The evolution of strategic timing in collective-risk dilemmas

In collective-risk dilemmas, a group needs to collaborate over time to avoid a catastrophic event. This gives rise to a coordination game with many equilibria, including equilibria where no one contributes, and thus no measures against the catastrophe are taken. In this game, the timing of contributions becomes a strategic variable that allows individuals to interact and influence one another. Herein, we use evolutionary game theory to study the impact of strategic timing on equilibrium selection. Depending on the risk of catastrophe, we identify three characteristic regimes. For low risks, defection is the only equilibrium, whereas high risks promote equilibria with sufficient contributions. Intermediate risks pose the biggest challenge for cooperation. In this risk regime, the option to interact over time is critical; if individuals can contribute over several rounds, then the group has a higher chance to succeed, and the expected welfare increases. This positive effect of timing is of particular importance in larger groups, where successful coordination becomes increasingly difficul

Incentives and opportunism: From the carrot to the stick

Cooperation in public good games is greatly promoted by positive and negative incentives. In this papr, we use evolutionary game dynamics to study the evolution of opportunism (the readiness to be swayed by incentives) and the evolution of trst (the propensity to cooperate in the absence of information on the co-players). If both positive and negative incentives are available, evlution leads to a population where defectors are punished and players cooperate, except when they can get away with defection. Rewarding behaviourdoes not become fixed, but can play an essential role in catalysing the emergence of cooperation, especially if the information level is low

Reputation effects drive the joint evolution of cooperation and social rewarding

People routinely cooperate with each other, even when cooperation is costly. To further encourage such pro-social behaviors, recipients often respond by providing additional incentives, for example by offering rewards. Although such incentives facilitate cooperation, the question remains how these incentivizing behaviors themselves evolve, and whether they would always be used responsibly. Herein, we consider a simple model to systematically study the co-evolution of cooperation and different rewarding policies. In our model, both social and antisocial behaviors can be rewarded, but individuals gain a reputation for how they reward others. By characterizing the game’s equilibria and by simulating evolutionary learning processes, we find that reputation effects systematically favor cooperation and social rewarding. While our baseline model applies to pairwise interactions in well-mixed populations, we obtain similar conclusions under assortment, or when individuals interact in larger groups. According to our model, rewards are most effective when they sway others to cooperate. This view is consistent with empirical observations suggesting that people reward others to ultimately benefit themselves

Partners or rivals? Strategies for the iterated prisoner's dilemma

Within the class of memory-one strategies for the iterated Prisoner's Dilemma, we characterize partner strategies, competitive strategies and zero-determinant strategies. If a player uses a partner strategy, both players can fairly share the social optimum; but a co-player preferring an unfair solution will be penalized by obtaining a reduced payoff. A player using a competitive strategy never obtains less than the co-player. A player using a zero-determinant strategy unilaterally enforces a linear relation between the two players' payoffs. These properties hold for every strategy used by the co-player, whether memory-one or not

Evolution of direct reciprocity in group-structured populations

People tend to have their social interactions with members of their owncommunity. Such group-structured interactions can have a profound impact on thebehaviors that evolve. Group structure affects the way people cooperate, andhow they reciprocate each other's cooperative actions. Past work has shown thatpopulation structure and reciprocity can both promote the evolution ofcooperation. Yet the impact of these mechanisms has been typically studied inisolation. In this work, we study how the two mechanisms interact. Using agame-theoretic model, we explore how people engage in reciprocal cooperation ingroup-structured populations, compared to well-mixed populations of equal size.To derive analytical results, we focus on two scenarios. In the first scenario,we assume a complete separation of time scales. Mutations are rare compared tobetween-group comparisons, which themselves are rare compared to within-groupcomparisons. In the second scenario, there is a partial separation of timescales, where mutations and between-group comparisons occur at a comparablerate. In both scenarios, we find that the effect of population structuredepends on the benefit of cooperation. When this benefit is small,group-structured populations are more cooperative. But when the benefit islarge, well-mixed populations result in more cooperation. Overall, our resultsreveal how group structure can sometimes enhance and sometimes suppress theevolution of cooperation.<br

Introspection dynamics: a simple model of counterfactual learning in asymmetric games

Social behavior in human and animal populations can be studied as an evolutionary process.Individuals often make decisions between different strategies, and those strategies that yield afitness advantage tend to spread. Traditionally, much work in evolutionary game theory considerssymmetric games: individuals are assumed to have access to the same set of strategies, and theyexperience the same payoff consequences. As a result, they can learn more profitable strategies byimitation. However, interactions are oftentimes asymmetric. In that case, imitation may beinfeasible (because individuals differ in the strategies they are able to use), or it may be undesirable(because individuals differ in their incentives to use a strategy). Here, we consider an alternativelearning process which applies to arbitrary asymmetric games,introspection dynamics. Accordingto this dynamics, individuals regularly compare their present strategy to a randomly chosenalternative strategy. If the alternative strategy yields a payoff advantage, it is more likely adopted. Inthis work, we formalize introspection dynamics for pairwise games. We derive simple and explicitformulas for the abundance of each strategy over time and apply these results to severalwell-known social dilemmas. In particular, for the volunteer’s timing dilemma, we show that theplayer with the lowest cooperation cost learns to cooperate without delay

Cooperation in alternating interactions with memory constraints

In repeated social interactions, individuals often employ reciprocal strategies to maintain cooperation. To explore the emergence of reciprocity, many theoretical models assume synchronized decision making. In each round, individuals decide simultaneously whether to cooperate or not. Yet many manifestations of reciprocity in nature are asynchronous. Individuals provide help at one time and receive help at another. Here, we explore such alternating games in which players take turns. We mathematically characterize all Nash equilibria among memory-one strategies. Moreover, we use evolutionary simulations to explore various model extensions, exploring the effect of discounted games, irregular alternation patterns, and higher memory. In all cases, we observe that mutual cooperation still evolves for a wide range of parameter values. However, compared to simultaneous games, alternating games require different strategies to maintain cooperation in noisy environments. Moreover, none of the respective strategies are evolutionarily stable

Cooperation and control in multiplayer social dilemmas

Direct reciprocity and conditional cooperation are important mechanisms to prevent free riding in social dilemmas. However, in large groups, these mechanisms may become ineffective because they require single individuals to have a substantial influence on their peers. However, the recent discovery of zero-determinant strategies in the iterated prisoner’s dilemma suggests that we may have underestimated the degree of control that a single player can exert. Here, we develop a theory for zero-determinant strategies for iterated multiplayer social dilemmas, with any number of involved players. We distinguish several particularly interesting subclasses of strategies: fair strategies ensure that the own payoff matches the average payoff of the group; extortionate strategies allow a player to perform above average; and generous strategies let a player perform below average. We use this theory to describe strategies that sustain cooperation, including generalized variants of Tit-for-Tat and Win-Stay Lose-Shift. Moreover, we explore two models that show how individuals can further enhance their strategic options by coordinating their play with others. Our results highlight the importance of individual control and coordination to succeed in large groups

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. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate

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. However, when two such “selfish” learners interact with each other, the outcome can be detrimental to both, especially when there are conflicts of interest. Here, we explore how a learner can align incentives with a selfish opponent. Moreover, we consider the dynamics that arise when learning rules themselves are subject to evolutionary pressure. By combining extensive simulations and analytical techniques, we demonstrate that selfish learning is unstable in most classical two-player repeated games. If evolution operates on the level of long-run payoffs, selection instead favors learning rules that incorporate social (other-regarding) preferences. To further corroborate these results, we analyze data from a repeated prisoner’s dilemma experiment. We find that selfish learning is insufficient to explain human behavior when there is a trade-off between payoff maximization and fairness