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Fragility and Robustness in Mean-Payoff Adversarial Stackelberg Games

Authors Mrudula Balachander, Shibashis Guha, Jean-François Raskin

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ACM Subject Classification
  • Theory of computation → Solution concepts in game theory
  • Theory of computation → Mathematical optimization
  • Theory of computation → Logic and verification
Keywords
  • mean-payoff
  • Stackelberg games
  • synthesis

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Abstract

Two-player mean-payoff Stackelberg games are nonzero-sum infinite duration games played on a bi-weighted graph by Leader (Player 0) and Follower (Player 1). Such games are played sequentially: first, Leader announces her strategy, second, Follower chooses his best-response. If we cannot impose which best-response is chosen by Follower, we say that Follower, though strategic, is adversarial towards Leader. The maximal value that Leader can get in this nonzero-sum game is called the adversarial Stackelberg value (ASV) of the game.
We study the robustness of strategies for Leader in these games against two types of deviations: (i) Modeling imprecision - the weights on the edges of the game arena may not be exactly correct, they may be delta-away from the right one. (ii) Sub-optimal response - Follower may play epsilon-optimal best-responses instead of perfect best-responses. First, we show that if the game is zero-sum then robustness is guaranteed while in the nonzero-sum case, optimal strategies for ASV are fragile. Second, we provide a solution concept to obtain strategies for Leader that are robust to both modeling imprecision, and as well as to the epsilon-optimal responses of Follower, and study several properties and algorithmic problems related to this solution concept.

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Mrudula Balachander, Shibashis Guha, and Jean-François Raskin. Fragility and Robustness in Mean-Payoff Adversarial Stackelberg Games. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CONCUR.2021.9

Author Details

Mrudula Balachander
  • Université libre de Bruxelles, Brussels, Belgium
Shibashis Guha
  • Tata Institute of Fundamental Research, Mumbai, India
Jean-François Raskin
  • Université libre de Bruxelles, Brussels, Belgium

Funding

This work is partially supported by the PDR project Subgame perfection in graph games (F.R.S.-FNRS), the ARC project Non-Zero Sum Game Graphs: Applications to Reactive Synthesis and Beyond (Fédération Wallonie-Bruxelles), the EOS project Verifying Learning Artificial Intelligence Systems (F.R.S.-FNRS and FWO), and the COST Action 16228 GAMENET (European Cooperation in Science and Technology).

References

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