Exponga algunos criterios que permitan el perfeccionamiento del sistema de actividades

Few studies have explored the notion of convention emergence in dynamic topologies despite the fundamental differences that allowing nodes and edges to be added and removed brings to the network dynamics. Some work has been performed in the related field of norm emergence but is primarily concerned with essential rather than conventional norms [Mungovan et al., 2010; Savarimuthu et al., 2007]. Savarimuthu et al. [2007] show that norms are able to emerge un- der a number of conditions and settings of dynamic topologies, but their work differs from ours due to the requirements placed on agents. The interaction model used requires agents to maintain an internal norm as well as being able to query other agents. We make minimal assumptions about agent internals or the information available. Additionally, our work investigates themanipulation

of convention emergence, something not considered by Savarimuthu et al. for norms.

Mihaylov et al. [Mihaylov et al., 2014] briefly consider convention emergence in dynamic topologies using the coordination game. However, their work focuses on a new proposed method of learning, rather than on the emergence itself. In particular, they do not consider fixed strategy agents, or the action that emerges as a convention. In this thesis, we consider both convention emergence in dynamic topologies and the use of fixed strategy agents to understand the impact of network dynamics.

We seek to establish the performance and characteristics in dynamic net- works compared to static ones and as such make use of two dynamic topology generators throughout this thesis.

Gonz´alez model

We utilise a particle-based simulation, developed by Gonz´alez et al. [Gonz´alez et al., 2006a; Gonz´alez et al., 2006b], to model dynamic network topologies with characteristics comparable to those observed in real-world networks. Agents are represented as colliding particles and the topology is modified by collisions

creating links between the agents. A population ofN agents, represented as a set of particles with radiusr, is placed within a 2D box with sides of lengthL. Initially, all agents are distributed uniformly at random within the space and are assigned a velocity of constant magnitudev0 and random direction.

Each timestep, agents move according to their velocity and detect collisions with other agents. When two agents collide, an edge is added between them in the network topology if one does not already exist. Both agents then move away in a random direction with a speed proportional to their degree multiplied by a speed factor, ¯v . Thus, higher degree nodes have an increased probability of further collisions, which in turn further increases their degree. In this way, the model exhibits preferential attachment, a characteristic found in static scale-free networks [Barab´asi & Albert, 1999].

Additionally, all agents are assigned a Time-To-Live (TTL) when created. This is drawn uniformly at random between zero and the maximum TTL, Tl. After each timestep agents’ TTLs are decremented by one. When an agent’s TTL = 0 the agent and all its edges are removed. A new agent is placed at the same location within the simulation with the randomised initial properties discussed above. In this manner, the topology is constantly changing.

Different topologies can be characterised by the value ofTl/T0 where T0 is

the characteristic time between collisions. This can be expressed as:

Tl T0 =2 √ 2πrN v0Tl L2 (2.2)

Gonz´alez et al. show that this value dictates key characteristics of the gen- erated topology, primarily the average degree and degree distribution and in [Gonz´alez et al., 2006b] they show that these are good approximations of the actual social networks amongst students in a school.

The concept of a quasi-stationary state (QSS) is discussed by Gonz´alez et al., such that a QSS emerges after a number of timesteps and is characterised by macro-scale stability of network characteristics. Micro-scale characteristics,

for individual agents, remain in flux. In [Gonz´alez et al., 2006a] it is shown that the QSS can be described as any timestep,t, wheret_&2Tl.

Ichinose model

Ichinose et al. [2013] build a dynamic network as an extension of the Barab´asi- Albert model. As such it has the same useful features of that model, namely a scale-free nature and short average path length. The presence of these features will allow comparison between the similar static and dynamic networks in terms of the convention emergence upon them.

The Ichinose model begins by building a Barab´asi-Albert graph of the re- quested size with the same parameters,m,m0. Then, each iteration, a node is

removed and a new one inserted into the topology with the number of edges in the system kept the same. In this manner, both the number of nodes and edges in the topology will remain constant with only their arrangement changing.

Ichinose et al. specify 2 different methods of node removal: targeted, where the highest degree node in the topology is removed, andrandom, where a node is removed at random. The degree of the removed node is noted asn. A new node is then created with degreemorn, whichever is lower. The edges of these nodes are then attached to others using two other methods: preferential, where the node is chosen with probability proportional to their degree (as in the Barab´asi- Albert model) and random, where the node is chosen uniformly at random. If the number of edges in the network is less than it was before, edges are inserted into the system from source nodes (chosen uniformly at random) to target nodes which are selected the same way as the new node’s edges, preferentially or at random.

Thus there are four possible modes that the Ichinose model can operate in:

• Randomremoval andRandom addition(RR)

• Randomremoval andPreferential addition(RP)

• Targeted removal andPreferential addition(TP)

In the paper the model is introduced they investigate the effect of their different topologies on the robustness and stability of the cooperation in the Prisoner’s Dilemma showing that the various modes have drastically varying effects on the level of cooperation with targeted removal reducing cooperation even with a low benefit to defection. They evaluate the model’s effect on numer- ous graph metrics compared to the original Barab´asi-Albert topology and show that all four reduce the degree variance in the network and shift the degree dis- tribution with the modes of targeted removal drastically decreasing the degree variance and maximum degree. These different behaviours highlight that the 4 settings produce dramatically different topologies and as such can be expected to have distinct influences on convention emergence.