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Dynamic Games and Applications

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09-01-2023 | Research

Complexity of Behavioural Strategies and Cooperation in the Optional Public Goods Game

Authors: Shirsendu Podder, Simone Righi

Published in: Dynamic Games and Applications | Issue 4/2023

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Abstract

The problem of collective action where—beside the standard options of cooperating and defecting—there is also the possibility of opting out has been extensively studied through the optional public good game (OPGG). Within this and other social dilemma games, reputation systems, composed of a social norm—assigning reputations to agents—and a set of behavioural strategies using this information to condition their behaviour, are able to sustain cooperation. However, while the relationship between the complexity of social norms and cooperation has been extensively studied, the same cannot be said with respect to behavioural strategies, due to high dimensionality of the strategy spaces involved. We deal with this problem by building an agent-based model where agents adopt simple social norms, play the OPGG and learn behavioural strategies through a genetic algorithm. We show that while social norms which assign different reputations to defectors and to agents opting out achieve the highest levels of cooperation, the social norms that do not distinguish between these actions do improve cooperation levels with respect to the baseline when behavioural strategies are sufficiently complex. Furthermore, we find that cooperation increases when the interaction groups are small enough for agents to accurately distinguish between different behaviours.

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This problem can be partially circumvented through punishment [7, 61] or alliances [32]

The emergence of these cycles of punishments have been challenged when loners cannot be punished [21].

Each individual looks at the average reputation computed across all other agents in the group, excluding herself.

[53] implement the execution errors as a small chance of an agent willing to cooperate being prevented from doing so. We chose to implement it symmetrically due to the addition of the third basic strategy in the OPGG.

In Fig. 2, \(n=5\), which means that there are only 9 possible levels of average reputation in a group.

Results for \(n<5\) are reported in Figure S5. For \(n=4\) our results are confirmed. When \(n=3\) once the maximum complexity of 5 (since the total number of possible average reputation values in a group of three individuals is \(2*3-1=5\)) is achieved, cooperation collapses, as increasing p only increase noise. Finally, when \(n=2\), strategies are only focused on the reputation of the single interacting partner, directly discriminating on the opponent’s reputation and leading to full cooperation regardless of complexity (there is no uncertainty as the average reputation of the group fully reveals the nature of the opponent allowing perfect discrimination).

If points lie on the grey line, it indicates that players are using the entirety of their strategies.

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Title: Complexity of Behavioural Strategies and Cooperation in the Optional Public Goods Game
Authors: Shirsendu Podder
Simone Righi
Publication date: 09-01-2023
Publisher: Springer US
Published in: Dynamic Games and Applications / Issue 4/2023
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-022-00485-5

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