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Patience Pays: Game Theoretic Model for the Developmental Competition at the Motor-Muscle System

Irit Nowik

We offer a new game theoretic approach to analyze the developmental competition that arises between neurons innervating a common muscle. The size principle-stating that neurons with successively higher activation-thresholds innervate successively larger portions of muscle-is thought to result from this competition, but it has not been known how, mainly because the existing experimental data on this issue seems contradictory. We define a multi-stage game in which neurons "compete'' to singly innervate a maximal number of muscle-fibers. At each stage of the game, the competition at a single muscle-fiber is resolved. We show that neurons with successively higher activation-thresholds tend to win in later stages of the game and prove that because resource is limited and is needed both for competing and for maintenance of the connections won, then in order to win more competitions, it is better to win in later competitions rather than in earlier ones.We then generalize the model to a game in which players with limited resource need to decide the size of investment at each stage