Periodic Reporting for period 2 - E-DIRECT (Evolution of Direct Reciprocity in Complex Environments)
Période du rapport: 2022-03-01 au 2023-08-31
Social interactions often show the characteristics of a dilemma: groups of individuals fare best if everyone cooperates, yet each individual is tempted to defect. Such dilemmas can arise at all scales of life. Among humans, they affect the dynamics in teams, families, and among nations. One key question in biology and the social sciences is: What mechanisms promote cooperation?
One important mechanism for cooperation is direct reciprocity. This mechanism is based on repeated interactions in stable groups. Repetition allows individuals to use conditional strategies, such as Tit-for-Tat. In that case, individuals cooperate as long as others do, and they stop cooperating once their interaction partner defects. Once sufficiently many group members adopt such conditional strategies, cooperation becomes optimal even for self-interested individuals.
Models of direct reciprocity have been extremely useful to explain food sharing among animals, price competition among firms, and the economics of favors among friends. Yet the corresponding models often make drastic simplifications. First, individuals are often assumed to be identical. They coincide in their ability to cooperate, and they equally benefit from each other’s’ cooperation. Second, individuals are often assumed to engage in the very same social dilemma over and over again. Each time, they have the same incentive to cooperate, irrespective of any changes in a group’s social or ecological environment.
With this project, we aim to explore the emergence and stability of reciprocity in more complex environments. The questions that we ask are the following: Which strategies can sustain cooperation when populations are heterogeneous, or when the nature of a social interaction can change in time? Which kinds of inequality are harmful to cooperation, and how can individuals cope with these inequalities? How should one define fairness in games that are inherently asymmetric? We address these questions both with mathematical and computational models, and using behavioral experiments with human subjects.
One important mechanism for cooperation is direct reciprocity. This mechanism is based on repeated interactions in stable groups. Repetition allows individuals to use conditional strategies, such as Tit-for-Tat. In that case, individuals cooperate as long as others do, and they stop cooperating once their interaction partner defects. Once sufficiently many group members adopt such conditional strategies, cooperation becomes optimal even for self-interested individuals.
Models of direct reciprocity have been extremely useful to explain food sharing among animals, price competition among firms, and the economics of favors among friends. Yet the corresponding models often make drastic simplifications. First, individuals are often assumed to be identical. They coincide in their ability to cooperate, and they equally benefit from each other’s’ cooperation. Second, individuals are often assumed to engage in the very same social dilemma over and over again. Each time, they have the same incentive to cooperate, irrespective of any changes in a group’s social or ecological environment.
With this project, we aim to explore the emergence and stability of reciprocity in more complex environments. The questions that we ask are the following: Which strategies can sustain cooperation when populations are heterogeneous, or when the nature of a social interaction can change in time? Which kinds of inequality are harmful to cooperation, and how can individuals cope with these inequalities? How should one define fairness in games that are inherently asymmetric? We address these questions both with mathematical and computational models, and using behavioral experiments with human subjects.
The project consists of four work packages (WP). It theoretically explores the impact of asymmetry (WP 1), of changing environments (WP2), and the possible interactions among these two sources of complexity (WP3). In addition, we empirically test human strategies of direct reciprocity (WP4).
For WP1, we have formalized a simple model that can be used to describe learning in asymmetric games (Couto et al, New J. Phys., 2022). This so-called introspection dynamics has very convenient mathematical properties, and it will allow us to analytically study strategic behavior in all kinds of asymmetric games. We have already applied this model to study (both theoretically and empirically) how people coordinate when they either differ in their endowments or their productivities (Wang et al, Phil. Transactions Royal Soc. B, 2022). In addition, we have introduced a notion of fairness that applies to weakly-asymmetric games (McAvoy et al, PNAS Nexus 2022).
For WP2, we have described a simple rule based on cumulative reciprocity that allows individuals to sustain cooperation in both static and changing environments (Li et al, Nature Computational Science, 2022). In addition, we currently explore the impact of imperfect information on cooperation in changing environments (Kleshnina et al, under review). Finally, we describe how individuals can learn fairness-enforcing strategies in simple stochastic games in ongoing work (McAvoy et al, in preparation).
For WP3 we have only done simple preliminary works. This working package will be important during the second half of the grant period. For WP4, we are currently exploring the dynamics of cooperation when individuals engage in several social dilemmas in parallel (Rossetti et al, in preparation). Several further experiments are currently at a design stage.
In addition to these projects directly tied to the individual work packages, we have also made progress on models of reciprocity that we did not anticipate at the time of the grant proposal. For example, we explored the interaction of direct and indirect reciprocity (Schmid et al, Nature Human Behaviour, 2021), the interaction of cooperation and social rewards (Pal & Hilbe, Nature Communications 2022), and the emergence of reciprocity in alternating games (Park et al, Nature Communications 2022).
For WP1, we have formalized a simple model that can be used to describe learning in asymmetric games (Couto et al, New J. Phys., 2022). This so-called introspection dynamics has very convenient mathematical properties, and it will allow us to analytically study strategic behavior in all kinds of asymmetric games. We have already applied this model to study (both theoretically and empirically) how people coordinate when they either differ in their endowments or their productivities (Wang et al, Phil. Transactions Royal Soc. B, 2022). In addition, we have introduced a notion of fairness that applies to weakly-asymmetric games (McAvoy et al, PNAS Nexus 2022).
For WP2, we have described a simple rule based on cumulative reciprocity that allows individuals to sustain cooperation in both static and changing environments (Li et al, Nature Computational Science, 2022). In addition, we currently explore the impact of imperfect information on cooperation in changing environments (Kleshnina et al, under review). Finally, we describe how individuals can learn fairness-enforcing strategies in simple stochastic games in ongoing work (McAvoy et al, in preparation).
For WP3 we have only done simple preliminary works. This working package will be important during the second half of the grant period. For WP4, we are currently exploring the dynamics of cooperation when individuals engage in several social dilemmas in parallel (Rossetti et al, in preparation). Several further experiments are currently at a design stage.
In addition to these projects directly tied to the individual work packages, we have also made progress on models of reciprocity that we did not anticipate at the time of the grant proposal. For example, we explored the interaction of direct and indirect reciprocity (Schmid et al, Nature Human Behaviour, 2021), the interaction of cooperation and social rewards (Pal & Hilbe, Nature Communications 2022), and the emergence of reciprocity in alternating games (Park et al, Nature Communications 2022).
The above-mentioned results go beyond the state of the art in several ways. While previous work on reciprocity usually considers simplistic strategies with one-round memory, we are now able to mathematically describe strategies that take into account the whole history of interactions (Li et al, Nature Computational Science 2022).
Similarly, we are now able to generalize the notion of ‘zero-determinant strategies’ (Press & Dyson, PNAS 2012) to new domains. Based on this theory, we describe how individuals can enforce fair outcomes in alternating games (Park et al, Nature Communications 2022), in games of indirect reciprocity (Schmid et al, Nature Human Behaviour 2021), or games in changing environments (McAvoy et al, in preparation).
We expect similar progress in the next years. In particular, we are interested in the question how fairness-enforcing strategies can be learnt most effectively (using tools of reinforcement learning). Another active area of research is the evolution of cooperation when individuals are asymmetric with respect to their cognitive abilities or their social preferences. Here, we also ask how such asymmetries might evolve in the first place.
Similarly, we are now able to generalize the notion of ‘zero-determinant strategies’ (Press & Dyson, PNAS 2012) to new domains. Based on this theory, we describe how individuals can enforce fair outcomes in alternating games (Park et al, Nature Communications 2022), in games of indirect reciprocity (Schmid et al, Nature Human Behaviour 2021), or games in changing environments (McAvoy et al, in preparation).
We expect similar progress in the next years. In particular, we are interested in the question how fairness-enforcing strategies can be learnt most effectively (using tools of reinforcement learning). Another active area of research is the evolution of cooperation when individuals are asymmetric with respect to their cognitive abilities or their social preferences. Here, we also ask how such asymmetries might evolve in the first place.