- Email: [email protected]
Call for papers: Special issue on evolutionary game theory of small groups and their larger societies
Chaos, Solitons and Fractals 103 (2017) 371–373
Contents lists available at ScienceDirect
Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos
Call for papers: Special issue on evolutionary game theory of small groups and their larger societies Paolo Grigolini Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427
a r t i c l e
i n f o
a b s t r a c t
Article history: Available online xxx
This is a call for papers that should contribute to the unification of behavioral sciences and team management, focusing on the biological origin of cooperation and swarm intelligence, moving from biology to psychology and from sociology to political science, with the help of the theoretical tools of complex networks. This issue should shed light into the origin of ergodicity breaking and contribute to establishing a connection, still lacking theoretical support, between complexity properties that are expected to be correlated. Examples are: non-Poisson renewal events and multi-fractality; complexity matching and chaos synchronization; criticality and extended criticality of small size systems. Although the emphasis is on systems of small size, and especially on the search of the size maximizing both information transport and cooperation emergence, special attention will be devoted to the interaction between small groups and their larger societies. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction
physics, is now successfully studied using the tool of game theory [9] and this surprising success suggests, on the other side, that the emergence of cooperation, which can be mistakenly related to the beginning of civilization, has a much earlier origin, coinciding with the origin itself of life. Cooperation implies interaction between units, thereby raising the important question of the optimal size of generating cooperation groups, with the surprising discovering that the small size of these groups may favor the emergence of cooperation [10].
The unification of behavioral sciences is one of the most challenging cultural issues of our times [1]. It is harder than the unification of chemistry and physics that yet, in spite of a widespread belief on the contrary, is not satisfactorily realized [2]. As pointed out in Ref. [3], biological processes are non-ergodic and ergodicity breaking, currently observed and deeply studied [4], is at variance with the ergodic assumption adopted for the foundation of statistical physics [5]. The evolution of cooperation resting on the Prisoner’s Dilemma game applied to elementary biological organisms such as bacteria [6] shows that sociological concepts can be surprisingly applied with success to overcome the difficulty for theory of evolution since Darwin. As we move from biology to neurophysiology and to psychology we meet another difficult problem, that of explaining the emergence of cognition, which is usually approached using either the concept of machine learning [7] or of swarm intelligence [8]. The main purpose of this special issue is to give suggestions that may help the ambitious project of unification of behavioral sciences, from physics to anthropology, as outlined in the following sections. 2. Biology and game theory Enzyme chemistry, which has been for many years a stimulus to do research work along the lines of non-equilibrium statistical E-mail address: [email protected] http://dx.doi.org/10.1016/j.chaos.2017.06.020 0960-0779/© 2017 Elsevier Ltd. All rights reserved.
3. Decision making in finite-size systems A decision-making system at criticality is characterized by a strong sensitivity to external stimuli and the exchange of information between two complex networks reaches the maximal efficiency when both networks are at criticality. There exists a dependence on the group size indicating that temporal complexity, namely the intensity of correlated fluctuations responsible for the transformation transport, increases with decreasing the group’s size [11]. However, when the size of the group is very small, temporal complexity is strongly reduced, thereby leading us to the conjecture that an optimal intermediate size exists, in what would be a surprising and encouraging agreement with the tenets of evolutionary biology. Temporal complexity is generated by the criticality of small systems and this form of criticality, characterized by the lack of the singularities of ordinary phase transition occurring in the thermodynamic limit, should be more properly referred to as extended criticality. This would be equivalent to
372
P. Grigolini / Chaos, Solitons and Fractals 103 (2017) 371–373
stressing the importance of the viewpoint of Longo and Montévil [12] under the key condition of network small size. 4. Complexity matching Recent experimental results concerning the influence of a multifractal metronome on the brain [13] and the exchange of information between two interlocutors [14] lead us to search for a theoretical approach to the transmission of information from a driving complex network to a driven complex network so as to set on a solid scientific basis the attempt at unraveling the power of imitation, enhanced by charisma, in the face-to-face social networks [15]. The heuristic arguments adopted in Ref. [16] for the foundation of complexity matching rest on the crucial action of non-Poisson renewal events and extended criticality [11] is the source of renewal events, thereby making it natural the search for a deep connection between multi-fractality and criticality-induced renewal events. Are criticality-induced renewal events connected to the relational events adopted to analyze group interaction processes [17]? Self-organized criticality, on the other hand, may be a natural form of extended criticality, a peculiar property of small groups that is expected to help finding procedures to resolve psychological conflicts in small groups so as to prevent a bad apple from spoiling the bunch [18]. 5. Management of small teams The last few years have seen a revival of interest for the management of small groups [19] and the study of their dynamics seems to get new opportunities by the availability of big data [20]. Contrary to the conjecture that the data deluge may make the end of theory, the authors of [21] argue that the availability of big data will speed up the progress of the theory of teams, insofar as it gives incentive to address and solve the issue of \ why, when, how, and to what end individuals form relationships needed for teams to function in unison toward the accomplishment of collective goals". Does swarm intelligence [22] afford a proper way to interpret big data? The authors of Ref. [23] showed that under certain conditions the users of coarse-grained information may successfully compete with agents having access to more and better data [23]. Haimovici and Marsili [24] argued that relevance has a non-monotonic dependence on resolution, implying criticality of most informative samples. This interesting observation generates the important question of how to interpret big data, and the results of this discussion are expected to contribute significant advances to machine learning and swarm intelligence. 6. Small groups and their larger societies During the past 40 years, an extensive literature has been developed in the understanding of small group actions, organization and development. Much has been learned about recruitment, organization, leadership, and specialization of function in small groups. This has had considerable application in business organizations and management as well as in the study of productivity, employee motivation and occupational stress. However, there has been comparatively little research on the application of small group approaches to modern military activity and social conflict (e.g., Oxford Textbook of Military Psychology). In the 21st century, nevertheless, the knowledge of small group behaviour has become crucial to an understanding of cyberspace and battlefield warfare and, especially, terrorism. However, understanding the small group contributions to modern physical and cyberwarfare is only the first step, and concerns tactical objectives. Strategic and policy objectives of these small
group activities involve other disciplines than small group psychology [25]. The strategic and policy questions concern why those small groups exist in the first place, in specific areas, and what is their long-term threat and potential harm to society, the economy, and loss of life. To deal with these larger, and more encompassing, problems, we need to understand the contexts in which these small groups (and their larger networks) are embedded. In the specific case of the war against terrorism [26,27] the adoption of the tools of anthropology [28] may lead to shed light into the unpredictability of ISIS-induced terrorist attacks. 7. Science and human behavior The title of this section is borrowed from the book of Ref. [29], an important contribution to the foundation of behavioral science, emphasizing the dependence of the behavior of an individual on the culture of his/her society. The observation that “… the conception of the individual which emerges from a scientific analysis is distasteful to most of those who have been strongly affected by democratic philosophies" may be properly rephrased if the biological origin of cooperation is taken into account. The controlling agencies, government, religion, psychotherapy, economic control, education, act on individuals biologically predisposed to cooperation. This editorial has the purpose of attracting contributions that may help the unification project outlined in the earlier sections through the connection with the theory of phase transitions that it is not yet properly taken into account in the literature of evolutionary game theory and behavioral science. There are signs of interest in this direction, as proved, for instance, by the interesting paper of Ref. [30] suggesting that the behavioral concepts of reinforcement and aversion may be the key ingredients for a pitchfork bifurcation that should be extended to the small group size condition. Supplementing evolutionary game theory with criticality [31] is expected to facilitate the exploration of the complex path from the dynamics of bacteria to that of human societies reinforcing at the same time the conviction that criticality plays a central role [32] for the emergence of cognition [1] as well as for biology in general. Acknowledgment The author warmly thanks ARO and Welch for support through Grant No. W911NF-15-1-0245 and No. B-1577, respectively. A special thank is due to ARO for support of the Denton Workshop through grant W911NF-16-1-0461. References [1] Grigolini P, Piccinini N, Svenkeson A, Pramukkul P, Lambert D, West BJ. From neural and social cooperation to the global emergence of cognition. Front Bioeng Biotechnol 2015;3(78):1. [2] Primas H. Chemistry, quantum mechanics and reductionism: perspectives in theoretical chemistry. Berlin: Springer; 1983. [3] Grigolini P. Emergence of biological complexity: Criticality, renewal and memory. Chaos Solitons Fract 2015;81:575. [4] Metzler R, Jeon J-H, Cherstvya AG, Barkai E. Anomalous diffusion models and their properties: and non-stationarity, non-ergodicity, ageing at the centenary of single particle tracking. Phys Chem Chem Phys 2014;16:24128. [5] Lebowitz JL, Penrose O. Modern ergodic theory. Phys Today 1973;26:23. [6] Axelrod R, Hamilton WD. The evolution of cooperation. Science 1981;211:1390. [7] Smola A, Vishwanathan SVN. Introduction to machine learning. Cambridge University Press; 2008. [8] Bonabeau E, Dorigo M, Theraulaz G. Swarm intelligence: from natural to artificial system. New York: Oxford University Press; 1999. [9] Archetti M, Scheuring I. Evolution of optimal Hill coeffcients in nonlinear public goods games. J Theor Biol 2016;406:73. [10] Stewart A, Plotkin JB. Small groups and long memories promote cooperation. Scientific Report; June 2016. [11] Beig MT, Svenkeson A, Bologna M, West BJ, Grigolini P. Critical slowing down in networks generating temporal complexity. Phys Rev E 2015;91:012907. [12] Longo G, Montévil M. Extended criticality, phase spaces and enablement in biology. Chaos Solitons Fract 2013;55:64.
P. Grigolini / Chaos, Solitons and Fractals 103 (2017) 371–373 [13] Stephen DG, Dixon JA. Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors,. Chaos Solitons Fract 2011;44:160–8. [14] Abney DH, Paxton A, Dale R, Kello CT. Complexity matching in dyadic conversation. J Exp Psychol 2014;143:2304. [15] Pentland A. To signal is human. Am Sci 2010;98:204. [16] West BJ, Geneston EL, Grigolini P. Maximizing information exchange between complex networks. Phys Rep 2008;468:1. [17] Pilny A, Schecter A, Poole MS, Contractor N. An illustration of the relational event model to analyze group interaction processes. Group Dyn 2016;20:181. [18] Pincus D. One bad apple: experimental effects of psychological conict on social resilience. Interf Focus 2014(October). [19] N. Katz, D. Lazer, H. Arrow, N. Contractor, Network theory and small groups, Small Group Res, 35, 307 (2004). [20] C.A. Mattmann, A vision for data science, Nature, 493, 473 (2013). [21] Carter DR, Asencio R, Wax A, DeChurch LA, Contractor NS, Teams Little. Big data: big data provides new opportunities for teams theory. Ind Org Psychol 2015;8:550. [22] Carbone G, Giannoccaro I. Model of human collective decision-making in complex environments. Eur Phys J B 2015;88:339.
373
[23] V. Sasidevan, A. Kushal, S. Sinha, When big data fails! relative success of adaptive agents using coarse-grained information to compete for limited resources, arXiv:1609.08746 [physics.soc-ph](2016). [24] Haimovici A, Marsili M. Criticality of mostly informative samples: a Bayesian model selection approach. J Stat Mech 2015;1 (2015). [25] Brenner MH, Andreeva E, Theorell T, Goldberg M, Westerlund H, Leineweber C, et al. Organizational downsizing and depressive symptoms in the European recession The experience of workers in France, Hungary, Sweden and the United Kingdom; 2014. PLOS ONE, 9, e97063. [26] Eiselt HA, Bhadury J. The use of structures in communication networks to track membership in terrorist groups. J Terror Res 2015;6:1. [27] V.E. Kebs, Unlocking terrorist network, first Monday, 7, 1 April (2002). [28] Atran S, Sheikh H, Gomez A. Devoted actors sacrifice for close comrades and sacred cause. Proc Natl Acad Sci U S A 2014;111:17702. [29] Skinner BF. Science and human behavior. New York: The Free Press; 1953. [30] Hazy JK, Boyatzis RE. Emotional contagion and proto-organizing in human interaction dynamics. Front Psychol 2015;6:806. [31] Mahmoodi K, Grigolini P. Evolutionary game theory and criticality. J Phys A 2017;50:015101. [32] Chialvo D. Criticality and phase transitions in biology. Homunculus 2014(April 26).
Contents lists available at ScienceDirect
Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos
Call for papers: Special issue on evolutionary game theory of small groups and their larger societies Paolo Grigolini Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427
a r t i c l e
i n f o
a b s t r a c t
Article history: Available online xxx
This is a call for papers that should contribute to the unification of behavioral sciences and team management, focusing on the biological origin of cooperation and swarm intelligence, moving from biology to psychology and from sociology to political science, with the help of the theoretical tools of complex networks. This issue should shed light into the origin of ergodicity breaking and contribute to establishing a connection, still lacking theoretical support, between complexity properties that are expected to be correlated. Examples are: non-Poisson renewal events and multi-fractality; complexity matching and chaos synchronization; criticality and extended criticality of small size systems. Although the emphasis is on systems of small size, and especially on the search of the size maximizing both information transport and cooperation emergence, special attention will be devoted to the interaction between small groups and their larger societies. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction
physics, is now successfully studied using the tool of game theory [9] and this surprising success suggests, on the other side, that the emergence of cooperation, which can be mistakenly related to the beginning of civilization, has a much earlier origin, coinciding with the origin itself of life. Cooperation implies interaction between units, thereby raising the important question of the optimal size of generating cooperation groups, with the surprising discovering that the small size of these groups may favor the emergence of cooperation [10].
The unification of behavioral sciences is one of the most challenging cultural issues of our times [1]. It is harder than the unification of chemistry and physics that yet, in spite of a widespread belief on the contrary, is not satisfactorily realized [2]. As pointed out in Ref. [3], biological processes are non-ergodic and ergodicity breaking, currently observed and deeply studied [4], is at variance with the ergodic assumption adopted for the foundation of statistical physics [5]. The evolution of cooperation resting on the Prisoner’s Dilemma game applied to elementary biological organisms such as bacteria [6] shows that sociological concepts can be surprisingly applied with success to overcome the difficulty for theory of evolution since Darwin. As we move from biology to neurophysiology and to psychology we meet another difficult problem, that of explaining the emergence of cognition, which is usually approached using either the concept of machine learning [7] or of swarm intelligence [8]. The main purpose of this special issue is to give suggestions that may help the ambitious project of unification of behavioral sciences, from physics to anthropology, as outlined in the following sections. 2. Biology and game theory Enzyme chemistry, which has been for many years a stimulus to do research work along the lines of non-equilibrium statistical E-mail address: [email protected] http://dx.doi.org/10.1016/j.chaos.2017.06.020 0960-0779/© 2017 Elsevier Ltd. All rights reserved.
3. Decision making in finite-size systems A decision-making system at criticality is characterized by a strong sensitivity to external stimuli and the exchange of information between two complex networks reaches the maximal efficiency when both networks are at criticality. There exists a dependence on the group size indicating that temporal complexity, namely the intensity of correlated fluctuations responsible for the transformation transport, increases with decreasing the group’s size [11]. However, when the size of the group is very small, temporal complexity is strongly reduced, thereby leading us to the conjecture that an optimal intermediate size exists, in what would be a surprising and encouraging agreement with the tenets of evolutionary biology. Temporal complexity is generated by the criticality of small systems and this form of criticality, characterized by the lack of the singularities of ordinary phase transition occurring in the thermodynamic limit, should be more properly referred to as extended criticality. This would be equivalent to
372
P. Grigolini / Chaos, Solitons and Fractals 103 (2017) 371–373
stressing the importance of the viewpoint of Longo and Montévil [12] under the key condition of network small size. 4. Complexity matching Recent experimental results concerning the influence of a multifractal metronome on the brain [13] and the exchange of information between two interlocutors [14] lead us to search for a theoretical approach to the transmission of information from a driving complex network to a driven complex network so as to set on a solid scientific basis the attempt at unraveling the power of imitation, enhanced by charisma, in the face-to-face social networks [15]. The heuristic arguments adopted in Ref. [16] for the foundation of complexity matching rest on the crucial action of non-Poisson renewal events and extended criticality [11] is the source of renewal events, thereby making it natural the search for a deep connection between multi-fractality and criticality-induced renewal events. Are criticality-induced renewal events connected to the relational events adopted to analyze group interaction processes [17]? Self-organized criticality, on the other hand, may be a natural form of extended criticality, a peculiar property of small groups that is expected to help finding procedures to resolve psychological conflicts in small groups so as to prevent a bad apple from spoiling the bunch [18]. 5. Management of small teams The last few years have seen a revival of interest for the management of small groups [19] and the study of their dynamics seems to get new opportunities by the availability of big data [20]. Contrary to the conjecture that the data deluge may make the end of theory, the authors of [21] argue that the availability of big data will speed up the progress of the theory of teams, insofar as it gives incentive to address and solve the issue of \ why, when, how, and to what end individuals form relationships needed for teams to function in unison toward the accomplishment of collective goals". Does swarm intelligence [22] afford a proper way to interpret big data? The authors of Ref. [23] showed that under certain conditions the users of coarse-grained information may successfully compete with agents having access to more and better data [23]. Haimovici and Marsili [24] argued that relevance has a non-monotonic dependence on resolution, implying criticality of most informative samples. This interesting observation generates the important question of how to interpret big data, and the results of this discussion are expected to contribute significant advances to machine learning and swarm intelligence. 6. Small groups and their larger societies During the past 40 years, an extensive literature has been developed in the understanding of small group actions, organization and development. Much has been learned about recruitment, organization, leadership, and specialization of function in small groups. This has had considerable application in business organizations and management as well as in the study of productivity, employee motivation and occupational stress. However, there has been comparatively little research on the application of small group approaches to modern military activity and social conflict (e.g., Oxford Textbook of Military Psychology). In the 21st century, nevertheless, the knowledge of small group behaviour has become crucial to an understanding of cyberspace and battlefield warfare and, especially, terrorism. However, understanding the small group contributions to modern physical and cyberwarfare is only the first step, and concerns tactical objectives. Strategic and policy objectives of these small
group activities involve other disciplines than small group psychology [25]. The strategic and policy questions concern why those small groups exist in the first place, in specific areas, and what is their long-term threat and potential harm to society, the economy, and loss of life. To deal with these larger, and more encompassing, problems, we need to understand the contexts in which these small groups (and their larger networks) are embedded. In the specific case of the war against terrorism [26,27] the adoption of the tools of anthropology [28] may lead to shed light into the unpredictability of ISIS-induced terrorist attacks. 7. Science and human behavior The title of this section is borrowed from the book of Ref. [29], an important contribution to the foundation of behavioral science, emphasizing the dependence of the behavior of an individual on the culture of his/her society. The observation that “… the conception of the individual which emerges from a scientific analysis is distasteful to most of those who have been strongly affected by democratic philosophies" may be properly rephrased if the biological origin of cooperation is taken into account. The controlling agencies, government, religion, psychotherapy, economic control, education, act on individuals biologically predisposed to cooperation. This editorial has the purpose of attracting contributions that may help the unification project outlined in the earlier sections through the connection with the theory of phase transitions that it is not yet properly taken into account in the literature of evolutionary game theory and behavioral science. There are signs of interest in this direction, as proved, for instance, by the interesting paper of Ref. [30] suggesting that the behavioral concepts of reinforcement and aversion may be the key ingredients for a pitchfork bifurcation that should be extended to the small group size condition. Supplementing evolutionary game theory with criticality [31] is expected to facilitate the exploration of the complex path from the dynamics of bacteria to that of human societies reinforcing at the same time the conviction that criticality plays a central role [32] for the emergence of cognition [1] as well as for biology in general. Acknowledgment The author warmly thanks ARO and Welch for support through Grant No. W911NF-15-1-0245 and No. B-1577, respectively. A special thank is due to ARO for support of the Denton Workshop through grant W911NF-16-1-0461. References [1] Grigolini P, Piccinini N, Svenkeson A, Pramukkul P, Lambert D, West BJ. From neural and social cooperation to the global emergence of cognition. Front Bioeng Biotechnol 2015;3(78):1. [2] Primas H. Chemistry, quantum mechanics and reductionism: perspectives in theoretical chemistry. Berlin: Springer; 1983. [3] Grigolini P. Emergence of biological complexity: Criticality, renewal and memory. Chaos Solitons Fract 2015;81:575. [4] Metzler R, Jeon J-H, Cherstvya AG, Barkai E. Anomalous diffusion models and their properties: and non-stationarity, non-ergodicity, ageing at the centenary of single particle tracking. Phys Chem Chem Phys 2014;16:24128. [5] Lebowitz JL, Penrose O. Modern ergodic theory. Phys Today 1973;26:23. [6] Axelrod R, Hamilton WD. The evolution of cooperation. Science 1981;211:1390. [7] Smola A, Vishwanathan SVN. Introduction to machine learning. Cambridge University Press; 2008. [8] Bonabeau E, Dorigo M, Theraulaz G. Swarm intelligence: from natural to artificial system. New York: Oxford University Press; 1999. [9] Archetti M, Scheuring I. Evolution of optimal Hill coeffcients in nonlinear public goods games. J Theor Biol 2016;406:73. [10] Stewart A, Plotkin JB. Small groups and long memories promote cooperation. Scientific Report; June 2016. [11] Beig MT, Svenkeson A, Bologna M, West BJ, Grigolini P. Critical slowing down in networks generating temporal complexity. Phys Rev E 2015;91:012907. [12] Longo G, Montévil M. Extended criticality, phase spaces and enablement in biology. Chaos Solitons Fract 2013;55:64.
P. Grigolini / Chaos, Solitons and Fractals 103 (2017) 371–373 [13] Stephen DG, Dixon JA. Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors,. Chaos Solitons Fract 2011;44:160–8. [14] Abney DH, Paxton A, Dale R, Kello CT. Complexity matching in dyadic conversation. J Exp Psychol 2014;143:2304. [15] Pentland A. To signal is human. Am Sci 2010;98:204. [16] West BJ, Geneston EL, Grigolini P. Maximizing information exchange between complex networks. Phys Rep 2008;468:1. [17] Pilny A, Schecter A, Poole MS, Contractor N. An illustration of the relational event model to analyze group interaction processes. Group Dyn 2016;20:181. [18] Pincus D. One bad apple: experimental effects of psychological conict on social resilience. Interf Focus 2014(October). [19] N. Katz, D. Lazer, H. Arrow, N. Contractor, Network theory and small groups, Small Group Res, 35, 307 (2004). [20] C.A. Mattmann, A vision for data science, Nature, 493, 473 (2013). [21] Carter DR, Asencio R, Wax A, DeChurch LA, Contractor NS, Teams Little. Big data: big data provides new opportunities for teams theory. Ind Org Psychol 2015;8:550. [22] Carbone G, Giannoccaro I. Model of human collective decision-making in complex environments. Eur Phys J B 2015;88:339.
373
[23] V. Sasidevan, A. Kushal, S. Sinha, When big data fails! relative success of adaptive agents using coarse-grained information to compete for limited resources, arXiv:1609.08746 [physics.soc-ph](2016). [24] Haimovici A, Marsili M. Criticality of mostly informative samples: a Bayesian model selection approach. J Stat Mech 2015;1 (2015). [25] Brenner MH, Andreeva E, Theorell T, Goldberg M, Westerlund H, Leineweber C, et al. Organizational downsizing and depressive symptoms in the European recession The experience of workers in France, Hungary, Sweden and the United Kingdom; 2014. PLOS ONE, 9, e97063. [26] Eiselt HA, Bhadury J. The use of structures in communication networks to track membership in terrorist groups. J Terror Res 2015;6:1. [27] V.E. Kebs, Unlocking terrorist network, first Monday, 7, 1 April (2002). [28] Atran S, Sheikh H, Gomez A. Devoted actors sacrifice for close comrades and sacred cause. Proc Natl Acad Sci U S A 2014;111:17702. [29] Skinner BF. Science and human behavior. New York: The Free Press; 1953. [30] Hazy JK, Boyatzis RE. Emotional contagion and proto-organizing in human interaction dynamics. Front Psychol 2015;6:806. [31] Mahmoodi K, Grigolini P. Evolutionary game theory and criticality. J Phys A 2017;50:015101. [32] Chialvo D. Criticality and phase transitions in biology. Homunculus 2014(April 26).