“Cooperation Under Uncertainty: What Is New, What Is True, And What Is Important”

Bendor, Jonathan, Roderick Kramer, and Piotr Swistak. (April,

1996). American Sociological Review.

This Article as a Criticism of Kollock’s 1993 Study, “An Eye for an Eye Leaves Everyone Blind: Cooperation and Accounting Systems”:

“Unfortunately, in the case of Kollock’s 1993 study (henceforward Kollock) of the iterated Prisoner’s Dilemma (IPD) under monitoring uncertainty (‘noise’), … much of what is true (and significant) in Kollock’s paper is not new, and much of what is new is either not true or not significant”

» their review of Kollock’s study on these three points (of importance, significance, truth) indirectly shows us what has been done thus far in the field

True and Significant, but Not New…» Kollock’s Problem: “what he identifies as ‘the key issue… the compromise that must be made between vulnerability to exploitation… and vulnerability to needless cycles of recrimination’ (p. 769), was clearly identified as a problem by Axelrod a decade ago”

» Kollock’s Method: “yet Kollock’s method- a computer simulation of a round robin tournament of strategies playing the IPD- is not new either”

» Kollock’s Central Conclusion: “‘strategies that use a more relaxed accounting system* than TIT FOR TAT often have important advantages’ (p. 784)… is not new… the main finding of Bendor et al.’s noisy IPD tournament was that: ‘…TFT preformed rather poorly. In contrast, strategies that were generous (i.e. cooperated more than their partners did) were quite effective’”* Kollock defines relaxed accounting systems as those with “some degree of credit,” which do not need to be balanced right away

New, but Problematic…

“Lack of originality is a significant weakness, but a study may still be valuable as a source of new perspectives or observations, or even as a replication of earlier results”

Kollock’s study’s two major errors:

» Under the heading: “Substantive Problems: Understanding the Effects of Noise”

» Under the heading: “Methodological Issues”

Kollock’s Portrayal of Noise* (Uncertainty) and its Effects

“Kollock portrays uncertainty as having only negative consequences. While… uncertainty’s benign effects may well be more important”

» benign effects directly related to evolution of cooperation via both its emergence and its stability

* Kollock defines noise as “errors in the implementation or perception of behavior [Bendor 1987]” in his 1993 paper

Emergence of Cooperation

“Kollock’s observation on how noise can facilitate the emergence of cooperation in ecologies of certain ‘not nice’ strategies, such as SUSPICIOUS TIT FOR TAT* (a strategy in his simulation), is so understated that it borders on inaccurate”

» Bendor et al. criticize, but do not dispute, Kollock’s observation about how “‘a little noise is a boon because an occasional distortion in a positive direction can lead to [cooperation]’ (p. 776)”

» any amount of noise causes SUSPICIOUS TIT FOR TAT to cooperate as often as TFT (can be proven deductively)

* Kollock describes SUSPICIOUS TIT FOR TAT as “risk-averse (i.e. it is willing to cooperate if the partner does, but starts with an initial contribution of 0),” implying it is a mean TFT (first one to defect, as it defects right away but then mimics its opponent)

Stability of Cooperation (Equilibrium)

“In this matter Kollock commits two errors: First, he attempts to study stability inductively (something that cannot be done), second, he offers insights and conjectures that are known to be false”

» evolutionary stability in IPD without noise has lots of problems!- all conveniently disappear with the introduction of noise, which sometimes helps people begin cooperating

» first issue: “Kollock’s claim that ‘In the absence of noise, … once TIT FOR TAT has established itself and created a world of mutual cooperation, it cannot be invaded by other strategies’… is false”

» any TFT population can always be invaded by ALL C or any nice cooperating strategy since without noise these strategies are all “observationally equivalent” (they all C with each other)

» with noise, TFT and ALL C become “behaviorally distinguishable”* » second issue: “TFT can be eliminated [and outscored] by the more successful mutant” (“observation by Boyd and Lorberbaum”)» all of these results = deductive, not inductive

“Stability can be established analytically, and stable strategies have already been identified (Boyd 1989)… If evolutionary stability can be studied deductively, then using simulations to study it is inappropriate”

* the article states this as if it is completely obvious, though it is a logical observation, as noise only affects one turn at a time, so depending on their opponent’s reaction (imitating their last move or just cooperating as always in the past) a player can discern whether their opponent is a TFT or ALL C, thus no longer “observationally equivalent”

Methodology Fallacies

“Given the title* of the section and the structure of the presentation, the reader is clearly led to believe- though Kollock never states it explicitly- that his simulation findings pertain to the evolutionary stability of some of these seven strategies”

» characterize Kollock’s conclusions as “inductive inferences,” which “can be misleading”

» go further to say “essence of a stable strategy is that it cannot be invaded by any mutant strategy, and this can only be established analytically”

* Title in reference from Kollock’s 1993 paper is “The Evolutionary Stability of Strategies,” although it is not explicitly stated in Bendor et al.’s paper

Credit for Kollock’s Two Contributions

“First, unlike most previous noisy tournaments (e.g., Donniger 1986; Bendor et al. 1991), Kollock’s simulation varies the amount of uncertainty (noise), which yielded a very interesting finding. When all seven strategies were included in the simulation the two stingiest strategies placed first and second in the tournament at the highest levels of noise (Figure 6, p. 781) ”

» shows disadvantages of generosity in ultra-noisy or uncertain environments

» note: with just 5 or 6 strategies in the tournament this trend did not reoccur (stingy guys no longer were found dominating in high noise levels)

» questions about Kolloch’s choice of strategies

Strategy Selection: Another Methodology Issue

“Unfortunately, the method he used to select strategies departs from standard practice, and his paper suffers thereby: It is unclear what, if any, generalizations can be drawn from Kollock’s simulations”

» preferred: systematic selection

» Kollock’s strategies: all self-selected (thus “runs the risk of idiosyncratic choice”- accidentally homogeneous sample, skewed, cognitive biases), most of them were “minor variants of TFT”

» contrast to Axelrod’s experiments with submitted strategies (more variety, 63 in second tournament, “representative sample” of intellectual population)

Bendor et al.’s Concluding SentenceBendor et al.’s Concluding Sentence“Thus, methodologically Kollock’s study is in the worst of all possible worlds: it applies the wrong tools to analyze some issues, and where it is appropriate to use these tools it does not exploit their full power”