The Adversarial Stackelberg Value in Quantitative Games

by   Emmanuel Filiot, et al.

In this paper, we study the notion of adversarial Stackelberg value for two-player non-zero sum games played on bi-weighted graphs with the mean-payoff and the discounted sum functions. The adversarial Stackelberg value of Player 0 is the largest value that Player 0 can obtain when announcing her strategy to Player 1 which in turn responds with any of his best response. For the mean-payoff function, we show that the adversarial Stackelberg value is not always achievable but epsilon-optimal strategies exist. We show how to compute this value and prove that the associated threshold problem is in NP. For the discounted sum payoff function, we draw a link with the target discounted sum problem which explains why the problem is difficult to solve for this payoff function. We also provide solutions to related gap problems.


page 1

page 2

page 3

page 4


Stackelberg Mean-payoff Games with a Rationally Bounded Adversarial Follower

Two-player Stackelberg games are non-zero sum strategic games between a ...

On Satisficing in Quantitative Games

Several problems in planning and reactive synthesis can be reduced to th...

Balancing Two-Player Stochastic Games with Soft Q-Learning

Within the context of video games the notion of perfectly rational agent...

Energy mean-payoff games

In this paper, we study one-player and two-player energy mean-payoff gam...

Symbolic Approximation of Weighted Timed Games

Weighted timed games are zero-sum games played by two players on a timed...

The graph structure of two-player games

In this paper we analyse two-player games by their response graphs. The ...

Playing Stackelberg Opinion Optimization with Randomized Algorithms for Combinatorial Strategies

From a perspective of designing or engineering for opinion formation gam...