Final answer:
The statement is false; players can have dominant strategies but may choose mixed strategies in response to other players' unpredictability, which can create a mixed strategy equilibrium.
Step-by-step explanation:
The statement "In a game, if there is a mixed strategy equilibrium, no player has his dominant strategy." is false. Players can still have a dominant strategy in games that have mixed strategy equilibria, but it's possible that the dominant strategy is not the best response to the strategies chosen by other players. In a mixed strategy equilibrium, each player's strategy is a best response to the strategies chosen by the others, meaning that they are indifferent between several strategies because they yield the same expected payoff.
Let's consider a hypothetical example. Assuming we have a game between two players, Player A and Player B. Player A may have a dominant strategy, which usually is the best choice regardless of what Player B does. However, if Player B is unpredictable and chooses different strategies randomly, Player A might opt for a mixed strategy to best respond to Player B's randomness. Hence, the existence of a mixed strategy doesn't negate the possibility of a dominant strategy; it only indicates that employing a mixed strategy might be a better response in certain scenarios.