Amaral, M.A., et al., 2016. Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas. Phys. Rev. E, 94, pp.032317. Publisher's Version
Amaral, M.A., et al., 2016. Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity. Physical Review E, 93.Abstract
Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two different games. While in well-mixed populations the random mixture of the two games is always equivalent to the average single game, in structured populations this is not always the case. We show that the outcome is, in fact, strongly dependent on the distance of separation of the two games in the parameter space. Effectively, this distance introduces payoff heterogeneity, and the average game is returned only if the heterogeneity is small. For higher levels of heterogeneity the distance to the average game grows, which often involves the promotion of cooperation. The presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin, and they also emphasize the importance of the population structure in amplifying facilitators of cooperation.
Junior, E.J.S., Wardil, L.L. & da Silva, J.K.L., 2016. Inactive sites and the evolution of cooperation. EPL, 116, pp.18004.
Wardil, L. & Hauert, C., 2016. (Behavioural experiment) Targeted Cooperative Actions Shape Social Networks. PLOS ONE, 11, pp.e0147850.Abstract
Individual acts of cooperation give rise to dynamic social networks. Traditionally, models for cooperation in structured populations are based on a separation of individual strategies and of population structure. Individuals adopt a strategy – typically cooperation or defection, which determines their behaviour toward their neighbours as defined by an interaction network. Here, we report a behavioural experiment that amalgamates strategies and structure to empirically investigate the dynamics of social networks. The action of paying a cost c to provide a benefit b is represented as a directed link point from the donor to the recipient. Participants can add and/or remove links to up to two recipients in each round. First, we show that dense networks emerge, where individuals are characterized by fairness: they receive to the same extent they provide. More specifically, we investigate how participants use information about the generosity and payoff of others to update their links. It turns out that aversion to payoff inequity was the most consistent update rule: adding links to individuals that are worse off and removing links to individuals that are better off. We then investigate the effect of direct reciprocation, showing that the possibility of direct reciprocation does not increase cooperation as compared to the treatment where participants are totally unaware of who is providing benefits to them.
Amaral, M.A., Wardil, L. & da Silva, J.K.L., 2015.

Cooperation in two-dimensional mixed-games

. Journal of Physics A, 48.Abstract
Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two individuals is uniformly drawn from a sample of two different games. Using the master equation approach we show that the random mixture of two games is equivalent to play the average game when (i) the strategies are statistically independent of the game distribution and (ii) the transition rates are linear functions of the payoffs. We also use Monte-Carlo simulations in a two-dimensional lattice and mean-field techniques to investigate the scenario when the two above conditions do not hold. We find that even outside of such conditions, several quantities characterizing the mixed-games are still the same as the ones obtained in the average game when the two games are not very different.
Wardil, L. & Hauert, C., 2015.

Cooperation and co-authorship in academic publishing Physical Review

. Physical Review E, 91.Abstract
Research collaboration occurs more frequently today than in the past. As a consequence, cooperation and competition are crucial determinants of academic success. In multiauthored publications, not all authors contribute evenly. Hence, some authors end up with less time or resources to work on parallel projects, decreasing their number of publications. Although detailed information on the contribution of each author in multiauthored publications is generally not available, the order of authors often discloses information on differential contributions. Here we analyze the full data set of Physical Review journals to show that, along with the increasingly number of multiauthored publications, first authors incur costs and last authors are bestowed benefits in terms of number of publications. In other words, authors publishing more often as first authors have fewer publications in the short-term than authors publishing more often as last authors. Using a simplified network representation where direct links represent the costly action of first authors towards last authors, we analyze the evolution of cooperation in multiauthored publications.
Wardil, L. & Hauert, C., 2014.

Origin and structure of dynamic cooperative networks

. Scientific Reports , 4.Abstract
Societies are built on social interactions among individuals. Cooperation represents the simplest form of a social interaction: one individual provides a benefit to another one at a cost to itself. Social networks represent a dynamical abstraction of social interactions in a society. The behaviour of an individual towards others and of others towards the individual shape the individual’s neighbourhood and hence the local structure of the social network. Here we propose a simple theoretical framework to model dynamic social networks by focussing on each individual’s actions instead of interactions between individuals. This eliminates the traditional dichotomy between the strategy of individuals and the structure of the population and easily complements empirical studies. As a consequence, altruists, egoists and fair types are naturally determined by the local social structures, while globally egalitarian networks or stratified structures arise. Cooperative interactions drive the emergence and shape the structure of social networks.
Wardil, L. & da Silva, J.K.L., 2013.

The evolution of cooperation in mixed games Chaos, Solitons and Fractals

. Chaos, Solitons and Fractals, 56.Abstract
Cooperation has been studied in the context of game evolutionary theory by assuming that individuals play always the same game. Here we consider a mixture of two games G1 and G2. In each interaction of two individuals, they can play the games G1 or G2 with probabilities w and 1 - w, respectively. We define the evolutionary model and study the cooperation evolution in a well-mixed population and in a cycle. We show that in the well-mixed population the evolution is equivalent to the evolution given by the average game. In a cycle, we show that the intensity of selection plays an important role in the promotion or inhibition of cooperation, depending on the games that are mixed.
Wardil, L. & da Silva, J.K.L., 2011.

The evolution of cooperation in heterogeneous networks when opponents can be distinguished

. Journal of Physics A, 44.Abstract
Cooperation has been widely studied in the context of evolutionary games on graphs. Usually the players are set on the nodes of a network and adopt the same strategy, cooperation or defection, against all of their neighbors. In heterogeneous networks, it was shown that cooperation is highly sustained, although when the cumulative payoff is normalized by the connectivity, the cooperation is severely weakened. Here, we study the evolution of cooperation in heterogeneous networks when it is possible to adopt different strategies against different opponents. We study numerically different types of heterogeneous networks, including scale-free networks, that differ in the extent of the role of the highly connected nodes, usually called hubs. The remarkable result is that cooperation is maintained irrespective of whether the payoff is the total one or the normalized one, and, in spite of such blindness, we still find that the topology has a strong effect. When the presence of the hubs is more prominent, we find that the cooperation level decreases for synchronous update but remains almost unchanged for the asynchronous update. It is also shown that cooperation is robust against errors in the update rule.
Wardil, L. & da Silva, J.K.L., 2010. Distinguishing the opponents promotes cooperation in well-mixed populations. PHYSICAL REVIEW E, 81.Abstract
Cooperation has been widely studied when an individual strategy is adopted against all coplayers. In this context, some extra mechanisms, such as punishment, reward, memory, and network reciprocity must be introduced in order to keep cooperators alive. Here, we adopt a different point of view. We study the adoption of different strategies against different opponents instead of adoption of the same strategy against all of them. In the context of the prisoner dilemma, we consider an evolutionary process in which strategies that provide more benefits are imitated and the players replace the strategy used in one of the interactions furnishing the worst payoff. Individuals are set in a well-mixed population, so that network reciprocity effect is excluded and both synchronous and asynchronous updates are analyzed. As a consequence of the replacement rule, we show that mutual cooperation is never destroyed and the initial fraction of mutual cooperation is a lower bound for the level of cooperation. We show by simulation and mean-field analysis that (i) cooperation dominates for synchronous update and (ii) only the initial mutual cooperation is maintained for asynchronous update. As a side effect of the replacement rule, an ``implicit punishment'' mechanism comes up in a way that exploitations are always neutralized providing evolutionary stability for cooperation.
Wardil, L. & Siva, J.K.L., 2009.

Adoption of simultaneous different strategies against distinct opponents

. EPL, 2009.Abstract
The emergence of cooperation has been widely studied in the context of game theory on structured populations. Usually the individuals adopt one strategy against all their neighbors. The structure can provide reproductive success for the cooperative strategy, at least for low values of defection tendency. Other mechanisms, such as punishment, can also be responsible for cooperation emergence. But what happens if the players adopt simultaneously different strategies against each one of their opponents, not just a single one? Here we study this question in the prisoner dilemma scenario structured on a square lattice and on a ring. We show that if an update rule is defined in which the players replace the strategy that furnishes the smallest payoff, a punishment response mechanism against defectors without imputing cost to the punishers appears, cooperation dominates and, even if the tendency of defection is huge, cooperation still remains alive.
Wardil, L. & da Siva, J.K.L., 2008.

A discrete inhomogeneous model for the yeast cell cycle Brazilian Journal of Physics

. Brazilian Journal of Physics, 38.Abstract
We study the robustness and stability of the yeast cell regulatory network by using a general inhomogeneous discrete model. We find that inhomogeneity, on average, enhances the stability of the biggest attractor of the dynamics and that the large size of the basin of attraction is robust against changes in the parameters of inho- mogeneity. We find that the most frequent orbit, which represents the cell-cycle pathway, has a better biological meaning than the one exhibited by the homogeneous model.