We study the effect of a payoff advantage, symmetric payoff change and policymakers interaction on choices in tax competition games. To examine the first two effects a standard symmetric game is respectively compared to an asymmetric game where one player has a payoff advantage and to another symmetric game where both players have symmetrically higher payoffs. When payoffs are asymmetric, we find that if policymakers have a payoff disadvantage they are more likely to compete. Instead policymakers with a payoff advantage are keener to tax above equilibrium. Our results also show there is a payoff size effect where choices are brought closer to equilibrium when payoffs are symmetrically higher. These two effects are further studied when players interact repeatedly. With repeated interaction cooperation is sustained only in the symmetric games but fail to materialise in the asymmetric game. A regression analysis of our results reveals further differences between these games.