Opinion Diversity and the Resilience of Cooperation in Dynamical Networks

Abstract

Across various scenarios, individuals cooperate with others to contribute towards a shared goal and ensure self-preservation. In game theory, the act of cooperation is considered as an individual producing some form of benefit to be utilised by others, under the expectation others will return the favour. In several scenarios, individuals make use of their own information to aid with their decision about who to connect and cooperate with. However, the choice of cooperation can be taken advantage of by opportunistic defectors, which can lead to significant disruption. This paper investigates how the diversity of opinion can contribute to the structure and mechanics of a dynamical network model and to the resilience of cooperation, by utilising a computational model where individuals make use of both public and private information to implement their decision. Our results show that increasing diversity leads to more stable, less connected and less prosperous networks coupled to more frequent, but shallower information cascades. Our work generally shows that the outcome of the conflict between cooperators and cheaters strongly depends on the interplay between population structure, individual decision making and individual opinions.

Cooperation dynamics in dynamical networks with history-based decisions

“…The first set of these simulations utilises private information as the primary indication for if a connection should be formed ( p = 0.25, q = 0.75). As can be observed in Fig 9a , the average level of cooperation gradually increases as τ is increased, which aligns with what has been observed in previous works [ 17 , 21 ]. However, further increasing τ past a value of 1 eventually results in a collapse of average cooperation ( Fig 9a ).…”

“…For the next series of simulations, networks are configured to prioritise public information over private information ( p = 0.75, q = 0.25) when newcomers determine which potential neighbours they should form connections with. In previous works [ 17 , 21 ] and simulations utilising connection average ( Fig 10 ), prioritising public information leads to some changes in network metrics, although they still largely resemble trends that occur in networks that prioritise private information ( Fig 9 ). However, in networks where the ‘Bikchandani’ method is utilised, the result is stagnation, which we consider here as no significant increases or decreases in cooperation and connections, across all networks that utilise different τ values ( Fig 12 ).…”

“…All newcomers in the presented model utilise the same method of interpreting information available to individuals. In a previous work [ 21 ], it has been considered the case where private opinion can vary amongst individuals. It’s likely that individuals in scenarios similar to what is simulated here will interpret information in their own way and may also be influenced by other criteria such as their past experiences or individual preferences.…”

“…The findings highlight that the way the previous decisions are taken into account can influence both the well-being of these networks, their cooperation and as well as the emergence of information cascades, particularly when using all of the available information rather than just examining the difference in previous accepted and rejected connections. As part of future work, it may be worth exploring other methods of evaluating previous decisions, as well as the possibility of considering networks where individuals could choose to interpret the previous decision in an non-homogeneous way [ 21 , 27 , 28 ].…”

“…To understand how public information based on previous decisions can influence structured populations. we review a type of public information, referred to as connection average (see Fig 2 ), that has been studied in previous works [ 17 , 21 ], which does not consider previous decisions but only the current connections of a potential neighbour. In this case, public information will be obtained by examining the number of connections a node x possesses and if that count exceeds the average connection count across the network.…”