Connectivity Games over Dynamic Networks

TL;DR

This paper introduces a game-theoretic model for dynamic networks involving node failures and restorations, analyzing the conditions for network connectivity and providing algorithms based on winning strategies.

Contribution

It presents a novel two-player game model for dynamic networks with node failures and restorations, analyzing decidability and complexity of connectivity objectives.

Findings

Decidability conditions for Constructor's success are identified.

Complexity bounds and algorithms for winning strategies are established.

Safety and reachability objectives are treated separately due to asymmetry.

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.