Reputation and punishment sustain cooperation in the optional public goods game

Abstract

Cooperative behaviour has been extensively studied as a choice between cooperation and defection. However, the possibility to not participate is also frequently available. This type of problem can be studied through the optional public goods game. The introduction of the ‘Loner’ strategy' allows players to withdraw from the game, which leads to a cooperator–defector–loner cycle. While pro-social punishment can help increase cooperation, anti-social punishment—where defectors punish cooperators—causes its downfall in both experimental and theoretical studies. In this paper, we introduce social norms that allow agents to condition their behaviour to the reputation of their peers. We benchmark this with respect both to the standard optional public goods game and to the variant where all types of punishment are allowed. We find that a social norm imposing a more moderate reputational penalty for opting out than for defecting increases cooperation. When, besides reputation, punishment is also possible, the two mechanisms work synergically under all social norms that do not assign to loners a strictly worse reputation than to defectors. Under this latter set-up, the high levels of cooperation are sustained by conditional strategies, which largely reduce the use of pro-social punishment and almost completely eliminate anti-social punishment. This article is part of the theme issue ‘The language of cooperation: reputation and honest signalling’.

Evaluating mechanisms that could support credible reputations and cooperation: cross-checking and social bonding

“…In this regard, running out of time was equivalent to defection (cf. [ 78 ]), so it could not be used as a costly punishment action. In the first round, 63 players (26.9%) ran out of time, and 44 (18.8%) in the sixth round.…”

The language of cooperation: reputation and honest signalling

“…Finally, they highlight the need to better understand how distinct tactics to intervene against offences impact reputations. Podder et al [24,25] investigated cooperation problems in which individuals have a choice to opt out of the interaction (the optional Public Goods game). The assignment of reputations is more complex in these interactions as there is more than a collectively good (cooperation) and bad (defection) choice.…”

“…A reputation system based on aggregated experiences includes (i) a set of decision rules to guide how individuals should be evaluated based on their actions, usually called social norms; (ii) a communication system that allows for the exchange of experiences and evaluations; and (iii) a set of decision rules that guides the actions towards individuals with different reputations, usually called behavioural norms or action rules [20][21][22][23][24][25].…”

Authority or Autonomy? Exploring Interactions between Central and Peer Punishments in Risk-Resistant Scenarios

“…Therefore, how to solve such social dilemmas to promote cooperation is of great importance to the functioning of society and has received a lot of attention from various scholars [ 12 , 13 , 14 , 15 ]. Behavioral economics has proposed various game models [ 16 , 17 , 18 ] that vividly demonstrate the conflict between the group cooperation and the individual free-riding behavior, such as the dictator game [ 19 , 20 , 21 ], public goods game [ 22 , 23 , 24 , 25 ], prisoner’s dilemma game [ 20 , 26 , 27 ], etc. In addition, various measures have been proposed to promote cooperation and find a way out of the social dilemma [ 13 , 22 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ].…”

“…Many researchers have noted punishment for its cooperation boosting effects [ 22 , 35 , 36 , 37 ]. In a nutshell, punishment can reduce the gain of individuals in a group who hold a certain strategy.…”