Rewards and penalties are common practical tools that can be used to promote cooperation in social institutions. The evolution of cooperation under reward and punishment incentives in joint enterprises has been formalized and investigated, mostly by using compulsory public good games. Recently, Sasaki et al. (2012, Proc Natl Acad Sci USA 109:1165-1169) considered optional participation as well as institutional incentives and described how the interplay between these mechanisms affects the evolution of cooperation in public good games. Here, we present a full classification of these cases of evolutionary dynamics. Specifically, whenever penalties are large enough to cause the bi-stability of both cooperation and defection in cases in which participation in the public good game is compulsory, these penalties will ultimately result in cooperation if participation in the public good game is optional. The global stability of coercion-based cooperation in this optional case contrasts strikingly with the bi-stability that is observed in the compulsory case We also argue that optional participation is not as effective under rewards as under punishment.
Rewards and penalties are common practical tools that can be used to promote cooperation in social institutions. The evolution of cooperation under reward and punishment incentives in joint enterprises has been formalized and investigated, mostly by using compulsory public good games. Recently, Sasaki et al. (2012, Proc Natl Acad Sci USA 109:1165-1169) considered optional participation as well as institutional incentives and described how the interplay between these mechanisms affects the evolution of cooperation in public good games. Here, we present a full classification of these cases of evolutionary dynamics. Specifically, whenever penalties are large enough to cause the bi-stability of both cooperation and defection in cases in which participation in the public good game is compulsory, these penalties will ultimately result in cooperation if participation in the public good game is optional. The global stability of coercion-based cooperation in this optional case contrasts strikingly with the bi-stability that is observed in the compulsory case We also argue that optional participation is not as effective under rewards as under punishment.
Materials that possess nontrivial topology and magnetism is known to exhibit exotic quantum phenomena such as the quantum anomalous Hall effect. Here, we fabricate a novel magnetic topological heterostructure Mn4Bi2Te7/Bi2Te3 where multiple magnetic layers are inserted into the topmost quintuple layer of the original topological insulator Bi2Te3. A massive Dirac cone (DC) with a gap of 40–75 meV at 16 K is observed. By tracing the temperature evolution, this gap is shown to gradually decrease with increasing temperature and a blunt transition from a massive to a massless DC occurs around 200–250 K. Structural analysis shows that the samples also contain MnBi2Te4/Bi2Te3. Magnetic measurements show that there are two distinct Mn components in the system that corresponds to the two heterostructures; MnBi2Te4/Bi2Te3 is paramagnetic at 6 K while Mn4Bi2Te7/Bi2Te3 is ferromagnetic with a negative hysteresis (critical temperature ~20 K). This novel heterostructure is potentially important for future device applications. ; T.H. was supported by JSPS KAKENHI Grant Number 18H03877, the Murata Science Foundation (No. H30-084), the Asahi Glass Foundation, Tokyo Tech. Challenging Research Award, and the Iketani Science and Technology Foundation (No. 0321083-A). M.K. was supported by the Spintronics Research Network of Japan (Spin-RNJ). The ARPES measurements were performed under the UVSOR proposal Nos. 29-837, 30-571, 30-860 and the SARPES measurements were performed under the HiSOR proposal No. 16BG001. The XMCD measurements were performed at JAEA beamline BL-23SU in SPring-8 (Proposal No. 2018B3843) and also at PF-KEK (PF PAC No. 17P006). The work at SPring-8 was performed under the Shared Use Program of JAEA Facilities (Proposal No. 2018B-E21) with the approval of Nanotechnology Platform project supported by the Ministry of Education, Culture, Sports, Science and Technology (Proposal No. A-18-AE-0039). The support by Tomsk State University competitiveness improvement program (No. 8.1.01.2018), the Saint Petersburg State University (Project ID 51126254), the Russian Science Foundation (Grant No. 18-12-00169) and the Government research assignment for ISPMS SB RAS, project No. III.23.2.9 is gratefully acknowledged. M.M.O. acknowledges the support by Spanish Ministerio de Ciencia e Innovación (Grant No. PID2019-103910GB-I00). ; Peer reviewed
