Invited Session Wed.1.MA 005

Wednesday, 10:30 - 12:00 h, Room: MA 005

Cluster 8: Game theory [...]

Games over networks


Chair: Asu Ozdaglar



Wednesday, 10:30 - 10:55 h, Room: MA 005, Talk 1

Asu Ozdaglar
Network security and contagion

Coauthors: Daron Acemoglu, Azarakhsh Malekian


This paper develops a network model of investments in security. The connections introduce the possibility of cascading failures. With exogenous attacks, a single attack takes place in one part of the network determined at random. Each agent chooses their level of security investment ex ante (before knowing where the attack will take place) according to a potentially-heterogeneous cost function. We establish existence of a pure-strategy equilibrium and provide conditions for its uniqueness, which require the cost functions for security investments to be sufficiently convex. Under the same conditions, the expected number of total infections will be lower in the social welfare maximum than in the equilibrium. Neither the uniqueness nor the efficiency result is true in general. With endogenous attacks, the attacker is modeled as choosing a probability distribution over the location of the attack. In contrast to the model with exogenous attacks, there is now an economic force for pervasive overinvestment in security. By increasing security investments, an agent discourages attacks to his part of the network, shifting the attack to other parts, and creating a negative externality.



Wednesday, 11:00 - 11:25 h, Room: MA 005, Talk 2

Pablo A. Parrilo
Near-potential network games

Coauthors: Ozan Candogan, Asuman Ozdaglar


It is known that "natural'' distributed dynamics such as best-response converge to an equilibrium only for restrictive classes of games, such as potential games. These considerations lead to natural and important questions: What makes potential games "special''? Can we approximately characterize the properties of a given network game, by analyzing a potential game that is close to it?
In this talk we provide an optimization-based framework for finding, and characterizing the properties, of the closest potential game to a given network game. We focus on both bilateral and multilateral interaction games, where the payoff of each agent can be written as a function of its neighbors' strategies. We show that the closest potential game to a multilateral interaction game is a second-order multilateral interaction game, i.e., a game where the payoff of each player is a function of strategies of its neighbors, and their neighbors. Our results indicate that a network game and the closest potential game have similar structural features, and these can be used to characterize static and dynamic properties of the original network game.



Wednesday, 11:30 - 11:55 h, Room: MA 005, Talk 3

Ali Jadbabaie
A game-theoretic model of competitive contagion and product adoption in social networks

Coauthor: Arastoo Fazeli


We propose and and analyze a strategic model of marketing and product adoption in social networks. Two firms compete for the spread of their products. Given a fixed budget, each firm has to decide how much to invest in their product and as a result, determine the payoff the customers get by adopting each firm's product, as the well as the number of the initial seeds in the network. Once the payoff is determined, agents in the social network play a local coordination game over the network which determines the dynamics of the spreading.
Assuming myopic best response dynamics, agents choose a product based on the received payoff (which depends on the firm's decision) by looking at actions of their neighbors. This local update dynamics results in a game-theoretic diffusion process in the network.
We derive an explicit characterization of these bounds based on the payoff of products offered by firms, the initial number of adoptions and the underlying structure of the network. We then study the equilibrium of the game between firms and analyze the tarde off between investment in product's quality vs. increasing the number of initial seeds.


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