Competitive dynamics of lexical innovations in multi-layer networks

We study the introduction of lexical innovations into a community of language users. Lexical innovations, i.e., new terms added to people's vocabulary, play an important role in the process of language evolution. Nowadays, information is spread through a variety of networks, including, among others, online and offline social networks and the World Wide Web. The entire system, comprising networks of different nature, can be represented as a multi-layer network. In this context, lexical innovations diffusion occurs in a peculiar fashion. In particular, a lexical innovation can undergo three different processes: its original meaning is accepted; its meaning can be changed or misunderstood (e.g., when not properly explained), hence more than one meaning can emerge in the population; lastly, in the case of a loan word, it can be translated into the population language (i.e., defining a new lexical innovation or using a synonym) or into a dialect spoken by part of the population. Therefore, lexical innovations cannot be considered simply as information. We develop a model for analyzing this scenario using a multi-layer network comprising a social network and a media network. The latter represents the set of all information systems of a society, e.g., television, the World Wide Web and radio. Furthermore, we identify temporal directed edges between the nodes of these two networks. In particular, at each time step, nodes of the media network can be connected to randomly chosen nodes of the social network and vice versa. In so doing, information spreads through the whole system and people can share a lexical innovation with their neighbors or, in the event they work as reporters, by using media nodes. Lastly, we use the concept of "linguistic sign" to model lexical innovations, showing its fundamental role in the study of these dynamics. Many numerical simulations have been performed.Comment: 23 pages, 19 figures, 1 tabl

Is Poker a Skill Game? New Insights from Statistical Physics

During last years poker has gained a lot of prestige in several countries and, beyond to be one of the most famous card games, it represents a modern challenge for scientists belonging to different communities, spanning from artificial intelligence to physics and from psychology to mathematics. Unlike games like chess, the task of classifying the nature of poker (i.e., as 'skill game' or gambling) seems really hard and it also constitutes a current problem, whose solution has several implications. In general, gambling offers equal winning probabilities both to rational players (i.e., those that use a strategy) and to irrational ones (i.e., those without a strategy). Therefore, in order to uncover the nature of poker, a viable way is comparing performances of rational versus irrational players during a series of challenges. Recently, a work on this topic revealed that rationality is a fundamental ingredient to succeed in poker tournaments. In this study we analyze a simple model of poker challenges by a statistical physics approach, with the aim to uncover the nature of this game. As main result we found that, under particular conditions, few irrational players can turn poker into gambling. Therefore, although rationality is a key ingredient to succeed in poker, also the format of challenges has an important role in these dynamics, as it can strongly influence the underlying nature of the game. The importance of our results lies on related implications, as for instance in identifying the limits poker can be considered as a `skill game' and, as a consequence, which kind of format must be chosen to devise algorithms able to face humans.Comment: 12 pages, 4 figure

Statistical Physics of the Spatial Prisoner's Dilemma with Memory-Aware Agents

We introduce an analytical model to study the evolution towards equilibrium in spatial games, with `memory-aware' agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner's Dilemma, as it constitutes an emblematic example of a game whose Nash equilibrium is defection. Previous investigations showed that, under opportune conditions, it is possible to reach, in the evolutionary Prisoner's Dilemma, an equilibrium of cooperation. Notably, it seems that mechanisms like motion may lead a population to become cooperative. In the proposed model, we map agents to particles of a gas so that, on varying the system temperature, they randomly move. In doing so, we are able to identify a relation between the temperature and the final equilibrium of the population, explaining how it is possible to break the classical Nash equilibrium in the spatial Prisoner's Dilemma when considering agents able to increase their payoff over time. Moreover, we introduce a formalism to study order-disorder phase transitions in these dynamics. As result, we highlight that the proposed model allows to explain analytically how a population, whose interactions are based on the Prisoner's Dilemma, can reach an equilibrium far from the expected one; opening also the way to define a direct link between evolutionary game theory and statistical physics.Comment: 7 pages, 5 figures. Accepted for publication in EPJ-

Fermionic Networks: Modeling Adaptive Complex Networks with Fermionic Gases

We study the structure of Fermionic networks, i.e., a model of networks based on the behavior of fermionic gases, and we analyze dynamical processes over them. In this model, particle dynamics have been mapped to the domain of networks, hence a parameter representing the temperature controls the evolution of the system. In doing so, it is possible to generate adaptive networks, i.e., networks whose structure varies over time. As shown in previous works, networks generated by quantum statistics can undergo critical phenomena as phase transitions and, moreover, they can be considered as thermodynamic systems. In this study, we analyze Fermionic networks and opinion dynamics processes over them, framing this network model as a computational model useful to represent complex and adaptive systems. Results highlight that a strong relation holds between the gas temperature and the structure of the achieved networks. Notably, both the degree distribution and the assortativity vary as the temperature varies, hence we can state that fermionic networks behave as adaptive networks. On the other hand, it is worth to highlight that we did not find relation between outcomes of opinion dynamics processes and the gas temperature. Therefore, although the latter plays a fundamental role in gas dynamics, on the network domain its importance is related only to structural properties of fermionic networks.Comment: 19 pages, 5 figure

Gaussian Networks Generated by Random Walks

We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to perform community detection, exploration tasks and to study temporal networks. Moreover, they have been used also to generate scale-free networks. In this work, we define a random walker that plays the role of "edges-generator". In particular, the random walker generates new connections and uses these ones to visit each node of a network. As result, the proposed model allows to achieve networks provided with a Gaussian degree distribution, and moreover, some features as the clustering coefficient and the assortativity show a critical behavior. Finally, we performed numerical simulations to study the behavior and the properties of the cited model.Comment: 12 pages, 6 figure

Poker Cash Game: a Thermodynamic Description

Poker is one of the most popular card games, whose rational investigation represents also one of the major challenges in several scientific areas, spanning from information theory and artificial intelligence to game theory and statistical physics. In principle, several variants of Poker can be identified, although all of them make use of money to make the challenge meaningful and, moreover, can be played in two different formats: tournament and cash game. An important issue when dealing with Poker is its classification, i.e., as a `skill game' or as gambling. Nowadays, its classification still represents an open question, having a long list of implications (e.g., legal and healthcare) that vary from country to country. In this study, we analyze Poker challenges, considering the cash game format, in terms of thermodynamics systems. Notably, we propose a framework to represent a cash game Poker challenge that, although based on a simplified scenario, allows both to obtain useful information for rounders (i.e., Poker players), and to evaluate the role of Poker room in this context. Finally, starting from a model based on thermodynamics, we show the evolution of a Poker challenge, making a direct connection with the probability theory underlying its dynamics and finding that, even if we consider these games as `skill games', to take a real profit from Poker is really hard.Comment: 9 pages, 1 figure. Contribute to the proceedings "Mathematical Physics: from Theory to Applications" (European Physics Press

Poker as a Skill Game: Rational vs Irrational Behaviors

In many countries poker is one of the most popular card games. Although each variant of poker has its own rules, all involve the use of money to make the challenge meaningful. Nowadays, in the collective consciousness, some variants of poker are referred to as games of skill, others as gambling. A poker table can be viewed as a psychology lab, where human behavior can be observed and quantified. This work provides a preliminary analysis of the role of rationality in poker games, using a stylized version of Texas Hold'em. In particular, we compare the performance of two different kinds of players, i.e., rational vs irrational players, during a poker tournament. Results show that these behaviors (i.e., rationality and irrationality) affect both the outcomes of challenges and the way poker should be classified.Comment: 15 pages, 5 figure

An Evolutionary Strategy based on Partial Imitation for Solving Optimization Problems

In this work we introduce an evolutionary strategy to solve combinatorial optimization tasks, i.e. problems characterized by a discrete search space. In particular, we focus on the Traveling Salesman Problem (TSP), i.e. a famous problem whose search space grows exponentially, increasing the number of cities, up to becoming NP-hard. The solutions of the TSP can be codified by arrays of cities, and can be evaluated by fitness, computed according to a cost function (e.g. the length of a path). Our method is based on the evolution of an agent population by means of an imitative mechanism, we define `partial imitation'. In particular, agents receive a random solution and then, interacting among themselves, may imitate the solutions of agents with a higher fitness. Since the imitation mechanism is only partial, agents copy only one entry (randomly chosen) of another array (i.e. solution). In doing so, the population converges towards a shared solution, behaving like a spin system undergoing a cooling process, i.e. driven towards an ordered phase. We highlight that the adopted `partial imitation' mechanism allows the population to generate solutions over time, before reaching the final equilibrium. Results of numerical simulations show that our method is able to find, in a finite time, both optimal and suboptimal solutions, depending on the size of the considered search space.Comment: 18 pages, 6 figure

Social Influences in Opinion Dynamics: the Role of Conformity

We study the effects of social influences in opinion dynamics. In particular, we define a simple model, based on the majority rule voting, in order to consider the role of conformity. Conformity is a central issue in social psychology as it represents one of people's behaviors that emerges as a result of their interactions. The proposed model represents agents, arranged in a network and provided with an individual behavior, that change opinion in function of those of their neighbors. In particular, agents can behave as conformists or as nonconformists. In the former case, agents change opinion in accordance with the majority of their social circle (i.e., their neighbors); in the latter case, they do the opposite, i.e., they take the minority opinion. Moreover, we investigate the nonconformity both on a global and on a local perspective, i.e., in relation to the whole population and to the social circle of each nonconformist agent, respectively. We perform a computational study of the proposed model, with the aim to observe if and how the conformity affects the related outcomes. Moreover, we want to investigate whether it is possible to achieve some kind of equilibrium, or of order, during the evolution of the system. Results highlight that the amount of nonconformist agents in the population plays a central role in these dynamics. In particular, conformist agents play the role of stabilizers in fully-connected networks, whereas the opposite happens in complex networks. Furthermore, by analyzing complex topologies of the agent network, we found that in the presence of radical nonconformist agents the topology of the system has a prominent role; otherwise it does not matter since we observed that a conformist behavior is almost always more convenient. Finally, we analyze the results of the model by considering that agents can change also their behavior over time.Comment: 22 pages, 12 figures, appears in Physica A: Statistical Mechanics and its Applications (volume 414) 201