Quantifying the Role of Homophily in Human Cooperation Using Multiplex Evolutionary Game Theory.

Nature shows as human beings live and grow inside social structures. This assumption allows us to explain and explore how it may shape most of our behaviours and choices, and why we are not just blindly driven by instincts: our decisions are based on more complex cognitive reasons, based on our connectedness on different spaces. Thus, human cooperation emerges from this complex nature of social network. Our paper, focusing on the evolutionary dynamics, is intended to explore how and why it happens, and what kind of impact is caused by homophily among people. We investigate the evolution of human cooperation using evolutionary game theory on multiplex. Multiplexity, as an extra dimension of analysis, allows us to unveil the hidden dynamics and observe non-trivial patterns within a population across network layers. More importantly, we find a striking role of homophily, as the higher the homophily between individuals, the quicker is the convergence towards cooperation in the social dilemma. The simulation results, conducted both macroscopically and microscopically across the network layers in the multiplex, show quantitatively the role of homophily in human cooperation

Payoff Matrices of the Prisoner’s Dilemma Game.

<p>Payoff Matrices of the Prisoner’s Dilemma Game.</p

Centrality distribution in the multiplex network.

<p>The multiplex is made of <i>N</i> = 1000 nodes embedded within <i>M</i> = 3 layers, each one modelled by a different scale-free network. The size of nodes is proportional to centrality measure.</p

Critical mass density.

<p>The Critical Mass Density as a function of the population’s size <i>N</i> and the number of layers <i>M</i>.</p

Evolution of cooperation considering different interlayer interaction strength.

<p>The evolution of cooperation against the round as a function of interlayer interaction strength. The ‘blue’ plot represents the case of constant interlayer strength: <i>ω</i>_<i>αβ</i> = 0.4. The ‘red’ plot represents the case of variable interlayer strength (one dominant layer): <i>ω</i>_<i>αβ</i> = 0.3 between layers 1 and 3; <i>ω</i>_<i>αβ</i> = 0.6 between the layer 2 and the other layers of the multiplex. We show the evolution of cooperation until 200 rounds as, in correspondence of that value, the convergence has already been reached. It can be observed that the emergence of cooperation is quicker considering a variable interlayer strength (one dominant layer), than the constant case. The dominant layer acts as a behaviour’s polarizer of the nodes in the other layers.</p

Schematic example of a multiplex network.

<p>The multiplex is made of N = 5 nodes embedded within M = 3 layers, each one containing 3 links. The size of nodes is proportional to centrality measure. The dashed lines represent interlayer connections, while the continuous lined represent the intra-layer connections.</p

Temporal evolution of cooperation.

<p>The figure highlights the microscopic emergence of cooperation in the evolutionary process. The formation of cooperative groups in the network and also the group size depend on the homophily value. Figs <b>A</b>, <b>B</b>, <b>C</b>—in the low homophily case (<i>σ</i> = 8), the defective behaviour tends to persist more in the population, not favouring the formation of cooperative groups and globally slowing the emergence of cooperation. Yet, the group size will be smaller in this case of low homophily. Figs <b>D</b>, <b>E</b>, <b>F</b>—in the high homophily case (<i>σ</i> = 1), the convergence towards cooperation becomes quicker, and there is a natural formation of larger cooperative groups than in low homophily case. Analysing the corresponding figures of the evolution, we see clearly this difference, both in speed and size, in the formation of cooperative groups.</p

Emergence of cooperation over time.

<p>The figure illustrates the fraction of cooperative nodes against the rounds or time steps: low homophily (<b>A</b>) and high homophily (<b>B</b>). The figure shows the evolutionary dynamics of the PD game played between the interacting nodes in a multiplex network with <i>M</i> = 3 layers. In both cases <i>N</i> = 1000 nodes. The results are obtained choosing a fixed number of simulations and the colour corresponds to the density: ‘red’ indicates the highest density (that is the maximum number of overlapping points), while ‘blue’ means the lowest density. As can be observed, increasing the homophily value of the multiplex network <math><mi>M</mi></math>, we note a faster emergence of cooperation.</p