COMPUTER-BASED SUPPORT OF INDIVIDUAL AND COOPERATIVE RISKY

1. COMPUTER-BASED SUPPORT OF INDIVIDUAL AND COOPERATIVE RISKY • DECISIONS WITH USE OF THE UTILITY CONCEPT • Lech Kruś • Systems Research Institute, Polish Academy of • Sciences, Warsaw, Poland • Keywords: mathematical modeling, risk, utility, decision support, • computer-based systems, cooperative games. • Contents • Introduction • Decision support with use of the utility concept – structure of the computer based system • Support of education decisions • - model describing relations between students and private university, • - decision analysis, cooperation problem, • - selected computational results. • 4. Final remarks Lech Kruś CSM05

2. Introduction management of different forms of capital in the presence of risk (subjects developed in Roman Kulikowski group): Normative analysis of risky investments. Optimal allocation of capital among different investments in the presence of risk. Promotion and propagation of innovations. Management of capital in long term and spatial development. Optimal allocation of capital for preventive actions Concept of disutility describing losses which can be result of failures or disasters. Utility of contracts and cooperation. This paper: Construction of computer-based systems supporting analysis of individual and cooperative risky decisions. Example relating to support of education decisions. Applied methodologies Utility function concepts - Savage, A. Tversky, R. Kulikowski Multicriteria analysis – achievement function approach - A. P. Wierzbicki Multiple criteria optimization and decisions under risk - W. Ogryczak Multicriteria decision support in cooperative games - L. Kruś Lech Kruś CSM05

3. historical information experts’ opinions inquiry information Model Database Model (1): decision situation decision variables, exogenous variables, output quantities, criteria, model relations; Identification of model parameters, Model verification Procedures for estimation of model parameters and for model verification System analyst Editor Model (2): preferences of DMs Utility functions of decision makers Estimation of subjective parameters of utility functions Procedures for scaling utility function DM Graphical interface Module supporting individual decisions Generation of output quantities for given scenarios, as requested by DM. Derivation of optimal decisions. DM Solver Procedures serving interactive session Module supporting cooperative decisions generation of mediation proposals, supporting consensus seeking Lech Kruś CSM05

4. Flaws of students, Warsaw Information Technology (WIT University) candidates recruitment and initial exams Given, collected historical data including number of students passing exams, repeating, waiving. Calculated transiton tables and transition probabilities. students repeating 1-st year studies waiving 2-nd year studies 3-rd year studies specializations: a b c d 4-th year, master courses specializations: a b c d diploma semester a b c d graduates with engineer degree 5-th year, master courses specializations: a b c d graduates with master degree Lech Kruś CSM05

5. SUPPORT OF EDUCATION DECISIONS MODEL Students and private university are treated as partners in a joint venture. Model describes expenditures, receipts, profits, utilities, risk measures for student and for university, as dependent on tuition level, and on exogenous variables like: cost of living of the student during the studies, expected increase of wages after the studies, transition probabilities, probability that he will find the job after the studies, cost (constant and operating) per one place covered by university on different directions of studies, and others. Student Discounted expenditures Ie(c) for education during the studies : where: T0 – time of studies, m(t) – cost of living in the year t, c - tuition per year, ke - discount rate in the time of studies. Lech Kruś CSM05

6. Utility of sustainable development (R. Kulikowski) (extension of the ideas proposed by Savage, Tversky, Kahneman) Utility from the risky investment, characterized by the rate of return , which is random variable with expected value R and variance 2, is described by a function of two factors: where - expected long term profit, - share of expenditures I, in the total capital P of the investor, - safety index,   -  worst case profit, - subjective parameter, weight prescribed to the risk of the worst case. The form applied in the model: , , where  characterizes the investor’s enterprising parameter. Lech Kruś CSM05

7. Utility of the student at university: where xs(c)=Ie(c )/Ps , Rse(c) =(We-Ie(c))/Ie(c),Ps– capital of the student starting the studies, pe – probability that he will be graduated, and that he will find the job. University Tuition c per year per one student, operating cost co per one place, n – number of places prepared for students, k – number of expected students. Rate of return: Ru =c/co-1 with probability pu=k/n. It is assumed that the university has the capital Pu, part Iu=nco of it is used to prepare the places for n students. Utility of the university (in one year) : , where x=Iu/Pu Remark Subjective parameters s, s ,u , u, have to be evaluatedinteractively with decision makers (students, university representative). Procedures: Kulikowski (2005), Kruś (2005). Lech Kruś CSM05

8. Decision analysis in the presence of risk • Student • Comparison of utilities from studies on different directions, specializations, (different universities), taking into account probabilities that the student will pass the exams and be graduated, personal predispositions, difficulty of studies, probability of finding the job, cost of the studies, expected increase of wages, risk of failure. • Private university • Assessment of new directions of studies responding to the needs of education market, taking into account cost, expected number of students, risk of failure. Derivation of the tuition which is beneficial for the university, as well for students – cooperation problem – cooperative solutions. • Experimental computer-based system has been constructed • It supports financial analysis made by each party, enables analysis of • expected rate of return, • expected receipts and profit in comparison to the risk free investments, • assessment of risk: variance, semivariance, • utilities, safety indices, • impact of the risk on the cooperative solutions. Lech Kruś CSM05

9. Uu(c) Uud Us(c) Usd Tuition. Bargaining problem. Parties Student: max Use(c) University: max Uu(c) Model relations define the set A of attainable payoffs in the space of utilities. Acceptability conditions: university:Uu(c)Uud student: Us(c)Usd Lower bounds of acceptable utilities Uud , Usd are defined as the best alternatives to the negotiated agreement (Fisher’s BATNA concept). Decision problem: find a point from the set A mutually accepted by both parties. Decision support: generation (with use of computer-based system) of mediation proposals, interactive analysis, application of solution concepts formulated in the theory of cooperative games A Lech Kruś CSM05

10. Nash cooperative solution concept: (UsN, UuN)=arg max ((Us-Usd)(Uu-Uud)), dla (Us,Uu)A. In the considered education model the following optimization problem has to be solved: maxc[(Us(c)-Usd)(Uu(c)-Uud)], subject to the constraints: (Us(c), Uu(c))A. Properties of the proposed solution: Pareto optimal in the set A, symmetric, independent on affine transformations of utilities, independent on irrelevant alternatives. Lech Kruś CSM05

11. 120 UTILITIES OF THE STUDENT 100 utilities from employment after the studies tuition c=8000 PLN/year 80 tuition c=6000 PLN/year 60 40 minimal akceptable utilities 20 probability of employment after the studies 0 0,7 0,75 0,8 0,85 0,9 0,95 0,8 0,7 0,6 kappa 0,5 0,4 Safety index 0,3 0,2 minimal probabiltity of success 0,1 0 0 1 2 3 4 5 6 7 8 Reserves of capital Fig. 2. Utilities of the student, dependent on probability of employment after the studies. Fig. 3. Parameter , safety index S, and the minimal (lower bound) probability, that the student will succeed, dependent on his reserves of capital. Lech Kruś CSM05

12. Fig. 4. Student’s utilities dependent on the tuition. UTILITIES OF THE STUDENT 70 Utility from employment after the studies 65 60 55 50 Minimal acceptable utility 45 40 Nash solution 35 tuition 30 6 6,5 7 7,5 8 8,5 9 0,8 7000 Lower bound of probability the the university succeed UTILITIES OF THE UNIVERSITY 0,7 6000 Utility from the education activity 5000 0,6 Nash solution 4000 0,5 3000 Nash solution 0,4 2000 Minimal acceptable utility tuition 1000 0,3 6 6,5 7 7,5 8 8,5 9 0 6 6,5 7 7,5 8 8,5 9 tuition Fig. 6. Lower bound of probability that the university succeed. Fig. 5. Utilities of the university. Lech Kruś CSM05

13. FINAL REMARKS Construction of computer based systems supporting decision analysis in the presence of risk is presented on an example of education system. Goal of the system: support decisions made by candidates and students of private university, including financial analysis, selection of education area and specialization, as well as decisions of the university organizing the studies and fixing the tuition level. The decisions are made in the presence of risk. This paper includes new, extended version of the model taking into account new methodological achievements within utility concept, construction elements of computer-based system, and new computational results. The system is developed in cooperation with Warsaw Information Technology (WIT) University since 2003. Lech Kruś CSM05

14. Selected publications KRUŚ, L. , Multicriteria Decision Support in Negotiations. Control&Cybernetics Vol. (1996) No. 6, 1245-1260. KRUŚ L; A multicriteria approach to cooperation in the case of innovative activity. Control&Cybernetics, Vol. 33, No. 3, 2004. KRUŚ, L. (2004):A Computer Based System Supporting Analysis of Cooperative Strategies. In: Artificial Intelligence and Soft Computing - ICAISC 2004,Springer-Verlag, Heidelberg. KULIKOWSKIR. , L. KRUŚ, Support of education decisions. W: Group Decisions and Voting (J. Kacprzyk, D. Wagner eds), Akad. Oficyna Wyd. EXIT, Warszawa, 2003. KULIKOWSKI R., On general theory of risk management and decision support systems, Bulletin of the Polish Academy of Sciences, Sci. Tech., Vol. 51 (2003) No. 3. KULIKOWSKI R., Risk and utility of sustainable development, W: Grzegorzewski P., Krawczak M., Zadrożny S. (eds.) Soft Computing – Tools, Techniques and Applications, EXIT, 2004. KULIKOWSKI R. (2005) Support of risky decisions by using the concept of utility which enables the implementation of sustainable development strategies. CSM 2005.OGRYCZAK, W. (2002) Multiple criteria optimization and decisions under risk. Control and Cybernetics, 31,4. TVERSKY A., KAHNEMAN D., The framing of decisions and the psychology of choice, Science, Vol. 211, (1981) January. WIERZBICKI A., MAKOWSKI M., WESSELS J., (2001) Model Based Decision Support Methodology with Environmental Applications. Kluwer Acad. Publ.