The optimal control of Axelrod's social norm game

Jaber, Ahmed; Cojocaru, M

doi:10.1002/oca.2390

Cited by 2 publications

(4 citation statements)

References 23 publications

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“…A numerical method to solve this problem is the steepest descent (SD) method whose algorithm is presented in (Kirk, 2012) and (Wang, 2009). We used this method in similar work to solve an optimal control of a social norm game in (Jaber & Cojocaru, 2018) and to solve the optimal control of a preventive treatment game in (Cojocaru & Jaber, 2018) to maximize the number of players who choose to vaccinate in an epidemiological model.…”

Section: Optimal Control Of Infectious Populationsmentioning

confidence: 99%

Controlling infection in predator-prey systems with transmission dynamics

Cojocaru

Migot

Jaber

2020

Infectious Disease Modelling

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We propose in this paper a prophylactic treatment strategy for a predator-prey system. The objective is to fight against the propagation of an infectious disease within two populations, one of which preys on the other. This propagation is modeled by means of an SIS (susceptible-infectious-susceptible) epidemic model with vital dynamics and infection propagation in both species through contact and predation, including mortality rates in both populations due directly to the disease. Treatment strategies are represented by new parameters modeling the uptake rates in the populations. We analyze the effect of various treatment strategy scenarios (prey only, predator only, or both) via their uptake rates and possible cost structures, on the size of the infected populations. We illustrate if and when applying such preventive treatments lead to a disease prevalence drop in both populations. We conduct our study using an optimal control model seeking to minimize the treatment cost(s), subject to the transmission dynamics and predator-prey dynamics.

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Section: Optimal Control Of Infectious Populationsmentioning

confidence: 99%

Controlling infection in predator-prey systems with transmission dynamics

Cojocaru

Migot

Jaber

2020

Infectious Disease Modelling

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“…In [28] built a novel model to optimize cancer chemotherapy by studying it as an evolutionary game between cancer and the oncologist. In our most recent work, we applied optimal control to a replicator dynamics system of a norms game in a population, and we showed that the otherwise evolutionarily stable state of all defectors can be controlled towards a norm-dominated population [29].…”

Section: One Of the Common Ways To Analyze This Issue Ismentioning

confidence: 99%

“…Moreover, we are going to follow the same formulation as in [29] to build up a classical optimal control problem where we want to minimize the following functional problem:…”

Section: Optimal Control Of Vaccination Away From the Nash-pareto Statementioning

confidence: 99%

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Optimal Control of a Vaccinating Game toward Increasing Overall Coverage

Cojocaru¹,

Jaber²

2018

JAMP

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In this paper, we study an asymmetric game that characterizes the intentions of players to adopt a vaccine. The game describes a decision-making process of two players differentiated by income level and perceived treatment cost, who consider a vaccination against an infectious disease. The process is a noncooperative game since their vaccination decision has a direct impact on vaccine coverage in the population. We introduce a replicator dynamics (RD) to investigate the players' optimal strategy selections over time. The dynamics reveal the long-term stability of the unique Nash-Pareto equilibrium strategy of this game, which is an extension of the notion of an evolutionarily stable strategy pair for asymmetric games. This Nash-Pareto pair is dependent on perceived costs to each player type, on perceived loss upon getting infected, and on the probability of getting infected from an infected person. Last but not least, we introduce a payoff parameter that plays the role of cost-incentive towards vaccination. We use an optimal control problem associated with the RD system to show that the Nash-Pareto pair can be controlled to evolve towards vaccination strategies that lead to a higher overall expected vaccine coverage.

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The optimal control of Axelrod's social norm game

Cited by 2 publications

References 23 publications

Controlling infection in predator-prey systems with transmission dynamics

Controlling infection in predator-prey systems with transmission dynamics

Optimal Control of a Vaccinating Game toward Increasing Overall Coverage

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