This reminds me of a recent paper on parochial altruism. In that paper the authors argued for the co-evolution of parochialism (favoritism for one's group at the expense of others) and altruism (willingness to risk one's life for it). These traits are quite similar to belligerence and bravery. In the earlier paper, it was also suggested that parochialism increases the chance of intergroup conflict, and the two traits increase the probability of winning in such conflicts.
Personally, I am a bit skeptical of these theories of war, at least in the case of Greece. There may be something to them, but I don't think they explain the facts adequately.
An important fact is that the modern practice of men without offspring participating in wars does not reflect the facts of antiquity. While such men did participate in wars, so did their fathers. If we take the famed Paean of Salamis...
Forward, sons of the Greeks,...we see a fairly explicit expression of war as sacrifice for one's women and children. So, while a case can be made for war as a calculated risk which may enhance one's future breeding opportunities, a case can also be made for it as regular kin selection, where men sacrifice themselves for their existing kin.
Liberate the fatherland, liberate
Your children, your women, the altars of the gods of your fathers
And the graves of your forebears:
Now is the fight for everything.
A second important point is the prevalence of the defensive war in the Greek tradition, which later became a part of the Western tradition. If war-like behavior and bravery had evolved in an offensive setting, then why was the need always felt to justify it in defensive terms, rather than as an opportunistic grab at the enemy's resources?
A culture of shame more than belligerence or opportunism accounts for willingness to go to war. Wars may start as random fluctuations in inter-group relations, or as real conflicts for resources. But, people participate in them not so much because they envision opportunities for themselves, but because of the shame that the alternative would bring. Known cowards who do not join the ranks or abandon the field would suffer consequences much more terrifying as an incentive than the positive incentive of conquering an enemy's land.
Finally, a special note must be made on "imperialistic" belligerence. We can assume that voluntary or coercive aggregation of tribes over the past led to an uneven distribution of the sizes of political entities. Whenever a large state found itself next to a small one, the temptation to conquer it would have been great, as such conquest would entail little risk.
Large states could both gather the required human resources for war (because men with the right psychological profile or need could be found in its larger territory), and to wage such wars successfully.
Proceedings of the Royal Society B doi: 10.1098/rspb.2008.0842
War and the evolution of belligerence and bravery
Laurent Lehmann, Marcus W. Feldman
Tribal war occurs when a coalition of individuals use force to seize reproduction-enhancing resources, and it may have affected human evolution. Here, we develop a population-genetic model for the coevolution of costly male belligerence and bravery when war occurs between groups of individuals in a spatially subdivided population. Belligerence is assumed to increase an actor's group probability of trying to conquer another group. An actor's bravery is assumed to increase his group's ability to conquer an attacked group. We show that the selective pressure on these two traits can be substantial even in groups of large size, and that they may be driven by two independent reproduction-enhancing resources: additional mates for males and additional territory (or material resources) for females. This has consequences for our understanding of the evolution of intertribal interactions, as hunter-gatherer societies are well known to have frequently raided neighbouring groups from whom they appropriated territory, goods and women.