Avoider-Enforcer Game is NP-hard
Tillmann Miltzow, Milo\v{s} Stojakovi\'c
TL;DR
This paper proves that determining whether Avoider has a winning strategy in the Avoider-Enforcer game on a hypergraph is NP-hard, highlighting computational complexity challenges in combinatorial game theory.
Contribution
The paper establishes the NP-hardness of deciding Avoider's winning strategy in the Avoider-Enforcer game, a novel complexity result in combinatorial game analysis.
Findings
Deciding Avoider's winning strategy is NP-hard.
The problem remains hard even for specific hypergraph classes.
This result connects combinatorial game theory with computational complexity.
Abstract
In an Avoider-Enforcer game, we are given a hypergraph. Avoider and Enforcer alternate in claiming an unclaimed vertex, until all the vertices of the hypergraph are claimed. Enforcer wins if Avoider claims all vertices of an edge; Avoider wins otherwise. We show that it is NP-hard to decide if Avoider has a winning strategy.
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Taxonomy
TopicsArtificial Intelligence in Games · Game Theory and Applications · Advanced Graph Theory Research