As he lay dying, long before he or anyone else had expected, Alexander made a prediction: all of his companions, i.e. generals, would hold a great funeral contest over his empire. When asked to whom the empire would eventually fall, he would answer only "to the strongest". That was in 323. Over the next eleven years his successors had already fought three wars, the first to reject the original settlement, the second to re-apportion power after the death of the regent and the third because Antigonos in Asia Minor was attempting to become first among equals. Peace was restored by 311 more out of exhaustion and internal problems than because differences had been resolved. In the same year, hostilities were resumed as Seleukos with a small force had departed Egypt and conquered Babylonia from Antigonos, picking up troops along the way. From there he successfully invaded Persia and Medea.
Set-up
Ptolemaios:

The Republic of Carthage reflects approximately 350 years in the life of the ancient Carthaginian Republic. Players cooperate and compete to manage its fortunes, especially its politics, wars and trade in this simulation of political and mercantile life in Rome's ancient and most deadly enemy. In this game you must constantly balance personal advancement against the security of the state. Trade and fight to build up the empire. Vie for power in the Senate and on the battlefield. But to grow in size and power only attracts the unwelcome attention of rivals, not just your opponents, but also foreign powers like Syracuse, Pyrrhus and, most deadly of all, Rome. Are you smart and savvy enough to survive and thrive where Hannibal couldn't? Special rules even allow you to play this in conjunction with The Republic of Rome™ in a grand scenario that supports up to 12 players!

Eventually, three of Alexander's successors founded stable dynasties. The possibility of a fourth in Asia Minor did not happen mostly because of the incursions of the Celts. Eventually a number of smaller kingdoms arose there. Elsewhere, empires arose in Macedon, the Seleucid Empire founded by Seleukos and Ptolemaic Egypt. But the focus had shifted west where upstart Romans had defeated Phoenicians in Carthage in a war over Sicily, Sardinia and Corsica. Much like the interval between world wars I and II, Carthage waited some twenty years before renewing hostilities. Deprived of Sicily, Sardinia, Corsica and her war fleet, it was not easy going. First they needed to expand their holdings around New Carthage, which the Romans called Hispania. Then came Hannibal's famous elephant march over the Alps and into Rome.
Set-up
Carthage:

The Senate had come to fear Caesar's dual following, the first being his popularity with the masses and the second his loyal, battle-hardened legions. Just as Cato had centuries before, they prepared to prosecute him upon the end of his second five-year term to ensure that he did not become too powerful. When Caesar decided that the best way to prevent this was to march across the Rubicon (the exact location of this river is today unclear) and thus break the rule about entering Roman home territor with an army, Pompey and the Senate formed an uneasy alliance to stop him. Despite their apparently greater resources, nothing it seemed could withstand Caesar's genius. Eventually Pompey was defeated in the Greek peninsula and tracked to Egypt, where it was found that its perfidious leader had ordered him decapitated. There Caesar made acquaintance with Cleopatra and set in process that Egypt would eventually join the Empire. After more conquests he eventually did return to Rome, refused the title of king, but in effect had become Dictator for Life. We will never know how he would have fared against the Parthians, a campaign he was planning when with the last spark of the old spirit of the Republic, Marcus Brutus, Cassius and other Senators assassinated him on the Ides of March in 44 BC.

After the assassination, Caesar's will indicated not one but three heirs: a co-worker, a family member and a friend. His lieutenant was Marcus Antonius; his grandnephew and adopted son was Gaius Octavius and his friend and successor as Pontifex Maximus was Marcus Aemilius Lepidus. Although rivals for power, they joined forces to ensure the defeat of Brutus and Cassius, forming the second important triumverate in Roman history. Six years later, the mission accomplished apart from defeating youngest son of Pompey, they divided the empire, Antonius receiving the lion's share: the riches of the East, including alliance with Cleopatra's Egypt. Octavius, now renamed as Gaius Julius Caesar, retained the West including the city of Rome while Lepidus was fobbed off with Africa.
Set-up
Octavius:

One of the truths of the later empire is that for one reason or another it became weaker and its enemies more intractable. Historians argue over the reasons why. Perhaps it was simply a matter of the decay of the concept, the myth, of Rome itself. In any case, Romans found that more and more it was not sufficient to to rule from their capital in Italia and hope that all would be well at the frontiers. Instead, as the edges were threatened, it was necessary to create several large armies at decisive points throughout the very large empire. But this came with its own dangers as an army was a tool for an ambitious general to overthrow the emperor, usually triggering a devastating civil war in the process. But in fact, this had become an all-too-common way for emperors to succeed one another.

It took two centuries before Emperor Diocletian (284-305) came up with an innovative solution to that one. Since every general wanted a title, he decided to create more of them. From henceforth there would be not one ruler, but four. He called it the Tetrarchy. At the top were two leaders each called an Augustus, one for the east and one for the west. Then, to help them, each of these would choose a junior called a Caesar. Every two decades, both of the Augusti would retire and their juniors take their positions, appointing new Caesari to replace them. Obviously the system depended on the leaders selecting their successors wisely and for a while it worked quite well. Diocletian and his fellow emperor Maximinian were close friends who shared a common background as Illyrian military men. As colleagues they chose two more with the same background and values: Galerius Maximinianus and Julius Constantius respectively.

An impressive reformer, Diocletian also realized that hampering the empire were too many petty provinces and jurisdiction disputes. He ended this by creating groups of provinces into twelve large dioceses, each to be governed by a vicar. Military responsibilities were taken from the governors and the armies were now able to cut across provincial boundaries. At the same time, Italia lost its special tax-free status and for the first time was sub-divided into provinces like the rest of the empire. The Senate which had been in decline for a long time, lost further powers by being constrained to governing only two provinces. But Rome, too far from the frontiers which had been the constant concern of the emperors for a some time, had been in decline for just as long. Instead, new capitals developed wherever the rulers made their headquarters: in Milan (Cisalpina Gallia), Trier (Germania), Thessalonica (Macedonia) and Nicomedia (Pontus & Bithynia).

In 304, after 20 years, Diocletian was in ill health. He decided it was time to retire and persuaded Maximian, the other senior emperor, to retire at the same time, both abdicating on May 1, 305. Constantius and Galerius took up their roles, appointing Severus and Maximinus Daia, respectively, as their successors. The system seemed to be working well. Diocletian was content to grow spectacular cabbages at his splendid palace at Salonae (Split), but even before he was to die in 308, he was to see his dream fray and eventually split utterly.

It began already with the announcement of the successors. Galerius seems to have had a strong influence on the choices. Severus was his old friend while Maximinus was his son-in-law. These choices did not sit well with the sons of Maximian and Constantius, Maxentius and Constantinus (Constantine), who even though the new system was supposed to ignore heredity, were nevertheless both very ambitious men. Constantius was not only at loggerheads with Galerius, he was also in poor health, perhaps from leukemia. If he died he faced the prospect of being succeeded by someone he now considered an enemy. Sensing this, his army took matters into their own hands. When Constantius died at York on July 25, 306, they spontaneously proclaimed Constantine senior emperor in the west, ignoring Severus' rights. Constantine also claimed to have been appointed Augustus on Constantius' death bed. Of course this was in contravention of the rules, so when word finally got to Galerius, he refused to recognize it, although he was willing to compromise by allowing Constantine the position of Caesar in the west.

But with this example before him, Maxentius now decided to make his own move for advancement. Inflaming the already-aggrieved citizens of Italia, he got himself proclaimed emperor in Rome. Not only did Maxentius convince his father to come out of retirement to support him, he bolstered his holdings with plenty of funding from wealthy Rome. By now bursting at all sides, Diocletian's dream had instead paved the way to an even more complicated civil war than was usual.

Set-up
Constantinus:

Determined to do the job right himself, Galerius marched on Rome but suffered the same fate due to bribes and had plenty of trouble retreating safely. But flush with success, now it was Maxentius' turn to falter, mainly due to family problems in the form of his own father, Maximian, who decided it was time to usurp power. When this coup failed, Maximian took refuge with Constantine, his new son-in-law. This chaotic situation seemed to leave everyone powerless and like squabbling children, they beckoned Diocletian out of retirement for a summit at Carnuntum (a site in Austria recently rediscovered via ground radar). The conference settled most of the outstanding issues, appointing Licinius the Augustus in the west and confirming Constantine as Caesar. Maximian agreed to stand down. The only outstanding remaining problem was Maxentius, still independent and in control of Italia and Africa.

Licinius began making minor inroads in the north Italian peninsula while Maxentius was busy putting down a revolt in North Africa. Unfortunately, Maximian who had fled to Constantine decided in 310 to have yet one more fling at power. This coup was crushed by Constantine and Maximian perished in the process. This left Galerius and Maximinus Daia in the east, but the former died of cancer in 311, triggering a contest between the latter and Licinius. They marched their armies toward one another, but prudence won the day as they decided to split the eastern territories, albeit inequitably as Licinius held only the Balkans.

In 312 the ambitious Constantine decided he had had enough of Maxentius -- whose rule had endured mass riots and killings -- and defeated his forces at Turin and Verona. The climactic battle of the Milvian Bridge outside Rome sealed Constantine's control of the west. The next year Constantine made a marriage alliance with Licinius who then turned east and defeated Maximinus near Hadrianopolis. Rome had whittled down its leaders to just two co-rulers, a situation which survived about a decade until Constantine decided he had to have it all for himself, defeated Licinius and established a new dynasty and a new capital at Constantinople.

After the dynasty failed with Julian, the emperor who attempted to restore Rome's pagan religion, it was succeeded by the house of Valentinian, a Pannonian officer of humble origin. His brother Valens was in power in the east in 375 when the German tribe known as the Goths, who had formed a kingdom in the area north of the Black Sea fled west in vast numbers with the arrival of the Huns from across the steppes. A chain reaction among other tribes culminated in heavy attacks on Roman limes along the Rhine. Two large groups of Goths asked/threatened to move across the Danube. Valens, Emperor of the East, had an army only large enough to defeat one of them (most of his forces being entangled with the Persians), but the imperial ideology did not permit such an open acquiescence to threats from "barbarians". So eventually one group was permitted to settle on Imperial lands, only to discover it had all been a trick. One of Valens' lieutenants, the local commander Lupicinus, invited the Goth leaders to a banquet which turned out to be a trap. One of the leaders only escaped with difficulty while others were never heard from again. This prompted large scale revolt among the Goths. When Valens could extricate himself from Persia and return to the theater, he heard a rumor that the Goth force had been split in two. Seeing a chance to defeat them in detail, he joined battle at Hadrianopolis. This time it was the Goths who had played the trick. In fact their entire force was present and the Roman flank turned by those who Valens had supposed were not there. Valens actually lost his life in the ensuing defeat, considered by the Romans one of their worst disasters since Cannae. After another defeat followed by some successful counterattacking from the western empire, his successor Theodosius finally acquiesced in settling the Goths in the Balkans under their own leaders. After a while the Goths actually helped to man the Roman army and turn away other invaders.

When Theodosius died the empire was split between his two sons Arcadius and Honorius, but both were in fact puppets. Generals were the true powers, Stilicho in the West and in the East, first Rufinus and later Eutropius. The most significant development however was that thenceforward the two empires would follow their own courses, the West being headquartered not at Rome, but at swampy and more defensible Ravenna. Meanwhile the advance of the barbarians was inexorable. In 405-6 the Gothic king Radagaisus invaded Italy. Then, on the last day of 406, a whole host of peoples crossed the Rhine, including the Vandals, Alans (an Iranian people), Sueves, Burgundians and Huns. The Rhine frontier collapsed and Gallia and Hispania were settled by German tribes. Inevitably, Rome was sacked, the first time by Alaric and his Goths in 410. Alaric's group broke off from the other Gothic groups and settled in what is now southwest France, becoming known as the Visigoths. Revolts in Britannia caused Rome to renounce the distant province in the same year. Meanwhile the Huns moved up to the edge of Europe and even tried invading Thrace. They were repulsed with the help of a heavy annual tribute. Now instead of the combined might of the empire there stood only local potentates. One of the best of these was Aetius who was headquartered in northern Gallia. This army actually held out under varius commanders until finally defeated by Clovis and the Franks in 486. Effective as they were, unfortunately the commanders were as interested in intriguing and fighting one another as they were the invaders. The long term result was continued debilitation of the empire's ability to resist.

Note: this scenario is also basically the topic of the game Decline and Fall of the Roman Empire.
Set-up
Aetius:

Meanwhile, the Goth groups remaining in the Balkans came into constant conflict, both with the Romans and with each other. The clumsy efforts of Zeno, eastern emperor, to trick the groups into attacking one another had quite a different ultimate result, creation of a supergroup known as the Ostrogoths ruled by Theoderic the Great, yet another by the way who had learned Roman ways too well, having spent ten years a hostage at Constantinople.

The new kingdom was a powerful rival to the eastern empire and yet could not dominate it. Zeno and Theoderic, former allies, reached a mutually-agreed decision: Theodoric would conquer Italia in the name of the empire and depose Odoacer, whom Roman churchmen called demon-possessed. To accomplish it they could expect help from their fellow Goths, the Visigoths, but not in volume as they themselves were pressed from the north by the growing power of the Franks. Their leader, Clovis, had accepted baptism as a Roman Catholic following the Nicene creed which gave the Franks a popularity edge among the Gallic-Roman population as all of the Goths instead followed the so-called "Arian heresy". Faced with this, the Visigoths were glad of the opportunity of greater land opportunities in Hispania, conquering these areas from the Sueves, Alans and Vandals, the latter continuing on into Africa.
Set-up
Odoacer:

Sources:

• Timeline of Carthaginian History
• The Goths
• Chronicle of the Roman Emperors: The Reign-By-Reign Record of the Rulers of Imperial Rome
• The Atlas of the Ancient World
• The Germanic Invasions: The Making of Europe, AD 400-600
• The Anchor Atlas of World History
• Before France and Germany: The Creation and Transformation of the Merovingian World
• Decline and Fall of the Roman Empire (game)
• "Successors: The War for Alexander's Empire" by Brian Booker, Strategy & Tactics, June 1993, no. 161
• "The Great Funeral Contest" by Stuart K. Tucker, The General vol. 32, no. 2