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Games with Trading of Control

Authors Orna Kupferman, Noam Shenwald

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Author Details

Orna Kupferman
  • School of Engineering and Computer Science, Hebrew University, Jerusalem, Israel
Noam Shenwald
  • School of Engineering and Computer Science, Hebrew University, Jerusalem, Israel

Funding

Research is funded by the Israel Science Foundation, Grant 2357/19, and the European Research Council, Advanced Grant ADVANSYNT.

Cite AsGet BibTex

Orna Kupferman and Noam Shenwald. Games with Trading of Control. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CONCUR.2023.19

Abstract

The interaction among components in a system is traditionally modeled by a game. In the turned-based setting, the players in the game jointly move a token along the game graph, with each player deciding where to move the token in vertices she controls. The objectives of the players are modeled by ω-regular winning conditions, and players whose objectives are satisfied get rewards. Thus, the game is non-zero-sum, and we are interested in its stable outcomes. In particular, in the rational-synthesis problem, we seek a strategy for the system player that guarantees the satisfaction of the system’s objective in all rational environments. In this paper, we study an extension of the traditional setting by trading of control. In our game, the players may pay each other in exchange for directing the token also in vertices they do not control. The utility of each player then combines the reward for the satisfaction of her objective and the profit from the trading. The setting combines challenges from ω-regular graph games with challenges in pricing, bidding, and auctions in classical game theory. We study the theoretical properties of parity trading games: best-response dynamics, existence and search for Nash equilibria, and measures for equilibrium inefficiency. We also study the rational-synthesis problem and analyze its tight complexity in various settings.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Logic and verification
Keywords
  • Parity Games
  • Rational Synthesis
  • Game Theory
  • Auctions

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