Parallel Minority Game and it’s application in movement optimization during an epidemic

Abstract

We introduce a version of the Minority Game where the total number of available choices is , but the agents only have two available choices to switch. For all agents at an instant in any given choice, therefore, the other choice is distributed between the remaining options. This brings in the added complexity in reaching a state with the maximum resource utilization, in the sense that the game is essentially a set of MG that are coupled and played in parallel. We show that a stochastic strategy, used in the MG, works well here too. We discuss the limits in which the model reduces to other known models. Finally, we study an application of the model in the context of population movement between various states within a country during an ongoing epidemic. we show that the total infected population in the country could be as low as that achieved with a complete stoppage of inter-region movements for a prolonged period, provided that the agents instead follow the above mentioned stochastic strategy for their movement decisions between their two choices. The objective for an agent is to stay in the lower infected state between their two choices. We further show that it is the agents moving once between any two states, following the stochastic strategy, who are less likely to be infected than those not having (or not opting for) such a movement choice, when the risk of getting infected during the travel is not considered. This shows the incentive for the moving agents to follow the stochastic strategy.

An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics

“…But as soon as most of the population chooses this strategy, the amount of infected agents grows, resulting in a change of the best strategy, that becomes to self-quarantine. It is also worth mentioning that such scenario is akin to the minority-game (or El Farol Bar dilemma) [74] , [103] , [104] , where each single individual receives the optimal payoff if she chooses the least chosen strategy on average. Such payoff structure can be seen as a general anti-coordination game class, where the best strategy is to do the opposite of what your opponents are doing.…”

“…Recent works also investigated other mitigation strategies such as awareness campaigns [61] , wealth differences [62] , [63] , economic incentives [64] , social distancing [65] , [66] , information spreading [67] , [68] , multi-layer contact networks [69] , dynamic contacts [70] and others [71] , [72] , [73] , [74] , [75] . A general overview of these investigations shows the presence of a cycle, where effective mitigation measures lead to a low risk perception, which in turn weakens said mitigation strategies, bringing the disease back [2] .…”

Optimization strategies of human mobility during the COVID-19 pandemic: A review

“…The effects of imposing continued restrictions, modeled by taking the corresponding interaction matrices between different age groups, seen to lower the total infection rate. Also, an early lifting of such restrictions leads to secondary peaks (see also [30]). With a similar SEIR type model, it was shown in ref.…”

“…The quantity I max is important because, this gives the estimate of the maximum load the healthcare infrastructure needs to support. SIR models were used in studying effects of optimal migrations (see e.g., [30]). Indeed, in more realistic variants of the model, this is quantity that were estimated for various different countries in order to make the above mentioned load and also to design optimization strategies of implementing mitigating responses, including travel restrictions.…”

“…There is a clear positive correlation between the two quantities before imposition of restrictions. On the right hand side figure, simulations of SIR model with optimized mobility of individuals among different regions of varying degree of risks (see [30]) are shown. For different duration of travel restrictions (indicated by the start and end dates), the fraction of infected individuals moved correlate strongly with total infection fraction.…”