Pictured above is an actual Hellcat and Zero flying together for a Commemorative Air Force show. Air Combat Maneuvering is the school of dogfighting. While concepts have been adapted to advances in technology the fundamental rules have always been the same. Like so many lessons in war, the price of learning was often paid in blood which is why games such as Hellcat Ace that account for the unique challenges faced can be seen as more than fun diversions but also a tribute to those who fought and sacrificed in prevailing (and those who never got to return home).
World War One, the first full aerial war, has the distinction of air power not making a real difference in the outcome but still setting the stage for when use of aircraft would become decisive. Among the concepts realized were: 1) the importance of air superiority, 2) the role of specialized fighter units for achieving #1, and 3) what design of aircraft and use of team tactics best works to achieve #1. The foundations for #1 and #2 were documented and put into practice almost simultaneously on both sides: Germany's Jasta 2 led by Oswald Boelcke, and Britain's No. 24 Squadron led by Lanoe Hawker. Where they differed was in applying #3, and the only viable means of testing available then was actual combat.
Early aircraft in the Great War performed similarly; even the first dedicated fighter, the Fokker E. III, was cloned from the French Morane-Saulnier racer that had been pressed into service as a fighter. Fighter planes, then referred to as scouts, were attached to reconnaissance and bomber units (which often used the same aircraft for both roles) and often did not operate independently. With no sophisticated sensors of any kind encounters were rare, and with each scout armed with only one rifle-caliber machine gun that aimed poorly and frequently-jammed there were plenty of encounters that ended bloodlessly.
Soon enough, the Allied Powers met the Fokker Scourge with the introduction of their own dedicated fighter: France's Nieuport 11. While not strongly-built, this light sesquiplane could outpace the Fokkers and, with the aid of its rotary engine and new aileron system, outmaneuver them as well...though not by such a tremendous factor as to drive skilled Fokker pilots from the skies. As author Tom Clancy would point out, wars are won by men and not machines, and the edge given Germany by the Fokker Scourge was the greater caliber of its fighter pilots (since they survived enough to gain good experience) even as Britain rolled-out its own dedicated scout plane and scout squadron with the Airco D.H.2s of Hawker's 24th. At first, Germany deployed the Halberstadt D.II as a counter which, while a superior plane, did not achieve the impact of its successor: the powerful Albatros D.II with which Boelcke equipped his own scout squadron. This set the trend for much of the remainder of the air war, with exceptions to the rule (like dissenting opinions in court rulings) not having their full spotlight in the present but proving themselves in the long run.
For the Allies turning dogfighters were their highest achievers. The D.H.2 was standard in the Royal Flying Corps while the Sopwith line equipped Royal Navy Air Service squadrons until later 1917, then afterwards the Sopwith Camel became the top dogfighter of the new Royal Air Force. During mid-war the best British aces cut their teeth in the Nieuport 17, such that it became an official mount of the service despite being French-built (of course, even the French planes were equipped with British guns). The Aircos, Nieuports and Sopwiths were light and agile, if underpowered; a single .303 caliber machine gun was standard armament and equipping a second, while technically-feasible, would have resulted in performance degradation cutting down their maneuverability advantage. The British S.E.5 and French SPAD lines were the exception: the design focus of both was power and stability, which made them weaker dogfighters but was it worth the sacrifice?
After the Fokker E.III but before the Fokker D.VII all of Germany's standard scouts were of the Albatros line, which equipped double 7.92mm machine guns and stout airframes with strong in-line engines. The Pfalz D.III was an alternative built for strength, and the Fokker Dr. I (the most famous mount of Red Baron Richtofen) was a supreme dogfighter among faster and more stable companions. Germany's aircraft design focus was on power rather than agility, though superior late-war designs such as the Siemens Shuckert D.III and Fokker D.VII (plus the Sopwith Snipe for the Allies) proved that power need not be mutually-exclusive of sufficient agility. Nevertheless, the results speak for themselves: in particular "Bloody" April 1917 that saw the Albatros D.III nearly drive the British air forces into hiding proved to both sides that power, enabling the faster plane to control the conditions of the encounter, would more often then not prevail all things being equal.
Jumping ahead to WWII in the Pacific, the power superiority concept was fully-embraced in modern monoplane fighter design, but the finer details were not yet realized and each world power took its own approach to air superiority that they theorized would reign supreme in the next war everyone knew was coming. Poland and France, for instance, would face quick defeat in part because theory collapsed in the face of reality leaving them overwhelmingly-outmatched. Japanese air combat doctrine involved superior dogfighting, and this manifested not only with the infamous A6M Zero but also the many types flown by the Japanese Army Air Force. Like Imperial TIEs from Star Wars, "Jap" fighters were lighter, more vulnerable and not that well-armed, but rookies who tried WWI-style dogfighting with them often did not live to learn from their mistakes.
Until it became basically one-sided in favor of the United States in 1943, the air war in the Pacific was a real crucible in which tactics meet technology and the winning side is not necessarily the one with the starting advantage. No U.S. fighter in the opening of the war, whether the Navy F2A and F4F or Army P-39 and P-40, had a prayer in outmaneuvering the Japanese Nates, Oscars or Zeroes; except for the older Nate, they generally could not be outrun either. What U.S. fighters did have was good firepower (courtesy of clusters of .50 caliber Browning M2s) and better survivability with their advanced protections of critical systems. Those who studied what they were facing, such as the Flying Tigers and John Thach, learned that the means of defeating superior opponents rested in team-based tactics, judicious use of the 3rd dimension so as to deny the enemy a fair dogfight, and pressing the firepower advantage so as to hit the enemy fast and hard enough to not recover. It all only went so far as many American pilots still paid for their technological inferiority with their lives, but it worked to score enough victories to keep the enemy at bay until new planes could redress the difference for good. Once the more powerful Navy F4U and F6F along with the Army P-38 and P-47 were deployed in 1943, superior speed and strength proved more than equal to superior agility and now it was Japan's turn to struggle.
MicroProse's Hellcat Ace, while old and crude, still makes a valiant stab at replicating the qualitative differences of these WWII planes and necessity of using proper tactics to defeat the enemy: even in the swift supreme Hellcat, getting lulled into a turning dogfight is asking for defeat because that is just playing into the enemy's strengths. Its manual is only 8 pages long but still includes a section on maneuvers that use the 3rd dimension, maneuvers that really work even in the game's primitive engine. This is what makes Hellcat Ace deeper than the Red Baron it was designed to best despite weaker graphics and power, and the end result is a great respect to the actual Pacific air warriors who were the real pathfinders that set what would lead both to Grumman's ultimate feline mount, the F-14 Tomcat, and a certain ACM school made famous as the setting of a certain 1980s movie starring Tom Cruise.