A Consumer-Based Model of Competitive Diffusion of Two Goods: The Effects of Network Externalities and Local Interactions

The diffusion of two competitive, interchangeable, and durable goods is studied under the framework of a spatial game where consumers are distributed on a two-dimensional square lattice and play 3$\times$3 symmetric coordination-like games with their nearest neighbors. There are three strategies, either consuming a product A or B, or a strategy C of not consuming either A or B. The payoff matrix of the game contains the positive effects of network externality, that is, the payoffs are increasing functions of the number of agents adopting the strategies A or B. Both simulations and mean-field approximation show that the existence of the positive effects of the network externality amplifies any slight initial difference in the number of agents who adopt either A or B and eventually promotes the superior product to take over the entire market. On the other hand, without effects of the network externality the slight initial difference is not enlarged and both superior and inferior products are observed to coexist by forming clusters in the market. Moreover, the effects of innovation factors that help an inferior product to retake the market are studied. It is shown that both the timing and size of the innovation factor matter for an inferior product in order to retake the market.competitive diffusion, network externality, local interaction, global externality, local externality, evolutionary game, spatial game

Peer-to-Peer and Mass Communication Effect on Revolution Dynamics

Revolution dynamics is studied through a minimal Ising model with three main influences (fields): personal conservatism (power-law distributed), inter-personal and group pressure, and a global field incorporating peer-to-peer and mass communications, which is generated bottom-up from the revolutionary faction. A rich phase diagram appears separating possible terminal stages of the revolution, characterizing failure phases by the features of the individuals who had joined the revolution. An exhaustive solution of the model is produced, allowing predictions to be made on the revolution's outcome

Coevolutionary games - a mini review

Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries.Comment: 24 two-column pages, 10 figures; accepted for publication in BioSystem

Peer influence in network markets: a theoretical and empirical analysis

Network externalities spur the growth of networks and the adoption of network goods in two ways. First, they make it more attractive to join a network the larger its installed base. Second, they create incentives for network members to actively recruit new members. Despite indications that the latter "peer effect" can be more important for network growth than the installed-base effect, it has so far been largely ignored in the literature. We address this gap using game-theoretical models. When all early adopters can band together to exert peer influence-an assumption that fits, e.g., the case of firms supporting a technical standard-we find that the peer effect induces additional growth of the network by a factor. When, in contrast, individuals exert peer influence in small groups of size n, the increase in network size is by an additive constant-which, for small networks, can amount to a large relative increase. The difference between small, local, personal networks and large, global, anonymous networks arises endogenously from our analysis. Fundamentally, the first type of networks is "tie-reinforcing," the other, "tie-creating". We use survey data from users of the Internet services, Skype and eBay, to illustrate the main logic of our theoretical results. As predicted by the model, we find that the peer effect matters strongly for the network of Skype users-which effectively consists of numerous small sub-networks-but not for that of eBay users. Since many network goods give rise to small, local networks

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Complex Transition to Cooperative Behavior in a Structured Population Model

Cooperation plays an important role in the evolution of species and human societies. The understanding of the emergence and persistence of cooperation in those systems is a fascinating and fundamental question. Many mechanisms were extensively studied and proposed as supporting cooperation. The current work addresses the role of migration for the maintenance of cooperation in structured populations. This problem is investigated in an evolutionary perspective through the prisoner's dilemma game paradigm. It is found that migration and structure play an essential role in the evolution of the cooperative behavior. The possible outcomes of the model are extinction of the entire population, dominance of the cooperative strategy and coexistence between cooperators and defectors. The coexistence phase is obtained in the range of large migration rates. It is also verified the existence of a critical level of structuring beyond that cooperation is always likely. In resume, we conclude that the increase in the number of demes as well as in the migration rate favor the fixation of the cooperative behavior

Strength of Social Tie Predicts Cooperative Investment in a Human Social Network

Social networks – diagrams which reflect the social structure of animal groups – are increasingly viewed as useful tools in behavioural ecology and evolutionary biology. Network structure may be especially relevant to the study of cooperation, because the action of mechanisms which affect the cost:benefit ratio of cooperating (e.g. reciprocity, punishment, image scoring) is likely to be mediated by the relative position of actor and recipient in the network. Social proximity could thus affect cooperation in a similar manner to biological relatedness. To test this hypothesis, we recruited members of a real-world social group and used a questionnaire to reveal their network. Participants were asked to endure physical discomfort in order to earn money for themselves and other group members, allowing us to explore relationships between willingness to suffer a cost on another's behalf and the relative social position of donor and recipient. Cost endured was positively correlated with the strength of the social tie between donor and recipient. Further, donors suffered greater costs when a relationship was reciprocated. Interestingly, participants regularly suffered greater discomfort for very close peers than for themselves. Our results provide new insight into the effect of social structure on the direct benefits of cooperation

Adaptive and Bounded Investment Returns Promote Cooperation in Spatial Public Goods Games

The public goods game is one of the most famous models for studying the evolution of cooperation in sizable groups. The multiplication factor in this game can characterize the investment return from the public good, which may be variable depending on the interactive environment in realistic situations. Instead of using the same universal value, here we consider that the multiplication factor in each group is updated based on the differences between the local and global interactive environments in the spatial public goods game, but meanwhile limited to within a certain range. We find that the adaptive and bounded investment returns can significantly promote cooperation. In particular, full cooperation can be achieved for high feedback strength when appropriate limitation is set for the investment return. Also, we show that the fraction of cooperators in the whole population can become larger if the lower and upper limits of the multiplication factor are increased. Furthermore, in comparison to the traditionally spatial public goods game where the multiplication factor in each group is identical and fixed, we find that cooperation can be better promoted if the multiplication factor is constrained to adjust between one and the group size in our model. Our results highlight the importance of the locally adaptive and bounded investment returns for the emergence and dominance of cooperative behavior in structured populations