Cooperation in repeated interactions: A systematic review of Centipede game experiments, 1992–2016

Abstract

Cooperation is a fundamental form of social interaction, and turn-taking reciprocity one of its most familiar manifestations. The Centipede game provides a formal model of such alternating reciprocal cooperation, but a backward induction argument appears to prove logically that instrumentally rational players would never cooperate in this way. A systematic review of experimental research reveals that human decision makers cooperate frequently in this game, except under certain extreme conditions. Several task, situational, and individual difference variables have been investigated for their influence on cooperation. The most influential are aspects of the payoff function (especially the social gain from cooperation and the risk associated with a cooperative move), the number of players, repetitions of the game, group versus individual decisions, and players' social value orientations. Our review of experimental evidence suggests that other-regarding preferences, including prosocial behavioural dispositions and collective rationality, provide the most powerful explanation for cooperation.Keywords: backward induction, Centipede game, cooperation, game theory, reciprocity Supplemental materials: http://dx.doi.org/00.0000/x0000000.supp COOPERATION IN REPEATED INTERACTIONS 3 Cooperation in Repeated Interactions: A Systematic Review of Centipede Game Experiments, 1992-2016Cooperation is one of the most fundamental forms of human social interaction, and it plays a significant part in many areas of interpersonal, economic, and political life. In his last address as President of the Royal Society, Lord Robert May (2006) expressed the view that "the most important unanswered question in evolutionary biology, and more generally in the social sciences, is how cooperative behaviour evolved and can be maintained in human or other animal groups and societies" (p. 109). Cooperation frequently displays a pattern of repeated interactions in which Person A rewards Person B in some way, then B reciprocates by rewarding A, then A reciprocates by rewarding B again, and so on through several or many cycles of reciprocal cooperation. It is often reasonable to assume that each rewarding action incurs some cost c to the person performing it, financially, materially, or in terms of time, effort, or inconvenience, but that this cost is no larger than the benefit b to the recipient, so that c ≤ b. Typical everyday examples include next-door neighbours taking turns looking after each other's children to enable the parents to enjoy a night out, business associates taking turns providing each other with letters of recommendation for job applications, and academics taking turns providing feedback on each other's research grant applications.The Centipede game, introduced by Rosenthal (1981), provides a game-theoretic model of this class of repeated interactions. Formally, the Centipede game is a finite, extensive-form game (because players make their moves sequentially) with complete information (because they are fully informed abo...

Ambiguity and the Centipede Game: Strategic Uncertainty in Multi-Stage Games

“…This prediction is broadly con…rmed by the available experimental evidence, (for a survey see Krokow, Colman, and Pulford (2016)). …”

“…17 The centipede game was introduced by Rosenthal (1981) and studied in laboratory experiments by McKelvey and Palfrey (1992). A survey of subsequent experimental research can be found in Krokow, Colman, and Pulford (2016).…”

“…Because of this, we do not consider them in this review. For a survey see Krokow, Colman, and Pulford (2016). strategy of a "rational" player may involve imitating the "irrational" player in order to induce more favourable behaviour by his/her opponents.…”

Comparing Behavioral Models Using Data From Experimental Centipede Games

“…Krockow, Colman, and Pulford () highlight that different explanations have been suggested to rationalize the deviations from the game‐theoretic solution and classifies them to two broad categories: insufficient cognitive ability to perform backward induction reasoning and other‐regarding motives that interfere with rational, selfish decision‐making. In a systematic review of centipede game experiments, Krockow, Colman, and Pulford () conclude by summarizing the potential reasons why players cooperate and do not follow the rational prescription of backward induction reasoning. They include four explanations: (1) the hidden assumption explanation that expectations about co‐players' future actions are unaffected by observations of their past actions; (2) the cognitive burden explanation based on the idea that backward induction is cognitively taxing and therefore players do not realize that defecting at an earlier stage may be more beneficial; (3) the common knowledge breakdown explanation, where players do not expect their co‐players to be fully rational; and (4) the other regarding preferences explanation.…”

“…We do not aim to provide a thorough review of the literature given that there exist excellent recent reviews of the experimental literature (see Krockow, Colman, and Pulford and Dhami , chapter 12, p. 729).…”