* It's written that Caesar said he'd kill the pirates in jest, but he was a man of his word, so...
** It's possible Caesar considered himself their guest (as insane as that sounds, considering he was kidnapped) and expected to be treated as such (very well, especially given his station). Going from the retribution (execution), while insane by modern standards, would be somewhat more normal for the time ([[SacredHospitality hospitality was a big deal in the Classical World]]), if still harsh.
*** Ransoming nobles was a very different thing in ancient times. So long as you treated your captive decently and ransomed them for an acceptable price, you would not only receive your ransom, you would be considered generous and merciful for doing so (rather than executing them). Failure to treat a captive noble well would probably result in war if the grieved party was capable of it.
*** Piracy was seen as a major problem in the Mediterranean at the time, and for a "foreigner" to kidnap a Roman nobleman was considered a major crime against Rome in and of itself, and crimes against Rome (or perceived crimes against Rome, or imagined crimes for that matter) never went without disproportionate retribution. Let's face it, whole wars have, throughout time, started for the most petty reasons, because not everyone saw war as something to avoid.
[[https://en.wikipedia.org/wiki/Game_theory Game Theory]] [[note]]the scientific field studying strategic decision making, not the [[Fanfic/GameTheoryFanFic fanfic]] or the [[WebVideo/GameTheoryWebShow youtube series]][[/note]] has made some rather interesting discoveries over the years regarding disproportionate retribution. Two games of special interest here are [[https://en.wikipedia.org/wiki/Prisoner%27s_dilemma Prisoner's Dilemma]] and [[https://en.wikipedia.org/wiki/Peace_war_game The Peace-War Game]].

PrisonersDilemma, as many may already know, is a very useful reduction of social cooperation between two players to a simple scenario: Alice and Bob are [[PerpSweating criminals being interrogated]] about a crime they committed together. They have both [[ConfessToALesserCrime Confessed to a Lesser Crime]], but the prosecution ''really'' wants at least one of them to go down for the major crime. So the two are [[PleaBargain offered a deal: the first one to talk gets probation and community service]], the other [[TakingTheHeat gets a lengthy sentence]]. They both get a short sentence for the lesser crime if they both stay silent. The deal is off the table if they both talk, but they do get credit for testifying against each other.

||align=center border=1 width=50%
|| Prisoner's Dilemma ||||||
|| Bob ⇓ Alice ⇒ || Don't betray Bob || Betray Bob ||
|| Don't betray Alice || Alice and Bob both get a year || Alice goes free, Bob gets 3 years ||
|| Betray Alice || Alice gets 3 years, Bob goes free || Alice and Bob both get 2 years ||

One way this is used to test different strategies is to hold long tournaments repeating this game with different pairings each partnering for a few rounds, and seeing which strategies work out the best. As might be expected, Disproportionate Retribution is a bad strategy against anything but [[StupidGood "always cooperate"]]. A more surprising discovery, however, comes from the much famed Tit-for-Tat strategy (aka: EyeForAnEye).

While this strategy is generally dominant in simulations, being extremely effective against "smart algorithms" that remember past behavior, thriving in partnership with "always cooperate" players, and savvy enough to punish [[StupidEvil "Always Defect"]] players, it has a single, glaring, flaw: In computer simulations involving noise, where the simulated players occasionally get a wild hair and deviate from their normal patterns, a pair of Tit-for-Tat players can become locked in a CycleOfRevenge known as a Death Spiral. One randomly defects, so the other defects the next round, and they [[HeelFaceRevolvingDoor continue to swap back and forth]] this way, each offer of peace receiving a HeelFaceDoorSlam. Essentially, mutual pure eye-for-an-eye strategies inevitably become Disproportionate Retrobution over even the smallest betrayal. In these truer-to-life situations with noise, another strategy dominates: Tit-for-two-tats...aka, TurnTheOtherCheek.

The other game, Peace-War, is similar to prisoner's dilemma, but with slightly different rules and payoff matrix. It will likely be instantly familiar to anyone who has played a FourX game with the option for peaceful interaction with other factions/players. Each round a player gains 2 resource points. Combat costs both players one resource point, but attacking a player who is not counterattacking steals both of that player's points for that round.

||align=center border=1 width=50%
|| Peace-War ||||||
|| Bob ⇓ Alice ⇒ || Attack Bob || Seek Peace with Bob ||
|| Attack Alice || Alice and Bob both gain 1 resource || Alice loses 1 resource, Bob gains 3 resources ||
|| Seek Peace with Alice || Alice gains 3 resources, Bob loses 1 resource || Alice and Bob both gain 2 resources ||

There are three strategies that have been found to be be highly effective in this game: [[OneOfTheseIsNotLikeTheOthers Always Peace, Tit-for-two-tats]], and [[AttackAttackAttack AlwaysWar]]. The "always war" strategy, frequently compared to Genghis Khan's Empire, has been observed to dominate in the early-to-mid game. In most long-running simulations, however, these warlike nations suffer greatly when faced with a Tit-for-two-tats nation. Having spent many rounds building large reserves of resources for themselves and their neighbors with little loss, they can afford to be slow to counterattack. Upon being faced with a Always War nation, however, these nations proceed to counterattack until one or both nations are destroyed, even in the face of [[ISurrenderSuckers single-round offers of peace]].

Additionally, the always war nation has only the resources accumulated by conquest constantly being drained by nations which fight back. The more forgiving nations continue to be resupplied each round by trade with neighbors, thanks to the fact that they ignore random, sometimes false, war declarations designed to stir the simulation now and then.

These frequently knock out the more trigger-happy mixed strategy nations. For instance, another strategy, nicknamed the "Grim Trigger" strategy by game theorists, most purely embodies disproportionate retribution's hazards: These nations never forgive, but continue attacking infinitely once threatened, leading to eventual ruin as they declare blood feuds against former allies over the slightest provocation.

Quite a bit of debate can be generated about what all of these observations say about the wisdom of easy forgiveness vs making an example by disproportionate retribution. What is clear, however, is that disproportionate retribution can in some cases emerge from even the simplest of circumstances based on purely logical behavior, and that it inevitably has consequences which may prove costly to both parties involved -- particularly because it tends to burn bridges and trigger cycles of revenge.