Cooperation: popularity or cliquishness ?

We propose an analytical and computational insight about the role of endogenous networks in emergence and sustainability of cooperation and exhibits an alternative to the choice and refusal mechanism that is often proposed to explain cooperation.

A paradigmatic representation of situation where there is a conflict between collective interest and individual interests:

kinds of networks :

• the network of accessibility - whos can interact with who ?
• the activity network - who is actually interacting with who ?

Recent literature demonstrated that cooperation is favored by a high degree of cliquishness of the activity networks.

In case of endogenous networks

• What are the conditions under which local partner selection generates networks that can sustain cooperation?
• Other mechanisms than cliquishness ?

Parameters

• N agents playing a sequential PD game in discrete time.
• Each period, each agent has the opportunity to play only once as a first mover.
• With a probability of (1 − e), 0<e<1, first movers can choose their partner
• The network of accessibility is fully connected
• Agents have address books

Each round

1. each agent does a proposition (C or D) to a partner it has eventually chosen from address book,
2. each agent answers (D or C) as a second mover to every agent that has chosen it.

The directed network of activity develops during of the game.

Agents' types

Experiments reveal heterogenous populations of agents that can schematically be represented with 3 types (K. Clark and M. Sefton 2001 ; T.-K. Ahn et al. 2001) :

First mover

Second mover

Evolution of the distribution of types

• The sum of all payoffs are computed at the end of each round.
• Agents have a probability (1−theta) to be removed from the population at the end of each period.
• Each agent leaving the game is replaced by a new agent choosen according to a replicator dynamics indexed on this sum of payoffs.
• New agents have empty address book

Comparison between analytical predictions and simulations. For e = 0.3, p = 0.3, theta=0.99 the theoretical analysis predicts very well the behavior of the system.

• Line with circles: theoretical trajectory in case of infinite population size.
• Dotted lines: plots of 10 independent simulations with N = 500. Each circle is separated by 100 periods i.e. the agents’ mean lifetime expectancy. X-axis: proportion of altruists, Y-axis: proportion of reciprocators.

• Co-evolution between agents’ types and networks’ patterns can leads to characteristic networks’ structures that depart from the cliquish structures that traditionally account for heterogeneous cooperative equilibria.
• Cooperation can be sustainable due the increase in activity of popular (cooperative) agents.
• In real social networks, agents often do not have the same activity level due to differences in popularity. This phenomena shouldn't be forgotten in social networks modeling.