Connectivity Games over Dynamic Networks

Abstract

A game-theoretic model for the study of dynamic networks is analyzed. The model is motivated by communication networks that are subject to failure of nodes and where the restoration needs resources. The corresponding two-player game is played between "Destructor" (who can delete nodes) and "Constructor" (who can restore or even create nodes under certain conditions). We also include the feature of information flow by allowing Constructor to change labels of adjacent nodes. As objective for Constructor the network property to be connected is considered, either as a safety condition or as a reachability condition (in the latter case starting from a non-connected network). We show under which conditions the solvability of the corresponding games for Constructor is decidable, and in this case obtain upper and lower complexity bounds, as well as algorithms derived from winning strategies. Due to the asymmetry between the players, safety and reachability objectives are not dual to each other and are treated separately

Dynamic Connectivity Game for Adversarial Internet of Battlefield Things Systems

“…Due to the clear dependence between the goals and the actions of the attacker and the defender as well as the impact of the attacker and defender's actions on the IoBT network graph, the problem will be formulated as a noncooperative positional game [12] and [14], as explained next.…”

“…Connectivity games are game-theoretic models [12] that capture situations which require the maintainenance and restoration of the normal operations of a given network. Connectivity games typically involve two players: a constructor who is responsible for restoration of nodes as well as the addition of new nodes, and a destructor who removes nodes from the network.…”

“…The constructor in our game is the IoBT defender whereas the destructor is the attacker. A connectivity game [12] is an interactive game in which the constructor and the destructor play in alternation until one of the players wins the game. The winning condition for the constructor involves maintaining the connectivity of the network.…”

“…The winning condition for the constructor involves maintaining the connectivity of the network. In particular, there are two types of objectives considered in classsical connectivity games [12]: 1) A safety objective in which the constructor must maintain the connectivity of the network in every step of the game and 2) A reachability objective in which the constructor must obtain a connected network starting from a disconnected network.…”

“…The objective of the attacker and the defender is to maximize their sum of payoffs until the end of the military operation. • We formulate the connectivity problem in the IoBT using the framework of connectivity games [12] which are game-theoretic frameworks suitable for addressing problems that involve the maintenance and restoration of a network in presence of adversaries. However, in classical connectivity games, the sole objective is to restore or maintain the network connectivity, whereas in the IoBT, there are other performance metrics that must be considered such as the latency of communication.…”