Multi-Player Diffusion Games on Graph Classes

We study competitive diffusion games on graphs introduced by Alon et al. [1] to model the spread of influence in social networks. Extending results of Roshanbin [8] for two players, we investigate the existence of pure Nash equilibria for at least three players on different classes of graphs including paths, cycles, grid graphs and hypercubes; as a main contribution, we answer an open question proving that there is no Nash equilibrium for three players on (m x n) grids with min(m, n) >= 5. Further, extending results of Etesami and Basar [3] for two players, we prove the existence of pure Nash equilibria for four players on every d-dimensional hypercube.Comment: Extended version of the TAMC 2015 conference version now discussing hypercube results (added details for the proof of Proposition 1

Choosing Products in Social Networks

We study the consequences of adopting products by agents who form a social network. To this end we use the threshold model introduced in Apt and Markakis, arXiv:1105.2434, in which the nodes influenced by their neighbours can adopt one out of several alternatives, and associate with such each social network a strategic game between the agents. The possibility of not choosing any product results in two special types of (pure) Nash equilibria. We show that such games may have no Nash equilibrium and that determining the existence of a Nash equilibrium, also of a special type, is NP-complete. The situation changes when the underlying graph of the social network is a DAG, a simple cycle, or has no source nodes. For these three classes we determine the complexity of establishing whether a (special type of) Nash equilibrium exists. We also clarify for these categories of games the status and the complexity of the finite improvement property (FIP). Further, we introduce a new property of the uniform FIP which is satisfied when the underlying graph is a simple cycle, but determining it is co-NP-hard in the general case and also when the underlying graph has no source nodes. The latter complexity results also hold for verifying the property of being a weakly acyclic game.Comment: 15 pages. Appeared in Proc. of the 8th International Workshop on Internet and Network Economics (WINE 2012), Lecture Notes in Computer Science 7695, Springer, pp. 100-11

A Dynamic Game of Technology Diffusion under an Emission Trading Regulation: A Pilot Experiment

In this paper we investigate how the interaction between the product and the emission permit markets may affect firms' propensity to adopt cleaner technologies. The adoption of a cleaner technology has the direct effect of reducing the compliance cost of the firm, but it also involves a strategic decision, if the industry is not perfectly competitive. We look at this problem from both a theoretical and an experimental point of view. We develop a model of duopoly, in which two firms engage in quantity competition in the output market and behave as price takers in the permit market. Firms have the possibility of investing in a cleaner production technology, which is available on the market at some cost. We set up a dynamic game over an infinite horizon in order to investigate firms' investment decisions: in each period, each firm decides whether to invest in the new technology or not. The stationary equilibria to this game crucially depend on both the cost of switching to the cleanest technology and the emission cap. Technology diffusion is one of the possible equilibria of the game. In order to test the predictions of the theory, we design and implement an "innovation experiment" that replicates the "innovation game". The results of our pilot experiment suggest that firms' behaviour will eventually lead to innovation diffusion.tradable permits; technology adoption; oligopoly; laboratory experiments

Phonebanking

Banking;Market Structure;Game Theory

Information Diffusion on Social Networks

In this thesis we model the diffusion of information on social networks. A game played on a specific type of graph generator, the iterated local transitivity model, is examined. We study how the dynamics of the game change as the graph grows, and the relationship between properties of the game on a graph initially and properties of the game later in the graph’s development. We show that, given certain conditions, for the iterated local transitivity model it is possible to predict the existence of a Nash equilibrium at any point in the graph’s growth. We give sufficient conditions for the existence of Nash Equilibria on star graphs, cliques and trees. We give some results on potential games on the iterated local transitivity model. Chapter 2 provides an introduction to graph properties, and describes various early graph models. Chapter 3 describes some models for online social networks, and introduces the iterated local transitivity model which we use later in the thesis. In Chapter 4 various models for games played on networks are examined. We study a model for competitive information diffusion on star graphs, cliques and trees, and we provide conditions for the existence of Nash Equilibria on these. This model for competitive information diffusion is studied in detail for the iterated local transitivity model in Chapter 5. We discuss potential games in Chapter 6 and their existence on the iterated local transitivity model. We conclude with some suggestions on how to extend and develop upon the work done in this thesis

Firefighting as a game

The Firefighter Problem was proposed in 1995 [16] as a deterministic discrete-time model for the spread (and containment) of a fire. Its applications reach from real fires to the spreading of diseases and the containment of floods. Furthermore, it can be used to model the spread of computer viruses or viral marketing in communication networks. In this work, we study the problem from a game-theoretical perspective. Such a context seems very appropriate when applied to large networks, where entities may act and make decisions based on their own interests, without global coordination. We model the Firefighter Problem as a strategic game where there is one player for each time step who decides where to place the firefighters. We show that the Price of Anarchy is linear in the general case, but at most 2 for trees. We prove that the quality of the equilibria improves when allowing coalitional cooperation among players. In general, we have that the Price of Anarchy is in T(n/k) where k is the coalition size. Furthermore, we show that there are topologies which have a constant Price of Anarchy even when constant sized coalitions are considered.Peer ReviewedPostprint (author’s final draft

Mean-Field-Type Games in Engineering

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201