Read Note 2

Citation

Peters, Ole, and Alexander Adamou. “The Ergodicity Solution of the Cooperation Puzzle.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, no. 2227 (July 11, 2022): 20200425. https://doi.org/10.1098/rsta.2020.0425.

Abstract

The author uses the concept of ergodicity to show that cooperation can increase the time-average growth rate of resources, providing an evolutionary advantage.

Past Models

classical treatments works where direct and immediate benefits are created

• 1. complementarity in the shared resources
     • differences in resource types
• 1. a resource threshold
     • the whole is deterministically ‘more than the sum of its parts’

noisy multiplicative growth model

Cooperation protocol in GBM model

geometric Brownian motion (GBM) model

• a complex model of unconstrained self-reproduction

cooperation protocol

• Cooperation has no direct cost and benefit in this protocol

effects of cooperation protocol

• 1. the resources of each member of a cooperating pair grow faster than the resources of the corresponding non-cooperators
     • they also grow faster than the average resources of the non-cooperators, showing that cooperation and averaging are not equivalent operations
• 1. the volatility reduction achieved by the cooperators leads to faster growth
     • the time-average growth rate of resources is reduced by fluctuations
     • cooperation is enhanced by diversity in individual outcomes
• 1. larger cooperatives are favoured over smaller ones
     • as the cooperative expands, the benefit gained by adding each new member diminishes

two major implications of the theoretical finding

• 1. a candidate explanation for observed cooperation in real
     • aslo can explain simple setting such as from single cell to cell pair
• 1. a leading-order result from which deviations can be studied
     • cooperation should be considered the norm while the absence of cooperation requires special explanations
     • rethink of definitions of self-interest

result

• cooperation is attractive when resources are selfreproductive

  Other Considerations

• whether group and individual interests could become misaligned in the model
• entities pool and share resources only with those to whom they are connected
• risk management (by reducing fluctuation) has a rarely recognized significance

  Concepts

  Growth Rates

  Two fundamental growth rates are identified: the ensemble-average growth rate and the time-average growth rate, with the latter being influenced by the degree of cooperation

time-average growth rates

the average rate of growth that an individual entity

ensemble-average growth rates

the average growth rate across a large group or ensemble of entities

Ergodicity

A statistical property where the time average of a process equals the ensemble average the essence of the ergodicity debate >features emerging from fluctuations when averaging over a statistical ensemble do not, in general, also emerge in individual systems over time

Non-ergodicity

the difference (time<ensemble) between the ensemble-average growth rate and the time-average growth rate due to the correlated fluctuations

correlated fluctuations

entities experiencing consistently similar or dissimilar conditions

How this may affect the research field of overtourism

the background of overtourism

• from the micro level, it is the result of a time-space imbalance in growth of tourists
• from the macro level, it can be linked to the risk with globalization, in particular the accelerated movement of people and resources
• In contrast, the reduction in travel by people during the Covid-19 epidemic can be seen as the opposite extreme of overtourism (both of them are excessive volatility)

the connection between the model and overtourism

• overtourism often leads to the overdevelopment of resources and environmental stress, which is similar to how fluctuations impact resource growth in the model
• there are also entities (residents, tourists, govement, company…) who can choose whether to cooperate with other
• in case of overtourism, conflicts are more often since some entities think the devolop of destination will undermines their profits

how stakeholders can benefit from cooperation in overtourism

• cooperation among various stakeholders is necessary in managing the number of tourists and optimizing the distribution of tourism resources
• reducing volatility for long-term growth gives thought on measures to mitigate over-tourism
  • promoting alternative destinations
  • dispersaling the active area of tourists and residents
  • investing in infrastructure that can handle tourist influx
  • improve relationship between residents and tourists

summary

• Using the ergodicity solution of the cooperation puzzle for risk management in tourism promotes sustainable industry development, and also protects the interests of individual tourists and local communities.