With Robert J. Aumann, Kalai founded the Game Theory Society and served as its president from 2003 to 2006.

He is a Fellow of the American Academy of Arts and Sciences, of the Econometric Society,[1] was awarded an Honorary Doctorate (Doctorat Honoris Causa) by the University of Paris at Dauphine (2010), the Sherman Fairchild Distinguished Scholar position at the California Institute of Technology (1993), and was appointed the Oskar Morgenstern Research Professor at New York University (1991).

He later axiomatized the Egalitarian solution to bargaining problems and, with Dov Samet, formulated its extension to general (NTU) cooperative games, unifying it with the Shapley (TU) Value.

In particular, in Bayesian equilibria of repeated games all relevant private information eventually becomes common knowledge.

Cooperative Game Theory "Other Solutions to Nash's Bargaining Problems," Econometrica, 1975 (with M. Smorodinsky) "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, 1977 "Monotonic Solutions to General Cooperative Games," Econometrica, 1985 (with D. Samet) Non cooperative Game Theory "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, 1988 (with W. Stanford) "Rational Learning Leads to Nash Equilibrium," Econometrica, 1993 (with E. Lehrer) “Large Robust Games,” Econometrica, 2004 Probability and Learning "Bayesian Representations of Stochastic Processes Under Learning: deFinetti Revisited," Econometrica, 1999 (with M. Jackson and R. Smorodinsky) Economics "The Kinked Demand Curve, Facilitating Practices, and Oligopolistic Coordination," 1986 Northwestern DP (with M. Satterthwaite; published by Kluwer, 1996)) "Observable Contracts: Strategic Delegation and Cooperation," International Economic Review, 1991 (with C. Fershtman and K. Judd) "Complexity Considerations in Market Behavior," The RAND Journal of Economics, 1993 (with C. Fershtman) Social Choice "Aggregation Procedure for Cardinal Preferences: A Formulation and Proof of Samuelson's Impossibility Conjecture," Econometrica, 1977 (with D. Schmeidler) "Characterization of Domains Admitting Non-Dictatorial Social Welfare Functions and Non-Manipulable Voting Procedures," Journal of Economic Theory, 1977 (with E. Muller) "Path Independent Choices," Econometrica, 1980 (with N. Megiddo) Operations Research / Computer Science "Totally Balanced Games and Games of Flow," Mathematics of Operations Research, 1982 (with E. Zemel) "Optimal Service Speeds in a Competitive Environment," Management Science, 1992 (with M. Kamien and M. Rubinovitch) “Partially-Specified Large Games,” Lecture Notes in Computer Science, 2005 Mathematical Psychology "Strategic Polarization," Journal of Mathematical Psychology, 2001 (with A. Kalai)