(a) GarysGym does not have a dominant strategy. A dominant strategy is a strategy that is always the best choice for a player, regardless of the choices made by the other player. In this case, GarysGym does not have a strategy that is always the best choice. For example, if GarysGym chooses to maintain its price, it will receive a payoff of $350, but if it chooses to lower its price, it will receive a payoff of $80. Similarly, if GarysGym chooses to advertise, it will receive a payoff of $700, but if it chooses not to advertise, it will receive a payoff of $460.
(g) The Nash equilibrium in this game is for both GarysGym and E-Fitness to maintain their prices and not advertise. This is a Nash equilibrium because, given the strategies chosen by the other player, neither player can improve their payoff by changing their strategy. For example, if GarysGym chooses to maintain its price and E-Fitness chooses not to advertise, GarysGym will receive a payoff of $450 and E-Fitness will receive a payoff of $300. If GarysGym were to change its strategy to advertise, it would receive a payoff of $700, but E-Fitness would also receive a higher payoff of $350. Therefore, GarysGym has no incentive to change its strategy, and the same is