Analysis: Disproportionate Retribution

  • 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 (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.

Game Theory note  has made some rather interesting discoveries over the years regarding disproportionate retribution. Two games of special interest here are Prisoner's Dilema and The Peace-War Game.

Prisoners dilemma, as many may already know, is a very useful reduction of social cooperation between two players to a simple scenario: Alice and Bob are criminals being interrogated about a crime they committed together. They have both 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 offered a deal: the first one to talk gets probation and community service, the other 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.

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 "always cooperate". A more surprising discovery, however, comes from the much famed Tit-for-Tat strategy (aka: Eye For An Eye).

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 "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 Cycle of Revenge known as a Death Spiral. One randomly defects, so the other defects the next round, and they continue to swap back and forth this way, each offer of peace recieving a Heel-Face Door Slam. 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, Turn the Other Cheek.

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 4X 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.

Bob ⇓ Alice ⇒ Attack Bob Seek Peace with Bob
Attack Alice Alice and Bob both gain 1 resources 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: Always Peace, Tit-for-two-tats, and 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 counter attack. 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 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.