Ethical Norms Realizing Pareto-Efficiency in Two-Person Interactions:

1. 3rd-Joint-Conference (2005) June at Sapporo Ethical Norms Realizing Pareto-Efficiency in Two-Person Interactions: Game Theoretic Analysis with Social Motives Masayoshi MUTOTokyo Institute of Technology

2. 1 INTRODUCTION2 OR-UTILITY FUNCTION 3 GAME-TRANSFORMATION 4 CONCLUSIONS

3. Motivation of Research • In everyday life, people interact TAKING EACH OTHER INTO ACCOUNT • But we have few such theories in Game Theory I take Ann’s payoff into account. I take Bob’s payoff into account. Ann Bob

4. Overview • QUESTION How should we take others into account to realize PARETO-EFFICIENCY? • ANSWER In two-person interactions we should be ALTRUISTIC and IMPARTIAL

5. ＊Pareto Efficiency Pareto-Efficientunanimously better Pareto-Inefficientunanimously worse

6. Existing Research • “Other-Regarding Utility Function” （=OR-Utility Function） for explaining experiments data of few games • Prisoners’ Dilemma, Ultimatum Game... • But we don’t know what game is played in daily-life ↓ GeneralTheory about Ways of Other-Regarding in Many Situations

7. Scope Conditions • Situations: Any TWO-person games • Both players share AN Other-Regarding Utility Function • ex. altruism, egalitarianism, competition

8. 1 INTRODUCTION2 OR-UTILITY FUNCTION3 GAME-TRANSFORMATION 4 CONCLUSION

9. objective subjective Other-Regarding Utility Function 1 v(x ; y) = (1－p)x+ py • x my payoff • y the other’s payoff • p my WEIGHT for the other • v my subjective payoff But NOT expressing EGALITARIANISM ! MacClintock 1972

10. Other-Regarding Utility Function 2 • pif my payoff is BETTER than the other’s • q if my payoff is WORSE than the other’s Schulz&May 1989, Fehr&Schmidt 1999 －∞＜p＜+∞, －∞＜q＜+∞

11. much heavier →Egalitarianism p>0, q<0 is sufficient for weak Egalitarianism ＊Egalitarianism：(p－q ) is large

12. q ∞ 1 0.5 -∞ 0.5 O 1 ∞ -∞ ANTI-EGL. SACRIFICE Family ofOR-Utility Functions p＋q =1 ALTRUISM MAXMAX altruistic JOINT egalitarian p = q EGOISM MAXMIN p COMPETITION EGALITARIANISM

13. 1 INTRODUCTION 2 OR-UTILITY FUNCTION 3 GAME-TRANSFORMATION 4 CONCLUSION

14. Payoff Transform row-player’s subjective payoff

15. Payoff Transform row-player’s subjective payoff calculate

16. Payoff Transform row-player’s subjective payoff for both players

17. Payoff Transform row-player’s subjective payoff p =1, q =0 :MAXMIN ex.

18. 1 O 1 Payoff Transform by Some OR-Utility Functions q 0.5 MAXMIN (1, 0) p example 0.5 1

19. 1 O 1 Payoff Transform by Some OR-Utility Functions q ALTRUISM (1, 1) 0.5 MAXMIN (1, 0) p example 0.5 1

20. Problem in ALTRUISM p =1，q =1 INEFFICIENT!

21. INEFFICIENT! INEFFICIENT! Problem in EGALITARIANISM p→∞，q→－∞

22. WAYS of Other-Regarding existing Social States which are Pareto EFFICIENT in objective level and Pure Nash EQUILIBRIAin subjective level for any two-person games ALTRUISTICp,q≧0 and IMPARTIALp +q =1 Theorem ＝

23. q ∞ 1 0.5 -∞ 0.5 O 1 ∞ -∞ anti-egl sacrifice IMPARTIAL Ways IMPARTIAL p＋q =1 maxmax altruism joint maxmin egoism p egalitarian competition

24. q ∞ 1 0.5 -∞ 0.5 O 1 ∞ -∞ ALTRUISTICp, q≧0 anti-egl ALTRUISTIC and IMPARTIALWays MAXMAX altruism includingmixture JOINT MAXMIN egoism p egalitarian competition

25. q 1 0.5 0.5 O 1 ALTRUISTIC and IMPARTIALWays:Payoff Transformexample MAXMAX JOINT JOINT MAXMIN egoism p Objective LV

26. 1 INTRODUCTION 2 OR-UTILITY FUNCTION 3 GAME-TRANSFORMATION4 CONCLUSION

27. Implication 1 • p = 0.5, q =0.3appears to be good for Pareto efficiency ： If my payoff is better than the other’s, regard equallyIf my payoff is worse than the other’s, regard a little But not impartial (p+q = 0.8＜1) → Theorem requires a strict ethic

28. Implication 1 → Only altruistic and impartial ways of other regardingcan realize Pareto efficiency in ANY two-person games

29. Implication 2 • Extreme-Egalitarianism isn’t good weight for difference of payoffs (|e|) ≦ weight for sum of payoffs (1/2) ⇒ e =1/2 means “MAXMIN”

30. Implication 2 ↓ MAXMIN is the “Maximum Egalitarianismwith Pareto-Efficiency”in any two-person games

31. Summary • Altruistic and Impartial Ways of Other-Regarding(that is “from Maxmin to Maxmax”)are justified as the only ways realizing Pareto Efficiencyin any two-person interactions.

32. Bibliography • Shulz, U and T. May. 1989. “The Recording of Social Orientations with Ranking and Pair Comparison Procedures.” European Journal of Social Psychology 19:41-59 • MacClintock, C. G. 1972. “Social Motivation: A set of propositions.” Behavioral Science17:438-454. • Fehr, E. and K. M. Schmidt. 1999. “A Theory of Fairness, Competition, and Cooperation.” Quarterly Journal of Economics 114(3):817-868.

33. Defection through Egoism p =0，q =0 • In “Prisoners’ Dilemma”, Egoism causes Pareto non-efficiency.

34. ＊Mathematical Expression of Theorem • The following v expresses possible “ways of other-regarding” to realize Pareto-Efficiency in any two-person interaction. equilibrium action profiles in subjective level of game g two-person finite gameincluding m×nASYMMETRIC game efficient action profiles in objective level of game g existing {v | ∀gEff(g)∩NE(vg)≠φ} = {v | p +q =1, p≧0, q≧0 }