Multiplex Modeling of the Society

Kertesz, J., Torok, J., Murase, Y., Jo, H. H., & Kaski, K. (2016). Multiplex Modeling of the Society. arXiv preprint arXiv:1609.08381v1


The society has a multi-layered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when merging such WSN models, a sufficient amount of inter-layer correlation is needed to maintain the relationship between topology and link weights, while these correlations destroy the enhancement in the community overlap due to multiple layers. To resolve this, we devise a geographic multi-layer WSN model, where the indirect inter-layer correlations due to the geographic constraints of individuals enhance the overlaps between the communities and, at the same time, the Granovetterian structure is preserved. Furthermore, the network of social interactions can be considered as a multiplex from another point of view too: each layer corresponds to one communication channel and the aggregate of all them constitutes the entire social network. However, usually one has information only about one of the channels, which should be considered as a sample of the whole. Here we show by simulations and analytical methods that this sampling may lead to bias. For example, while it is expected that the degree distribution of the whole social network has a maximum at a value larger than one, we get with reasonable assumptions about the sampling process a monotonously decreasing distribution as observed in empirical studies of single channel data. We analyse the far-reaching consequences of our findings.

Evolution of Cooperation Under Social Pressure in Multiplex Networks

Pereda, M. (2016). Evolution of cooperation under social pressure in multiplex networks. Physical Review E, 94(3), 032314. DOI:


In this work, we aim to contribute to the understanding of human prosocial behavior by studying the influence that a particular form of social pressure, “being watched,” has on the evolution of cooperative behavior. We study how cooperation emerges in multiplex complex topologies by analyzing a particular bidirectionally coupled dynamics on top of a two-layer multiplex network (duplex). The coupled dynamics appears between the prisoner’s dilemma game in a network and a threshold cascade model in the other. The threshold model is intended to abstract the behavior of a network of vigilant nodes that impose the pressure of being observed altering hence the temptation to defect of the dilemma. Cooperation or defection in the game also affects the state of a node of being vigilant. We analyze these processes on different duplex networks structures and assess the influence of the topology, average degree and correlated multiplexity, on the outcome of cooperation. Interestingly, we find that the social pressure of vigilance may impact cooperation positively or negatively, depending on the duplex structure, specifically the degree correlations between layers is determinant. Our results give further quantitative insights in the promotion of cooperation under social pressure.

Hierarchy is Detrimental for Human Cooperation

Cronin, K. A., Acheson, D. J., Hernández, P., & Sánchez, A. (2015). Hierarchy is Detrimental for Human Cooperation. Scientific reports, 5, 18634. DOI: 10.1038/srep18634


Studies of animal behavior consistently demonstrate that the social environment impacts cooperation, yet the effect of social dynamics has been largely excluded from studies of human cooperation. Here, we introduce a novel approach inspired by nonhuman primate research to address how social hierarchies impact human cooperation. Participants competed to earn hierarchy positions and then could cooperate with another individual in the hierarchy by investing in a common effort. Cooperation was achieved if the combined investments exceeded a threshold, and the higher ranked individual distributed the spoils unless control was contested by the partner. Compared to a condition lacking hierarchy, cooperation declined in the presence of a hierarchy due to a decrease in investment by lower ranked individuals. Furthermore, hierarchy was detrimental to cooperation regardless of whether it was earned or arbitrary. These findings mirror results from nonhuman primates and demonstrate that hierarchies are detrimental to cooperation. However, these results deviate from nonhuman primate findings by demonstrating that human behavior is responsive to changing hierarchical structures and suggests partnership dynamics that may improve cooperation. This work introduces a controlled way to investigate the social influences on human behavior, and demonstrates the evolutionary continuity of human behavior with other primate species.

Cooperation Survives and Cheating Pays in a Dynamic Network Structure with Unreliable Reputation

Antonioni, A., Sánchez, A., & Tomassini, M. (2016). Cooperation Survives and Cheating Pays in a Dynamic Network Structure with Unreliable Reputation. Scientific reports, 6, 27160. DOI:10.1038/srep27160


In a networked society like ours, reputation is an indispensable tool to guide decisions about social or economic interactions with individuals otherwise unknown. Usually, information about prospective counterparts is incomplete, often being limited to an average success rate. Uncertainty on reputation is further increased by fraud, which is increasingly becoming a cause of concern. To address these issues, we have designed an experiment based on the Prisoner’s Dilemma as a model for social interactions. Participants could spend money to have their observable cooperativeness increased. We find that the aggregate cooperation level is practically unchanged, i.e., global behavior does not seem to be affected by unreliable reputations. However, at the individual level we find two distinct types of behavior, one of reliable subjects and one of cheaters, where the latter artificially fake their reputation in almost every interaction. Cheaters end up being better off than honest individuals, who not only keep their true reputation but are also more cooperative. In practice, this results in honest subjects paying the costs of fraud as cheaters earn the same as in a truthful environment. These findings point to the importance of ensuring the truthfulness of reputation for a more equitable and fair society.

Emotions and Strategic Behaviour: The Case of the Ultimatum Game

Tamarit, I., & Sánchez, A. (2016). Emotions and strategic behaviour: The case of the ultimatum game. PloS one, 11(7), e0158733.


Human behaviour in economic interactions has attracted an increasing amount of attention over the last decades. The economic assumption that people would behave focusing on their own material self-interest was proved incomplete, once the empirical evidence consistently showed that many other motives may influence such behaviour. Therefore, models that can incorporate rational decision process as well as other intervening factors are a key issue to both understand the observations from economic experiments and to apply the lessons learned from them. In this paper, we incorporate the influence of emotions to the utility function in an explicit manner, using the Ultimatum Game as a case study. Our model is amenable to analytical study, and is connected with the Circumplex model of emotions and with Kahneman’s two-system theory. The simplicity of the model allows to obtain predictions for the offers and acceptance thresholds. We study two specific examples, when the model parameters are distributed uniformly or normally, and show that in the latter case the results are already qualitatively correct. Although this work can be considered as a first approach, it includes what we believe are the main stylized facts, is able to qualitatively reproduce experimental results in a very simple manner, and can be straightforwardly extended to other games.

Conflict and Segregation in Networks: An Experiment on the Interplay Between Individual Preferences and Social Influence

Ellwardt, L., Hernández, P., Martínez-Canovas, G., & Muñoz-Herrera, M. (2014). Conflict and segregation in networks: An experiment on the interplay between individual preferences and social influence (No. 0114). University of Valencia, ERI-CES. DOI:10.3934/jdg.2016010


We examine the interplay between a person’s individual preference and the social influence others exert. We provide a model of network relationships with conflicting preferences, where individuals are better off coordinating with those around them, but where not all have a preference for the same action. We test our model in an experiment, varying the level of conflicting preferences between individuals. Our findings suggest that preferences are more salient than social influence, under conflicting preferences: subjects relate mainly with others who have the same preferences. This leads to two undesirable outcomes: network segregation and social inefficiency. The same force that helps people individually, hurts society.

The Complexity of Interacting Automata

Gossner, O., Hernández, P., & Peretz, R. (2016). The complexity of interacting automata. International Journal of Game Theory, 45(1-2), 461-496.DOI: 10.1007/s00182-015-0521-7


This paper studies the interaction of automata of size m. We characterise statistical properties satisfied by random plays generated by a correlated pair of automata with m states each. We show that in some respect the pair of automata can be identified with a more complex automaton of size comparable to mlogm. We investigate implications of these results on the correlated min–max value of repeated games played by automata.

Bounded Computational Capacity Equilibrium

Solan, E., & Hernandez, P. (2014). Bounded Computational Capacity Equilibrium (No. 0314). University of Valencia, ERI-CES.


A celebrated result of Abreu and Rubinstein states that in repeated games, when the players are restricted to playing strategies that can be implemented by finite automata and they have lexicographic preferences, the set of equilibrium payoffs is a strict subset of the set of feasible and individually rational payoffs. In this paper we explore the limitations of this result. We prove that if memory size is costly and players can use mixed automata, then a folk theorem obtains and the set of equilibrium payo is once again the set of feasible and individually rational payoffs. Our result emphasizes the role of memory cost and of mixing when players have bounded computational power.

A Formal Model Based on Game Theory for the Analysis of Cooperation in Distributed Service Discovery

Martínez-Cánovas, G., Del Val, E., Botti, V., Hernández, P., & Rebollo, M. (2016). A formal model based on Game Theory for the analysis of cooperation in distributed service discovery. Information Sciences, 326, 59-70.


New systems can be designed, developed, and managed as societies of agents that interact with each other by offering and providing services. These systems can be viewed as complex networks where nodes are bounded rational agents. In order to deal with complex goals, they require cooperation of the other agents to be able to locate the required services. The aim of this paper is formally and empirically analyze under which circumstances cooperation emerges in decentralized search of services. We propose a repeated game model that formalizes the interactions among agents in a search process where agents are free to choose between cooperate or not in the process. Agents make decisions based on the cost of their actions and the expected reward if they participate forwarding queries in a search process that ends successfully. We propose a strategy that is based on random-walks, and we study under what conditions the strategy is a Nash equilibrium. We performed several experiments in order to evaluate the model and the strategy and to analyze which network structures are more appropriate to promote cooperation.

Strategic Behaviour in Schelling Dynamics: Theory and Experimental Evidence

Benito-Ostolaza, J. M., Brañas-Garza, P., Hernández, P., & Sanchis-Llopis, J. A. (2015). Strategic behaviour in Schelling dynamics: Theory and experimental evidence. Journal of Behavioral and Experimental Economics, 57, 134-147.


In this paper we experimentally test Schelling’s (1971) segregation model and confirm the striking result of segregation. In addition, we extend Schelling’s model theoretically by adding strategic behaviour and moving costs. We obtain a unique subgame perfect equilibrium in which rational agents facing moving costs may find it optimal not to move (anticipating other participants’ movements). This equilibrium is far from full segregation. We run experiments for this extended Schelling model, and find that the percentage of full segregated societies notably decreases with the cost of moving and that the degree of segregation depends on the distribution of strategic subjects.

Bubble Formation and (In)Efficient Markets in Learning-to-Forecast and-optimise Experiments

Bao, T., Hommes, C. H., & Makarewicz, T. (2015). Bubble formation and (in) efficient markets in learning-to-forecast and-optimise experiments. Economic Journal, Forthcoming, 15-107.


This experiment compares the price dynamics and bubble formation in an asset market with a price adjustment rule in three treatments where subjects (1) submit a price forecast only, (2) choose quantity to buy/sell and (3) perform both tasks. We find deviation of the market price from the fundamental price in all treatments, but to a larger degree in treatments (2) and (3). Mispricing is therefore a robust finding in markets with positive expectation feedback. Some very large, recurring bubbles arise, where the price is 3 times larger than the fundamental value, which were not seen in former experiments.

Dynamics of Deceptive Interactions in Social Networks

Barrio, R. A., Govezensky, T., Dunbar, R., Iñiguez, G., & Kaski, K. (2015). Dynamics of deceptive interactions in social networks. Journal of The Royal Society Interface, 12(112), 20150798. DOI: 10.1098/rsif.2015.0798


In this paper, we examine the role of lies in human social relations by implementing some salient characteristics of deceptive interactions into an opinion formation model, so as to describe the dynamical behaviour of a social network more realistically. In this model, we take into account such basic properties of social networks as the dynamics of the intensity of interactions, the influence of public opinion and the fact that in every human interaction it might be convenient to deceive or withhold information depending on the instantaneous situation of each individual in the network. We find that lies shape the topology of social networks, especially the formation of tightly linked, small communities with loose connections between them. We also find that agents with a larger proportion of deceptive interactions are the ones that connect communities of different opinion, and, in this sense, they have substantial centrality in the network. We then discuss the consequences of these results for the social behaviour of humans and predict the changes that could arise due to a varying tolerance for lies in society.

Reputation Drives Cooperative Behaviour and Network Formation in Human Groups

Cuesta, J. A., Gracia-Lázaro, C., Ferrer, A., Moreno, Y., & Sánchez, A. (2015). Reputation drives cooperative behaviour and network formation in human groups. Scientific reports, 5. doi:10.1038/srep07843


Cooperativeness is a defining feature of human nature. Theoreticians have suggested several mechanisms to explain this ubiquitous phenomenon, including reciprocity, reputation, and punishment, but the problem is still unsolved. Here we show, through experiments conducted with groups of people playing an iterated Prisoner’s Dilemma on a dynamic network, that it is reputation what really fosters cooperation. While this mechanism has already been observed in unstructured populations, we find that it acts equally when interactions are given by a network that players can reconfigure dynamically. Furthermore, our observations reveal that memory also drives the network formation process, and cooperators assort more, with longer link lifetimes, the longer the past actions record. Our analysis demonstrates, for the first time, that reputation can be very well quantified as a weighted mean of the fractions of past cooperative acts and the last action performed. This finding has potential applications in collaborative systems and e-commerce.

Equilibrium Characterization of Networks under Conflicting Preferences

Hernández, P., Martínez-Cánovas, G., Muñoz-Herrera, M., & Sánchez, A. (2016). Equilibrium characterization of networks under conflicting preferences. Economics Letters.


In this work we characterize equilibrium introduced in configurations for networks with conflicting preferences. We use the model Hernández et al. (2013) to study the effect of three main factors: the strength of individual preferences, the level of integration in the network, and the intensity of conflict in the population. Our aim is to understand how likely is it that social outcomes are either those in which preferences dominate choices or those in which some individuals sacrifice their preferences to achieve consensus with others. Our results show that, the stronger individual preferences, the harder to achieve consensus in choices. However, in cases where the payoff ratio is less extreme, full coordination (consensus) is always an equilibrium. Finally, if the level of conflict is low, individual preferences become less relevant and all players choosing what they prefer is not an equilibrium anymore.

Humans Expect Generosity

Brañas-Garza, P., Rodriguez-Lara, I., & Sanchez, A. (2016). Humans expect generosity.


Mechanisms supporting human ultra-cooperativeness are very much subject to debate. One psychological feature likely to be relevant is the formation of expectations, particularly about receiving cooperative or generous behavior from others. Without such expectations, social life will be seriously impeded and, in turn, expectations leading to satisfactory interactions can become norms and institutionalize cooperation. In this paper, we assess people’s expectations of generosity in a series of controlled experiments using the dictator game. Despite differences in respective roles, involvement in the game, degree of social distance or variation of stakes, the results are conclusive: subjects seldom predict that dictators will behave selfishly (by choosing the Nash equilibrium action, namely giving nothing). The majority of subjects expect that dictators will choose the equal split. This implies that generous behavior is not only observed in the lab, but also expected by subjects. In addition, expectations are accurate, matching closely the donations observed and showing that as a society we have a good grasp of how we interact. Finally, correlation between expectations and actual behavior suggests that expectations can be an important ingredient of generous or cooperative behavior.