Section: New Results

Economics of Networks

Participants : François Baccelli, Emilie Coupechoux, Marc Lelarge.

The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. In [25] , we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination game with binary choice and give a condition for a new action to become widespread in a random network. We also analyze the possible equilibria of this game and identify conditions for the coexistence of both strategies in large connected sets. Finally we look at how can firms use social networks to promote their goals with limited information.

Our results differ strongly from the one derived with epidemic models. In particular, we show that connectivity plays an ambiguous role: while it allows the diffusion to spread, when the network is highly connected, the diffusion is also limited by high-degree nodes which are very stable. In the case of a sparse random network of interacting agents, we compute the contagion threshold for a general diffusion model and show the existence of (continuous and discontinuous) phase transitions. We also compute the minimal size of a seed of new adopters in order to trigger a global cascade if these new adopters can only be sampled without any information on the graph. We show that this minimal size has a non-trivial behavior as a function of the connectivity. Our analysis extends methods developed in the random graphs literature based on the properties of empirical distributions of independent random variables, and leads to simple proofs.

Malicious softwares or malwares for short have become a major security threat. While originating in criminal behavior, their impact are also influenced by the decisions of legitimate end users. Getting agents in the Internet, and in networks in general, to invest in and deploy security features and protocols is a challenge, in particular because of economic reasons arising from the presence of network externalities. In [24] , [42] , we focus on the question of incentive alignment for agents of a large network towards a better security. We start with an economic model for a single agent, that determines the optimal amount to invest in protection. The model takes into account the vulnerability of the agent to a security breach and the potential loss if a security breach occurs. We derive conditions on the quality of the protection to ensure that the optimal amount spent on security is an increasing function of the agent's vulnerability and potential loss. We also show that for a large class of risks, only a small fraction of the expected loss should be invested. Building on these results, we study a network of interconnected agents subject to epidemic risks. We derive conditions to ensure that the incentives of all agents are aligned towards a better security. When agents are strategic, we show that security investments are always socially inefficient due to the network externalities. Moreover alignment of incentives typically implies a coordination problem, leading to an equilibrium with a very high price of anarchy.