Question: In which battle occurred between the navy of Rhodes and the navy of  the dominant state of Hellenistic Greece?

Context paragraphs:
Vassal state: A vassal state is any state that is subordinate to another.  The vassal in these cases is the ruler, rather than the state itself.  Being a vassal most commonly implies providing military assistance to the dominant state when requested to do so; it sometimes implies paying tribute, but a state which does so is better described as a tributary state.  In simpler terms the vassal state would have to provide military power to the dominant state.  Today, more common terms are puppet state, protectorate or associated state.

Battle of Tonkin River: The Battle of Tonkin River was a major naval battle fought in northern Vietnam between the pirates of Shap Ng-tsai and the British Royal Navy with aid from the Qing Chinese navy and the Tonkinese.  The 1849 expedition led to the destruction of Shap Ng-tsai's fleet and the loss of over 2,000 men.  The battle occurred over a three-day period at the mouth of the Tonkin River, near present-day Hai Phong.

Battle of Lade (201 BC): The Battle of Lade was fought between the navy of Rhodes and the navy of Macedon.  The battle took place in 201 BC and it was part of the Cretan War.  The battle was fought off the shore of Asia Minor and the island of Lade, near Miletus.  The battle ended in a crushing victory for the Macedonians and it nearly spelled the end for the Rhodians but the result of this battle caused the Romans to intervene and Rhodes was saved.

Pierre Lévêque: Pierre Lévêque (] ; 11 August 1921, Chambéry – 5 March 2004, Paris) was a 20th-century French historian of ancient and Hellenistic Greece.

Battle of Calabria: The Battle of Calabria, (known to the Italian Navy as the Battle of Punta Stilo) was a naval battle during the Battle of the Mediterranean in the Second World War.  It was fought between the Italian Royal Navy ("Regia Marina") and the British Royal Navy and the Royal Australian Navy.  The battle occurred 30 miles to the east of Punta Stilo, Calabria, on 9 July 1940.  It was one of the few pitched battles of the Mediterranean campaign during the Second World War involving large numbers of ships on both sides.  Both sides claimed victory, but in fact the battle was a draw and everyone returned to their bases as soon as possible.

Macedonia (ancient kingdom): Macedonia or Macedon ( , ] , Greek: Μακεδονία , "Makedonía ") was an ancient kingdom on the periphery of Archaic and Classical Greece, and later the dominant state of Hellenistic Greece.  The kingdom was founded and initially ruled by the royal Argead dynasty, which was followed by the Antipatrid and Antigonid dynasties.  Home to the ancient Macedonians, the earliest kingdom was centered on the northeastern part of the Greek peninsula, and bordered by Epirus to the west, Paeonia to the north, Thrace to the east and Thessaly to the south.

Demetrius I of Bactria: Demetrius I (Greek: Δημήτριος Α΄ ) was a Greek king (reigned c. 200–180 BC) of Gandhara.  He was the son of Euthydemus and succeeded him around 200 BC, after which he conquered extensive areas in what is now Afghanistan and Pakistan, thus creating an Indo-Greek Kingdom far from Hellenistic Greece.  He was never defeated in battle and was posthumously qualified as the Invincible ("Aniketos") on the pedigree coins of his successor Agathocles.  Demetrius I may have been the initiator of the Yavana era, starting in 186-185 BC, which was used for several centuries thereafter.

Spartiate: The Spartiates (Greek: Σπαρτιάται , "Spartans") or Homoioi (Greek: , "those who are alike"; sing.  "homoios") were the males of Sparta known to the Spartans as "peers" or "men of equal status".  From a young age, male Spartiates were trained for battle and put through gruelling challenges intended to craft them into fearless warriors.  In battle, they had the reputation of being the best soldiers in Greece, and the strength of Sparta's hoplite forces let the city become the dominant state in Greece throughout much of the Classical period.  Other city-states were reluctant to attack Sparta even though it could muster a force of only about 8000 Spartiates during the zenith of its dominance, such was the reputation of its soldiers.

Battle of Havana (1748): The Battle of Havana was a naval engagement that took place between the British Caribbean squadron and a Spanish squadron based near Havana during the War of Jenkin's Ear.  The battle occurred on the morning of the 12th and ended on the 14th October 1748.  The belligerents consisted of two squadrons under the command of Admiral Don Andres Reggio of the Spanish Navy and Admiral Sir Charles Henry Knowles of the Royal Navy, respectively.  The British succeeded in driving the Spanish back to their harbour after capturing the "Conquistador" and ran the vice-admiral's ship "Africa" on shore, where she was blown up by her own crew after being totally dismasted and made helpless.  Although the advantage had clearly been with Knowles, he failed to use this to deliver a decisive blow.  The battle was the last major action in the War of Jenkin's Ear which had merged with the larger War of the Austrian Succession.

Hellenistic Greece: In the context of ancient Greek art, architecture, and culture, Hellenistic Greece corresponds to the period between the death of Alexander the Great in 323 BC and the annexation of the classical Greek heartlands by the Roman Republic.  This culminated at the Battle of Corinth in 146 BC, a crushing Roman victory in the Peloponnese that led to the destruction of Corinth and ushered in the period of Roman Greece.

Supporting paragraphs: Battle of Lade (201 BC) Macedonia (ancient kingdom)
Answer: The Battle of Lade