Cooperation in the spatial prisoner's dilemma game with probabilistic abstention

The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph

We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of selection, which governs replicator(-mutator) dynamics, based on a stratified interaction mechanism and a composite strategy update rule. Our findings suggest that the replication of a certain mutation in a strategy, leading to a shift from competition to cooperation in a well-mixed population, is equivalent to the replication of a strategy in a Bayesian-structured population without any mutation. Likewise, the replication of a strategy in a Bayesian-structured population with a certain mutation, resulting in a move from competition to cooperation, is equivalent to the replication of a strategy in a well-mixed population without any mutation. This equivalence holds when the transition rate from competition to cooperation is equal to the relative strength of selection acting on either competition or cooperation in relation to the selection differential between cooperators and competitors. Our research allows us to identify situations where cooperation is more likely, irrespective of the specific payoff levels. This approach provides new perspectives into the intended purpose of Price's equation, which was initially not designed for this type of analysis.

Dying to cooperate: the role of environmental harshness in human collaboration

It has been proposed that environmental stress acted as a selection pressure on the evolution of human cooperation. Through agent-based evolutionary modelling, mathematical analysis, and human experimental data we illuminate the mechanisms by which the environment influences cooperative success and decision making in a Stag Hunt game. The modelling and mathematical results show that only cooperative foraging phenotypes survive the harshest of environments but pay a penalty for miscoordination in favourable environments. When agents are allowed to coordinate their hunting intentions by communicating, cooperative phenotypes outcompete those who pursue individual strategies in almost all environmental and payoff scenarios examined. Data from human participants show flexible decision-making in face of cooperative uncertainty, favouring high-risk, high-reward strategy when environments are harsher and starvation is imminent. Converging lines of evidence from the three approaches indicate a significant role for environmental variability in human cooperative dynamics and the species-unique cognition designed to support it.

Effort Perception is Made More Accurate with More Effort and When Cooperating with Slackers

Recent research on the conditions that facilitate cooperation is limited by a factor that has yet to be established: the accuracy of effort perception. Accuracy matters because the fitness of cooperative strategies depends not just on being able to perceive others’ effort but to perceive their true effort. In an experiment using a novel effort-tracker methodology, we calculate the accuracy of human effort perceptions and show that accuracy is boosted by more absolute effort (regardless of relative effort) and when cooperating with a “slacker” rather than an “altruist”. A formal model shows how such an effort-prober strategy is likely to be an adaptive solution because it gives would-be collaborators information on when to abort ventures that are not in their interest and opt for ones that are. This serves as a precautionary measure against systematic exploitation by extortionist strategies and a descent into uncooperativeness. As such, it is likely that humans have a bias to minimize mistakes in effort perception that would commit them to a disadvantageous effort-reward relationship. Overall we find support for the idea that humans have evolved smart effort detection systems that are made more accurate by those contexts most relevant for cooperative tasks.

Direct reciprocity and model-predictive rationality explain network reciprocity over social ties

Since M. A. Nowak & R. May’s (1992) influential paper, limiting each agent’s interactions to a few neighbors in a network of contacts has been proposed as the simplest mechanism to support the evolution of cooperation in biological and socio-economic systems. The network allows cooperative agents to self-assort into clusters, within which they reciprocate cooperation. This (induced) network reciprocity has been observed in several theoreticalmodels and shown to predict the fixation of cooperation under a simple rule: the benefit produced by an act of cooperation must outweigh the cost of cooperating with all neighbors. However, the experimental evidence among humans is controversial: though the rule seems to be confirmed, the underlying modeling assumptions are not. Specifically, models assume that agents update their strategies by imitating better performing neighbors, even though imitation lacks rationality when interactions are far from all-to-all. Indeed, imitation did not emerge in experiments. What did emerge is that humans are conditioned by their own mood and that, when in a cooperative mood, they reciprocate cooperation. To help resolve the controversy, we design a model in which we rationally confront the two main behaviors emerging from experiments—reciprocal cooperation and unconditional defection—in a networked prisoner’s dilemma. Rationality is introduced by means of a predictive rule for strategy update and is bounded by the assumed model society. We show that both reciprocity and a multi-step predictive horizon are necessary to stabilize cooperation, and sufficient for its fixation, provided the game benefit-to-cost ratio is larger than a measure of network connectivity. We hence rediscover the rule of network reciprocity, underpinned however by a different evolutionary mechanism.

Nash Equilibria in the Response Strategy of Correlated Games

In nature and society, problems that arise when different interests are difficult to reconcile are modeled in game theory. While most applications assume that the players make decisions based only on the payoff matrix, a more detailed modeling is necessary if we also want to consider the influence of correlations on the decisions of the players. We therefore extend here the existing framework of correlated strategies by giving the players the freedom to respond to the instructions of the correlation device by probabilistically following or not following its suggestions. This creates a new type of games that we call “correlated games”. The associated response strategies that can solve these games turn out to have a rich structure of Nash equilibria that goes beyond the correlated equilibrium and pure or mixed-strategy solutions and also gives better payoffs in certain cases. We here determine these Nash equilibria for all possible correlated Snowdrift games and we find these solutions to be describable by Ising models in thermal equilibrium. We believe that our approach paves the way to a study of correlations in games that uncovers the existence of interesting underlying interaction mechanisms, without compromising the independence of the players.