This paper introduces an agent-based simulation model that integrates consumer behavior and innovation diffusion. Using the model, they formalize different network structures that represent different market characteristics and to examine the effects of these market characteristics on the innovation diffusions.
The two market characteristics investigated are
1. Levels of social influence – how much do consumers affect
each other?
2. The role of hubs: individuals with disproportionate
influence (VIPs).
The Social
Percolation Model
- A regular lattice F consists of L x L cells.
- Each cell is in one of two states, activated (1) or not (0)
- Each cell is activated with probability r.
- A cluster is defined as a spatially continuous group of activated neighbors, where each cell’s neighbors is the four nearest cells (von Neumann).
- Percolation occurs when a cluster is large enough to contain at least one cell of every row and column in F.
- The percolation threshold, r_c, is the minimum r for which percolation is observed.
A percolation model
of hits and flops of movies (from Solomon et al. 2000 and Weisbuch&
Stauffer 2000).
- Agents are heterogeneous in their preference, p_i.
- Some agents have already seen the movie and inform their 4 adjacent neighbors about the quality of the movie, q.
- When an agent i is informed about the movie, she evaluates it, and decides to see the movie if the quality is above her preference threshold, q > p_i. In the next time step, she informs her neighbors about the movie.
- In a classic percolation model, individual preferences are uniformly distributed in [0, 1].
- Although a full rational choice model assumes that all agents have perfect knowledge of the movie’s quality, the classical percolation model demonstrates that when information is propagated through a social network, the success of the movie depends on whether its quality exceeds the percolation threshold.
- The assumptions of a regular network and fixed individual preferences are very strong and not supported empirically.
Agent-based model for
innovation diffusions
- Agents decide whether to adopt the innovation according to a weighted utility of individual preference and social influence.
- If the average weight on social utility is low, then we are talking about very individualistic markets (e.g. furniture, durables). When it is high, the population is more socially susceptible (e.g. clothes).
- The social utility is just the fraction of i’s neighbors who have already adopted.
- The individual utility based on the individual’s preference threshold, p_i and the quality of the product, q. If q > p_i, the individual utility will be close to 1, otherwise it is close to 0.
- Agent i buys the product when she has been informed of it and when the utility is higher than its minimum utility requirement. This minimum is basically an aspiration level. If it is high, the agent is difficult to satisfy and only adopts if the utility of the product is very high.
- A simulation starts with a small percentage adopting the product (sims used 0.5% of the pop). Once an agent i adopts, she informs her neighbors about its quality. At the next time steps, those informed neighbors compute the utility of adopting and decide whether to adopt. The simulation ends when no more agents adopt.
- Agents are positioned in a social network with undirected links. Information can only be passed along links.
- Agents are heterogeneous: social/indiv utility weights, minimum utility, and preference thresholds all vary uniformly between 0 and 1.
Network structures
- Degree distribution. This paper focuses on scale-free networks. They use the “more realistic” scale-free network algorithm of Amaral et al. (2000, PNAS). Here, when a new node is introduced, the probability of all the other nodes being selected for attachment is proportional to the number of nodes they already have, but this decays exponentially due to a fixed probability h to become inactive at any point in the process. That is, once a node becomes inactive, it cannot accept new links. This produces a decaying tail for the degree distribution. The network will be come less central and more disperse for higher values of h.
- Weighted links. Two cases are considered: (1) The influence is equal for all the neighbors; and (2) the influence of each neighbor is proportional to the number of links it has. The second case models the notion that more connected people exert higher social influence.
- Directed links. Two cases were considered: (1) The probability of directing the link from i to j is simply 0.5; and (2) the probability of directing the link from i to j depends on the number of links that i and j have—that is, the more (less) links j has compared with i, the more (less) likely that i is directed to j. For the latter specification, it is assumed that among two neighbors it is more likely that the more connected agent attracts the attention of the other. The relinking process takes each link between node i and j and directs it with a probability p. Note that a link represents attention, not influence, so that if i is linked with j, then i is informed by j.
Simulation
Experiments and Results
Effects of social
networks
- First, they replicated the percolation model of Solomon et al. (2000) by turning off social influence. They found that a new product diffuses more in a scale-free network than it does in a regular lattice, with diffusion rates closer to that of a complete information model, especially for pickier agents (Figure 3). In other words, the scale-free network is much more efficient in spreading information.
- In the remaining experiments, only scale-free networks were used.
High vs. Low Social
Influence
- In scale-free networks of consumers, a higher level of social influence leads, on average, to a lower diffusion of the innovation.
- In scale-free networks of consumers, a higher level of social influence leads to a higher level of uncertainty about the final penetration of the innovation. There is more path dependency because high clustering can cause the spread of innovation rapidly, but low clustering can halt the spread of even a very good innovation.
Different Markets and
Different Networks
- A higher level of cost constraints for the number of neighbors of the agents (the parameter h, which curves the tail of the degree distribution and makes for a more dispersed network) leads to a lower diffusion of the innovation.
- A higher level of cost constraints for the number of neighbors of the agents leads to a higher level of uncertainty about the final penetration of the innovation.
- A higher level of social influence exerted by the more connected agents leads to a higher diffusion of the innovation.
- The more the agents direct their links to the VIPs, the higher the diffusion of the innovation.
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