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.evolutionary game theory | alliances | public goods game | volunteer's dilemma | cooperation C ooperation among self-interested individuals is generally difficult to achieve (1-3), but typically the free rider problem is aggravated even further when groups become large (4-9). In small communities, cooperation can often be stabilized by forms of direct and indirect reciprocity (10-17). For large groups, however, it has been suggested that these mechanisms may turn out to be ineffective, as it becomes more difficult to keep track of the reputation of others and because the individual influence on others diminishes (4-8). To prevent the tragedy of the commons and to compensate for the lack of individual control, many successful communities have thus established central institutions that enforce mutual cooperation (18)(19)(20)(21)(22).However, a recent discovery suggests that we may have underestimated the amount of control that single players can exert in repeated games. For the repeated prisoner's dilemma, Press and Dyson (23) have shown the existence of zero-determinant strategies (or ZD strategies), which allow a player to unilaterally enforce a linear relationship between the own payoff and the coplayer's payoff, irrespective of the coplayer's actual strategy. The class of zero-determinant strategies is surprisingly rich: for example, a player who wants to ensure that the own payoff will always match the coplayer's payoff can do so by applying a fair ZD strategy, like Titfor-Tat. On the other hand, a player who wants to outperform the respective opponent can do so by slightly tweaking the Tit-for-Tat strategy to the own advantage, thereby giving rise to extortionate ZD strategies. The discovery of such strategies has prompted several theoretical studies, exploring how dif...

Similarity search is an important function in many applications, which usually focuses on measuring the similarity between objects with the same type. However, in many scenarios, we need to measure the relatedness between objects with different types. With the surge of study on heterogeneous networks, the relevance measure on objects with different types becomes increasingly important. In this paper, we study the relevance search problem in heterogeneous networks, where the task is to measure the relatedness of heterogeneous objects (including objects with the same type or different types). A novel measure HeteSim is proposed, which has the following attributes: (1) a uniform measure: it can measure the relatedness of objects with the same or different types in a uniform framework; (2) a path-constrained measure: the relatedness of object pairs are defined based on the search path that connect two objects through following a sequence of node types; (3) a semi-metric measure: HeteSim has some good properties (e.g., self-maximum and symmetric), that are crucial to many data mining tasks. Moreover, we analyze the computation characteristics of HeteSim and propose the corresponding quick computation strategies. Empirical studies show that HeteSim can effectively and efficiently evaluate the relatedness of heterogeneous objects.

Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently, it has been introduced into evolutionary game theory. In evolutionary game dynamics, the probability to be imitated or to reproduce depends on the performance in a game. The influence of the game on the stochastic dynamics in finite populations is governed by the intensity of selection. In many models of both unstructured and structured populations, a key assumption allowing analytical calculations is weak selection, which means that all individuals perform approximately equally well. In the weak selection limit many different microscopic evolutionary models have the same or similar properties. How universal is weak selection for those microscopic evolutionary processes? We answer this question by investigating the fixation probability and the average fixation time not only up to linear but also up to higher orders in selection intensity. We find universal higher order expansions, which allow a rescaling of the selection intensity. With this, we can identify specific models which violate ͑linear͒ weak selection results, such as the one-third rule of coordination games in finite but large populations.

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