We present a new class of games, local-effect games (LEGs), which exploit structure in a different way from other compact game representations studied in AI. We show both theoretically and empirically that these games often (but not always) have pure-strategy Nash equilibria. Finding a potential function is a good technique for finding such equilibria. We give a complete characterization of which LEGs have potential functions and provide the functions in each case; we also show a general case where pure-strategy equilibria exist in the absence of potential functions. In experiments, we show that myopic best-response dynamics converge quickly to pure strategy equilibria in games not covered by our positive theoretical results.
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