Maintaining diversity in structured populations.

We examine population structures for their ability to maintain diversity in neutral evolution. We use the general framework of evolutionary graph theory and consider birth-death (bd) and death-birth (db) updating. The population is of size .

Unilateral incentive alignment in two-agent stochastic games.

Multiagent learning is challenging when agents face mixed-motivation interactions, where conflicts of interest arise as agents independently try to optimize their respective outcomes. Recent advancements in evolutionary game theory have identified a class of "zero-determinant" strategies, which confer an agent with significant unilateral control over outcomes in repeated games. Building on these insights, we present a comprehensive generalization of zero-determinant strategies to stochastic games, encompassing dynamic environments.

Stable strategies of direct and indirect reciprocity across all social dilemmas.

Social dilemmas are collective-action problems where individual interests are at odds with group interests. Such dilemmas occur frequently at all scales of human interactions. When dealing with collective-action problems, people often act reciprocally.

Hardware-optimal quantum algorithms.

Quantum hardware is inherently fragile and noisy. We find that the accuracy of traditional quantum error correction algorithms can be improved depending on the hardware. Given different hardware specifications, we automatically synthesize hardware-optimal algorithms for parity correction, qubit resetting, and GHZ (Greenberger-Horne-Zeilinger) state preparation.

Density amplifiers of cooperation for spatial games.

Spatial games provide a simple and elegant mathematical model to study the evolution of cooperation in networks. In spatial games, individuals reside in vertices, adopt simple strategies, and interact with neighbors to receive a payoff. Depending on their own and neighbors' payoffs, individuals can change their strategy.

Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating.

Populations evolve by accumulating advantageous mutations. Every population has some spatial structure that can be modeled by an underlying network. The network then influences the probability that new advantageous mutations fixate.

Efficiency and resilience of cooperation in asymmetric social dilemmas.

Direct reciprocity is a powerful mechanism for cooperation in social dilemmas. The very logic of reciprocity, however, seems to require that individuals are symmetric, and that everyone has the same means to influence each others' payoffs. Yet in many applications, individuals are asymmetric.

Evolutionary dynamics of mutants that modify population structure.

Natural selection is usually studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we explore how natural selection acts on mutants that have the same reproductive rate, but different population structures. In our framework, population structure is given by a graph that specifies where offspring can disperse.

The effect of environmental information on evolution of cooperation in stochastic games.

Many human interactions feature the characteristics of social dilemmas where individual actions have consequences for the group and the environment. The feedback between behavior and environment can be studied with the framework of stochastic games. In stochastic games, the state of the environment can change, depending on the choices made by group members.

Quantitative assessment can stabilize indirect reciprocity under imperfect information.

The field of indirect reciprocity investigates how social norms can foster cooperation when individuals continuously monitor and assess each other's social interactions. By adhering to certain social norms, cooperating individuals can improve their reputation and, in turn, receive benefits from others. Eight social norms, known as the "leading eight," have been shown to effectively promote the evolution of cooperation as long as information is public and reliable.

Evolutionary instability of selfish learning in repeated games.

Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one's own success.

Social balance on networks: Local minima and best-edge dynamics.

Structural balance theory is an established framework for studying social relationships of friendship and enmity. These relationships are modeled by a signed network whose energy potential measures the level of imbalance, while stochastic dynamics drives the network toward a state of minimum energy that captures social balance. It is known that this energy landscape has local minima that can trap socially aware dynamics, preventing it from reaching balance.

Direct reciprocity between individuals that use different strategy spaces.

In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore.

Infection dynamics of COVID-19 virus under lockdown and reopening.

Motivated by COVID-19, we develop and analyze a simple stochastic model for the spread of disease in human population. We track how the number of infected and critically ill people develops over time in order to estimate the demand that is imposed on the hospital system. To keep this demand under control, we consider a class of simple policies for slowing down and reopening society and we compare their efficiency in mitigating the spread of the virus from several different points of view.

The evolution of indirect reciprocity under action and assessment generosity.

Indirect reciprocity is a mechanism for the evolution of cooperation based on social norms. This mechanism requires that individuals in a population observe and judge each other's behaviors. Individuals with a good reputation are more likely to receive help from others.

Fast and strong amplifiers of natural selection.

Selection and random drift determine the probability that novel mutations fixate in a population. Population structure is known to affect the dynamics of the evolutionary process. Amplifiers of selection are population structures that increase the fixation probability of beneficial mutants compared to well-mixed populations.

A unified framework of direct and indirect reciprocity.

Direct and indirect reciprocity are key mechanisms for the evolution of cooperation. Direct reciprocity means that individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means that they also consider the experiences of others.

Mistakes can stabilise the dynamics of rock-paper-scissors games.

A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving.

The Moran process on 2-chromatic graphs.

Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color.

Limits on amplifiers of natural selection under death-Birth updating.

The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size.

Social dilemmas among unequals.

Direct reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans and is generally considered to undermine cooperation and welfare.

Publisher Correction: Partners and rivals in direct reciprocity.

In the version of this Review Article originally published, in Fig. 4 an arrow pointing from ALLC to ALLD was mistakenly omitted. This has now been corrected in all versions of the Review Article.

Partners and rivals in direct reciprocity.

Reciprocity is a major factor in human social life and accounts for a large part of cooperation in our communities. Direct reciprocity arises when repeated interactions occur between the same individuals. The framework of iterated games formalizes this phenomenon.

Population structure determines the tradeoff between fixation probability and fixation time.

The rate of biological evolution depends on the fixation probability and on the fixation time of new mutants. Intensive research has focused on identifying population structures that augment the fixation probability of advantageous mutants. But these amplifiers of natural selection typically increase fixation time.

Indirect reciprocity with private, noisy, and incomplete information.

Indirect reciprocity is a mechanism for cooperation based on shared moral systems and individual reputations. It assumes that members of a community routinely observe and assess each other and that they use this information to decide who is good or bad, and who deserves cooperation. When information is transmitted publicly, such that all community members agree on each other's reputation, previous research has highlighted eight crucial moral systems.