I actually got this by asking one of the chefs at a local Hibachi grill. He said he would give it to me only if I could correctly guess the main ingredient. I tasted it and then told him mayo, and he laughed loudly and gave me the recipe. I use this sauce whenever I make homemade Hibachi style dinner for my fiance and I. :)
Japanese Steakhouse Mayo sauce: 1 cup mayonnaise, 1/4 cup water, 1 tsp tomato paste, 1 tbsp melted butter, 1/2 tsp garlic powder, 1 tsp sugar, 1/4 teaspoon paprika, 1 dash cayenne pepper. Whisk all of the ingredients together until the sauce is creamy. Do not add all of the water at once. Add a little at a time, until you get the consistency you want. Refrigerate over night for best results.