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A Game of Pawns

Authors Guy Avni , Pranav Ghorpade, Shibashis Guha

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Author Details

Guy Avni
  • University of Haifa, Israel
Pranav Ghorpade
  • Chennai Mathematical Institute, India
Shibashis Guha
  • Tata Institute of Fundamental Research, Mumbai, India

Funding

  • Avni, Guy: Partially supported by ISF grant No. 1679/21.
  • Guha, Shibashis: Partially supported by the Indian Science and Engineering Research Board (SERB) grant SRG/2021/000466.

Cite AsGet BibTex

Guy Avni, Pranav Ghorpade, and Shibashis Guha. A Game of Pawns. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CONCUR.2023.16

Abstract

We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its next location. This leads to a path in the graph, which determines the winner. Traditionally, the control of vertices is predetermined and fixed. The novelty of pawn games is that control of vertices changes dynamically throughout the game as follows. Each vertex of a pawn game is owned by a pawn. In each turn, the pawns are partitioned between the two players, and the player who controls the pawn that owns the vertex on which the token is located, chooses the next location of the token. Control of pawns changes dynamically throughout the game according to a fixed mechanism. Specifically, we define several grabbing-based mechanisms in which control of at most one pawn transfers at the end of each turn. We study the complexity of solving pawn games, where we focus on reachability objectives and parameterize the problem by the mechanism that is being used and by restrictions on pawn ownership of vertices. On the positive side, even though pawn games are exponentially-succinct turn-based games, we identify several natural classes that can be solved in PTIME. On the negative side, we identify several EXPTIME-complete classes, where our hardness proofs are based on a new class of games called Lock & Key games, which may be of independent interest.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Graph games
  • Reachability games
  • Pawn games
  • Dynamic vertex control

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