Game Theory
note has made some rather interesting discoveries over the years regarding disproportionate retribution. Two games of special interest here are Prisoner's Dilemma and The Peace-War Game.
Prisoner's 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 receiving a Heel–Face Door-Slam. Essentially, mutual pure eye-for-an-eye strategies inevitably become Disproportionate Retribution 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.
| 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: Always Peace, Tit-for-two-tats, and Always War. 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 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.
