Stackelberg-Pareto Synthesis (Full Version)

TL;DR

This paper explores a new class of Stackelberg games with multiple objectives for Player 1, analyzing the computational complexity of synthesizing Player 0's strategies to ensure objectives are met despite rational responses.

Contribution

It introduces the Stackelberg-Pareto Synthesis problem with multiple objectives and characterizes its complexity for different game types, including fixed-parameter tractability and NEXPTIME-completeness.

Findings

The problem is fixed-parameter tractable for parity or reachability objectives.

The problem is NEXPTIME-complete for these objectives.

The problem is NP-complete for reachability objectives on trees.

Abstract

In this paper, we study the framework of two-player Stackelberg games played on graphs in which Player 0 announces a strategy and Player 1 responds rationally with a strategy that is an optimal response. While it is usually assumed that Player 1 has a single objective, we consider here the new setting where he has several. In this context, after responding with his strategy, Player 1 gets a payoff in the form of a vector of Booleans corresponding to his satisfied objectives. Rationality of Player 1 is encoded by the fact that his response must produce a Pareto-optimal payoff given the strategy of Player 0. We study the Stackelberg-Pareto Synthesis problem which asks whether Player 0 can announce a strategy which satisfies his objective, whatever the rational response of Player 1. For games in which objectives are either all parity or all reachability objectives, we show that this problem is fixed-parameter tractable and NEXPTIME-complete. This problem is already NP-complete in the simple case of reachability objectives and graphs that are trees.