The theme of this course is "social networks and decision making." This course deals with fundamental concepts and analysis methods of social and competitive decision making on social networks through lectures and working on exercise problems. Specifically, this course treats the topics such as "stability of social networks," "coalition formation in social networks," "Social networks and social decision making," "deadlock of meetings," "interaction consistency in selection and election groups," "social networks and competitive decision making," and "attitude analysis." These are fundamental concepts and analysis methods of social and competitive decision making on social networks, which the students are expected to understand upon the completion of this course.
Taking social and competitive decision making on social networks as an object, this course aims to cultivate the students’ abilities to: select an appropriate mathematical model for describing and analyzing an object; describe the object by a mathematical model; draw some insights from the results of analysis of the mathematical model; convey the analysis results to others concisely.
Upon completion of this course, taking social and competitive decision making on social networks as an object, students should be able to:
1) State the definitions of mathematical models using examples of the objects described by the mathematical models;
2) Apply analysis methods to examples of the objects described by the mathematical models, and explain the analysis results to others;
3) Select an appropriate mathematical model and describe an object; and
4) Apply analysis methods to an object described by a mathematical model, and explain the analysis results to others.
Stability of social networks; Coalition formation in social networks; Social networks and social decision making; Deadlock of meetings, Interaction consistency in selection and election groups, Social networks and competitive decision making; Attitude analysis
Specialist skills | ✔ Intercultural skills | ✔ Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
One class deals with one topic.
A lecture on the topic is presented, and the students work on exercise problems, first individually, second in pairs, then in groups of four, and finally with the class as a whole. At the end of the class, each student writes and submits a "summary report" on what he/she learned through individual observation, other students' ideas, the lecture, and exercise problems.
Course schedule | Required learning | |
---|---|---|
Class 1 | Guidance; Self introduction | State at least three topics this course treats. Find at least three new colleagues. |
Class 2 | Definition of social networks; Heider's stability; Separability | Find an example of social networks which are of three decision makers and stable in Heider's sense. Find an example of social networks which are of three decision makers and NOT stable in Heider's sense. |
Class 3 | Clusterability; Newcomb's stability; Positive/negative self attitude | Find an example of social networks which are of three decision makers, one of who is with negative self attitude, and stable in Newcomb's sense. Find an example of social networks which are of three decision makers, one of who is with negative self attitude, and NOT stable in Newcomb's sense. |
Class 4 | Definition of social decision making; Social networks and social decision making; Meetings; Deadlock of meetings | Find an example of meetings which are of three decision makers and at a deadlock. Find an example of meetings which are of three decision makers and NOT at a deadlock. |
Class 5 | Selection groups; Election groups; Interaction consistency; Bisectability; Quasi-clusterability; Approval voting | Find an example of social networks which are of three decision makers and have interaction consistency. Find an example of social networks which are of three decision makers and DO NOT have interaction consistency. |
Class 6 | Definition of competitive decision making; Games in normal form; Rationality analysis; Dominant strategies; Dominant strategy equilibria; Nash equilibria; Pareto optimal outcomes | Find all dominant strategies, dominant strategy equilibria, Nash equilibria, and Pareto optimal outcomes, if exist, in a prisoners’ dilemma game, a chicken game, a battle of sexes game, and a "the gift of the Magi" game. |
Class 7 | Social networks and competitive decision making; Social systems; Attitude analysis; Devoting replies; Aggressive replies; Relational replies; Totally relational replies; Relational dominant strategies; Relational dominant strategy equilibria; Relational Nash equilibria | Give examples of relational dominant strategies, relational dominant strategy equilibria, and relational Nash equilibria in social systems in which conflicts of interests are described by a prisoners’ dilemma game, a chicken game, a battle of sexes game, and a "the gift of the Magi" game. |
Class 8 | Summary and advanced topics; Analysis of "the gift of the Magi"; Interaction consistency of meetings; Agent-based approach to social network stability | (1) Compare two distinct social networks of three decision makers by using the results of stability analysis with Heider's stability and Newcomb's stability. (2) Considering meetings, selection groups, and election groups with the two social networks in (1), compare the two social networks by using the results of analysis on deadlock of meetings, interaction consistency, and decision by approval voting. (3) Considering social systems with the two social networks in (1), compare the two social networks by using the results of analysis of rationality analysis (dominant strategies, dominant strategy equilibria, Nash equilibria, and Pareto optimal outcomes) and attitude analysis (relational dominant strategies, relational dominant strategy equilibria, and relational Nash equilibria). |
D. Cartwright, F. Harary, Structural balance: a generalization of Heider’s theory, Psychol. Rev. 63 (1956) 277-293.
J.A. Davis, Clustering and structural balance in graphs, Hum. Relations 20 (1967) 181-187.
F. Heider, Attitudes and cognitive organization, J. Psychol. 21 (1946) 107-112.
T. Inohara, S. Takahashi and B. Nakano, On conditions for a meeting not to reach a deadlock, Applied Mathematics and Computation, Vol.90, No.1, pp.1-9, March, 1998.
T. Inohara, "Emotions and Perception," Keiso-syobo, 2002 (in Japanese) （Sec.1.2, Sec.2.1, Sec.2.2, Ch.4, Ch.5, Sec.6.1, Sec.6.3）(ISBN-10: 4326502231, ISBN-13: 978-4326502233).
T. Inohara, Characterization of clusterability of signed graph in terms of Newcomb's balance of sentiments, Applied Mathematics and Computation, Vol.133, No.1, pp.93-104, November, 2002.
T. Inohara, Clusterability of groups and information exchange in group decision making with approval voting system, Applied Mathematics and Computation, Vol.136, No.1, pp.1-15, March, 2003.
T. Inohara, Stability of reliance of information sources and clusterability of information sources, The 7th World Multi-Conference on Systemics, Cybernetics and Informatics (SCI 2003), Proceedings Volume VII, pp.225-229, Orlando, Florida, USA, July 27-30, 2003.
T. Inohara, Quasi-clusterability of signed graphs with negative self evaluation, Applied Mathematics and Computation, Vol.158, No.1, pp.201-215, October, 2004.
T. Inohara, Signed graphs with negative self evaluation and clusterability of graphs, Applied Mathematics and Computation, Vol.158, No.2, pp.477-487, November, 2004.
T. Inohara, Relational dominant strategy equilibrium as a generalization of dominant strategy equilibrium in terms of a social psychological aspect of decision making, European Journal of Operational Research, Vol.182, No.2, pp.856-866, October, 2007.
T. Inohara, Relational Nash equilibrium and interrelationships among relational and rational equilibrium concepts, Applied Mathematics and Computation, Vol.199, No.2, pp.704-715, June, 2008.
T. M. Newcomb, Interpersonal balance, in: R.P. Abelson, E. Aronson, W.J. McGuire, T. M. Newcomb, M.J. Rosenberg, P.H. Tannenbaum (Eds.), Theories of Cognitive Consistency: A Sourcebook, Rand-McNally, Chicago, IL, 1968.
K.O. Price, E. Harburg, T.M. Newcomb, Psychological balance in situations of negative interpersonal attitudes, J. Pers. Soc. Psychol. 3 (1966) 265–270.
T. Inohara, "Rationality and Flexibility," Keiso-syobo, 2002 (in Japanese) (ISBN-10: 4326502223, ISBN-13: 978-4326502226).
T. Inohara, On conditions for a meeting not to reach a recurrent argument, Applied Mathematics and Computation, Vol.101, No.2-3, pp.281-298, June, 1999.
Course materials are posted on OCW-i and/or provided during the classes.
Assessment will be based on "summary reports" written during each class (50% in total) and the final report (50%).
Prospective students should have interests in social networks and decision making.
Takehiro Inohara, inostaff[at]shs.ens.titech.ac.jp (Please replace from "[at]" to "[at]"(half-width character).)
Instructor’s office: Rm. 813, 8 Fl., West Bldg. 9. Contact by e-mail in advance to schedule an appointment.
This course consists of the content of science.