Understanding the game behavior with sentiment and unequal status in cooperation network

Highlights

• Game strategies include the positive and the negative cooperation.

• Unequal status players make asymmetric payoffs.

• The node reputation is calculated by an exponent function on its degree.

• Small nodes are more prone to choose positive cooperation relative to comparable big ones.

• The tacit knowledge encourages small nodes to cooperate with big ones positively.

Abstract

Cooperation network is one of the structural social relationships naturally formed in the evolution of human societies. Previous research has focused on well-mixed structures, and yet most individuals in real interactions have sentiments and unequal status in duration and changing in time. This raises the question of whether cooperation can persist despite different sentiments and unequal status of individuals. In this paper, sentiments are included the positive and the negative, and unequal statues are the small node and the big node based the node degree. We develop a game model to study cooperative behaviors based unequal statuses and sentiments, and experimentally examine the model by digital and real networks. Surprisingly, we find that small nodes are more prone to choose positive cooperation relative to comparable big nodes on the promise of enough profits of the tacit knowledge and the excess return. Our results reveal that the unequal status is the hidden mechanism for cooperative behaviors, and provide a new prospective to investigate the evolution of cooperation in more realistic environments.

Introduction

Cooperative behaviors are widely rooted in many scenarios, such as enterprises, actors, scholars, as well as animals. Scholars cooperate to meet their respective needs based on social contacts, trusts and sharing complementary resources [1], forming cooperation networks in science. The contributions of scientist cooperation are not only the breakthrough in unattainable achievements but also mutual transition and fusion of the knowledge. The social and professional collaborate relationships of scientists were proved to be popular cooperative behaviors [2]. The cooperation game is an effective tool to uncover the cooperative behaviors of individuals. The conditions that the emergence and sustainability of cooperative behaviors can be identified by the generalized classical game models, such as snow-drift game [3], [4], public goods game [5], [6] and prisoner’s dilemma game [7], [8], [9], [10]. All those classical games are the favorite mathematical methods to simulate social dilemma and identify Nash equilibrium.

In many real scenarios, the statuses of players are different and asymmetric in their power, wealth, influence and so on, such as social networks [5], [11] and biological systems [12], [13]. In academic cooperation, scholars’ status are often unequal, some scholars are academic leaders who have honorary titles, enough financial founds and other resources; while other scholars are invoices without financial support nor human resource. Hence, it is reasonable to assume that players have the different abilities or the influences on their neighbors’ evolving traits [14]. High prestige’s players are easy to spread their strategies and influence their neighbors’ strategy choices [15], and the popularity of an individual also affects the cooperation evolution [16]. Players’ connections and their weights can speed up the co-evolving of strategies and the network structure [3], [7], [8], [17].

Influence factors and structures of cooperations are two important aspects for evolutionary games. Influence factors impact on the strategy choice of the player. The effect of variations of cost-to-benefit ratios on evolution of cooperative behaviors was investigated through the novel classical games [3], the three-player game model [18] and three-strategy game model [19]. The continuous supporting policy for cooperators in donation game [20] and the increasing players who considered the affection of strategies and the environment together [21] can improve cooperation level.

The dynamic rewards, such as award factors and penalties aimed at accounting for the benefit including innovators in a group and the cost of unsuccessful insights over time, also influenced the cooperation level in scientific publications [22], [23]. One of the most important structural factors of players is the connection with neighborhood, called the node degree reflecting the number of resources and cooperators. The power of a player measured by its degree is to qualify the games between players [24]. The degrees of knowledge-sharing or knowledge spillover were measured by the networked evolutionary game [25], and represented by knowledge graphs [26]. There are also many other factors affecting the evolution of strategies or partners, such as the history behaviors of individuals [27] and the related memory length [28].

In the process of cooperation, some scholars show positive attitudes, and they pay much resource, costs and energies for cooperation research. While, some scholars agree to cooperate but display negative manners: they do not give enough supports or even provide nothing if the other side do not provide direct profits or maximize their interests. Such opportunistic behaviors of negative players like the free riding in the snow-drift game [3], [4]. Those sentiments were analyzed or detected by semi-supervised learning model [29], and the degree of intensity for sentiments was predicted using stacked ensemble method [30] for big social data. The positive or negative sentiments of scholars might impact the willingness and the process of cooperations. This raises the question of whether cooperation can persist despite different sentiments and unequal status of individuals. However, sentiments of scholars in their cooperation have attracted little attention in previous researches. As a result, cooperation sentiments, individuals status and influence factors including the involved members, the game rules and the social economic environment are worthy to be investigated.

In this paper, we develop a game model to study cooperative behaviors based unequal statuses and sentiments. The equilibrium points and stable points are analyzed by this model. The feasibility and efficiency of the model are shown by numerical simulations and real data analyses. Contributions of this paper include four aspects: the individual status represented by the node degrees is defined as the big node or the small node based the node degree greater than the average degree of network or not; and game strategies are partied into positive or negative based cooperation sentiments; unequal status players with asymmetric payoffs push the game evolving, and small nodes are more prone to choose positive cooperation relative to comparable big nodes on the promise of enough profits of the tacit knowledge and the excess return; the tacit knowledge encourages small nodes to cooperate with big ones positively. Our results provide a new prospective to investigate the evolution of cooperation in more realistic environments.

The rest of this work is arranged as follows: the evolutionary game model including parameters, the model and evaluating indexes is presented in Section 2; in Section 3, a theorem for equilibrium points and the numerical simulations on game model are analyzed; the experiments on real data of General Relativity and Quantum Cosmology (GR-QC) are taken in Section 4. The effects on the evaluating indexes are simulated with GR-QC data; and in the final Section 5, discussion and conclusion are given.