Question

prove by constructing an example that the Kalai-Smorodinsky solution (Kalai and Smorodinsky,1975) violates the independence of irrelevant alternatives axiom.

Answer 1

22227999 Kalai - Smorodinsky solutions (for ILA) Example s= Cocomp 2 (2,0) 1012 ) n R² + s'= Co comp? 0,1),(2,074 NR + d = 100). I refer below then Obiviously scs I Diagram K(5,0) = (1,) ES' Henie. Independence of irrelevant Axiom would require that the solution also chooses (1,1) in the problem (slid) but K15,0) = 142,23). so, kalci-Smoroding ky solution violates the ILA. eline a at alsd) k'lsid) =(4312) i Ve Kesa)-cm), kis,d) = (1,1) o atsa) she Ah, co * 2 player two has less Bargaining power in (s',d) than in (sd) and Kalai-somorodinsky Solution reflect that & The agreement (1,1) seems reasonable for (s, d) sime the problem ix symmetric, but it does not for the problem (5'd) So K-s-solution violates 1A.