Skill, complexity, and strategic interaction

We present a win-loss game between players with explicitly-modeled cognitive limitations. Differences in the players' abilities to analyze the available moves induce preferences over the complexity of the environment and hence incentives to manipulate that complexity. Other things equal, higher-skill players are more likely to win. In a class of long-horizon games with constant complexity, greater complexity reduces the advantage of the higher-skill player when the higher-skill player is the last mover. When the lower-skill player moves last, increasing complexity induces countervailing effects, either of which may dominate. Finally, when complexity can be manipulated over the course of the game, the benefits of strategic manipulation of complexity can override objective considerations about best move choice, resulting in purposeful departures from subgame perfect Nash equilibrium behavior.