Abstract
Network creation games have been extensively used as mathematical models to capture the key aspects of the decentralized process that leads to the formation of interconnected communication networks by selfish agents. In these games, each user of the network is identified by a node and selects which link to activate by strategically balancing his/her building cost with his/her usage cost (which is a function of the distances towards the other player in the network to be built). In these games, a widespread assumption is that players have a common and complete information about the evolving network topology. This is only realistic for small-scale networks as, when the network size grows, it quickly becomes impractical for the single users to gather such a global and fine-grained knowledge of the network in which they are embedded. In this work, we weaken this assumption, by only allowing players to have a partial view of the network. To this aim, we borrow three popular traceroute-based knowledge models used in network discovery: (i) distance vector, (ii) shortest-path tree view, and (iii) layered view. We settle many of the classical game theoretic questions in all of the above models. More precisely, we introduce a suitable (and unifying) equilibrium concept which we then use to study the convergence of improving and best response dynamics, the computational complexity of computing a best response, and to provide matching upper and lower bounds to the price of anarchy.
Highlights
The construction of large communication networks involves the interaction of many independent and selfish agents with competing interests and, in such a decentralized setting, the problem of understanding the formation process of a network arises naturally.More formally, we model the agents as a set of n vertices in a graph, each controlled by a player that wants to connect itself to all of the other participants of the network
Players prefer low-latency communication paths over longer paths and will always route messages along a shortest path. It is clear how tension stems from the desire of a player for efficient communication, and his/her interest in minimizing the number of activated links. The study of such a trade-off between a player’s building cost and her usage cost results in the corresponding study of a communication network creation game, known as network connection game
Small values of the Price of Anarchy (PoA) show that even if the network arises from a combination of selfish strategies, its quality will not be significantly worse than the best possible design
Summary
The construction of large communication networks involves the interaction of many independent and selfish agents with competing interests and, in such a decentralized setting, the problem of understanding the formation process of a network arises naturally. We model the agents (i.e., players) as a set of n vertices in a graph, each controlled by a player that wants to connect itself to all of the other participants of the network This can happen either directly, by the unilateral and costly activation of a corresponding logical or physical communication channel (i.e., a link), or indirectly by routing messages over (a subset of the) existing (bidirectional) links that were activated by other agents. Players prefer low-latency communication paths over longer paths and will always route messages along a shortest path It is clear how tension stems from the desire of a player for efficient communication, and his/her interest in minimizing the number of activated links. The study of such a trade-off between a player’s building cost (which is proportional to the number of links she decides to activate) and her usage cost (some function that depends on the distance between the player and the remaining agents in the resulting network) results in the corresponding study of a communication network creation game, known as network connection game ( NCG in the following)
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