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.

翻译：我们引入并研究了棋子博弈（pawn games）——一类双人零和回合制图博弈。回合制图博弈通过将一枚标记放置于初始顶点上展开，控制标记所在顶点的玩家决定其下一位置。该过程在图中生成一条路径，由路径决定胜负。传统模型中，顶点控制权是预设且固定的。棋子博弈的创新之处在于顶点控制权会随游戏进程动态变化：每个顶点归属于一枚棋子。每回合中，两玩家对棋子进行分配，控制当前标记所在顶点所属棋子的玩家，选择标记的下一位置。棋子控制权依据固定机制动态变化。具体而言，我们定义了若干基于抓取（grabbing-based）的机制，其中每回合结束时至多转移一枚棋子的控制权。我们研究了解棋子博弈的复杂度问题，重点关注可达性目标，并以所用机制和顶点所属棋子限制为参数进行分类。正面结果：尽管棋子博弈是指数级简洁的回合制博弈，我们仍识别出若干可在多项式时间内求解的自然类别。负面结果：我们发现了若干EXPTIME完全类，其困难性证明基于一类名为“锁与钥博弈”（lock & Key games）的新博弈，该博弈可能具有独立研究价值。