-Taylor experiment. Qualitatively, some of our observations share common mechanisms with instabilities of cooling lava flows or growing biofilms.

nlin.PS↗

arXiv2006

Motion of a Viscoelastic Micellar Fluid Around a Cylinder: Flow and Fracture

We present an experimental study of the motion of a viscoelastic micellar material around a moving cylinder, which ranges in response from fluid-like flow to solid-like tearing and fracture, depending on the cylinder radius and velocity. The observation of viscoelastic crack propagation driven by the cylinder indicates an extremely low tear strength, approximately equal to the steady state surface tension of the fluid. At the highest speeds a driven crack is observed in front of the cylinder, propagating with a fluctuating speed equal on average to the cylinder speed, here as low as 5% of the elastic wave speed in the medium.

cond-mat.soft↗

arXiv2002

Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere

We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem.

math-ph↗

arXiv2002

Oscillations of a solid sphere falling through a wormlike micellar fluid

We present an experimental study of the motion of a solid sphere falling through a wormlike micellar fluid. While smaller or lighter spheres quickly reach a terminal velocity, larger or heavier spheres are found to oscillate in the direction of their falling motion. The onset of this instability correlates with a critical value of the velocity gradient scale $Γ_{c}\sim 1$ s$^{-1}$. We relate this condition to the known complex rheology of wormlike micellar fluids, and suggest that the unsteady motion of the sphere is caused by the formation and breaking of flow-induced structures.

physics.flu-dyn↗

arXiv1999

Experimental study of Taylor's hypothesis in a turbulent soap film

An experimental study of Taylor's hypothesis in a quasi-two-dimensional turbulent soap film is presented. A two probe laser Doppler velocimeter enables a non-intrusive simultaneous measurement of the velocity at spatially separated points. The breakdown of Taylor's hypothesis is quantified using the cross correlation between two points displaced in both space and time; correlation is better than 90% for scales less than the integral scale. A quantitative study of the decorrelation beyond the integral scale is presented, including an analysis of the failure of Taylor's hypothesis using techniques from predictability studies of turbulent flows. Our results are compared with similar studies of 3D turbulence.

physics.flu-dyn↗