Quantitative Games under Failures

TL;DR

This paper extends sabotage games to infinite processes with dynamic weights and budgets, analyzing the computational complexity of strategy problems under various conditions.

Contribution

It introduces a quantitative extension of sabotage games with dynamic weights and budgets, and characterizes the complexity of related decision problems.

Findings

Determining if Runner can keep cost below a threshold is EXPTIME-complete for most cost functions.

With fixed Saboteur budget, the problem becomes PTIME for most cost functions.

Restricting game dynamics improves computational complexity.

Abstract

We study a generalisation of sabotage games, a model of dynamic network games introduced by van Benthem. The original definition of the game is inherently finite and therefore does not allow one to model infinite processes. We propose an extension of the sabotage games in which the first player (Runner) traverses an arena with dynamic weights determined by the second player (Saboteur). In our model of quantitative sabotage games, Saboteur is now given a budget that he can distribute amongst the edges of the graph, whilst Runner attempts to minimise the quantity of budget witnessed while completing his task. We show that, on the one hand, for most of the classical cost functions considered in the literature, the problem of determining if Runner has a strategy to ensure a cost below some threshold is EXPTIME-complete. On the other hand, if the budget of Saboteur is fixed a priori, then the problem is in PTIME for most cost functions. Finally, we show that restricting the dynamics of the game also leads to better complexity.