Abstract
How does one repeatedly choose actions so as to be fairest to the multiple beneficiaries of those actions? We examine approaches to discovering sequences of actions for which the worst-off beneficiaries are treated maximally well, then secondarily the second-worst-off, and so on. We formulate the problem for the situation where the sequence of action choices continues forever; this problem may be reduced to a set of linear programs. We then extend the problem to situations where the game ends at some unknown finite time in the future. We demonstrate that an optimal solution is intractable, and present two good approximation algorithms.
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Balan, G., & Luke, S. (2006). History-based traffic control. In Proceedings of the 5th international joint conference on autonomous agents and multi agent systems (pp. 616–621).
Balan, G., Luke, S., & Richards, D. (2008). Long-term fairness with bounded worst-case losses. In Proceedings of the 4th multidisciplinary workshop on advances in preference handling (AAAI) (pp. 7–12).
Bhaskar V. (2000) Egalitarianism and efficiency in repeated symmetric games. Games and Economic Behavior 32(2): 247–262
Borodin P. A. (2001) The Banach-Mazur theorem for spaces with asymmetric norm. Mathematical Notes 69: 298–305
Dubois D., Fortemps P., Pirlot M., Prade H. (2001) Leximin optimality and fuzzy set-theoretic operations. EJOR 130(1): 20–28
Finch S. R. (2003) Mathematical constants. Cambridge University Press, Cambridge
Florenzano, M., & Le Van, C. (2001). Finite dimensional convexity and optimization.
Garey M. R., Johnson D. S. (1979) Computers and intractability: A guide to the theory of NP-completeness. Freeman W.H, New York
Klein R. S., Luss H., Smith D. R. (1992) A lexicographic minimax algorithm for multiperiod resource allocation. Mathematical Programming 55(2): 213–234
Lau S.-H. P., Mui V.-L. (2008) Using turn taking to mitigate coordination and conflict problems in the repeated battle of the sexes game. Theory and Decision 65(2): 153–183
Lipschutz S., Lipson M. (2001) Schaum’s outline of theory and problems of linear algebra. McGraw-Hill Inc, New York, NY, USA
Ogryczak W. (1997) On the lexicographic minimax approach to location problems. European Journal of Operational Research 100: 566–585
Ogryczak W., Śliwiński T. (2003) On solving linear programs with the ordered weighted averaging objective. European Journal of Operational Research 148: 80–91
Peterson M., Hansson S. O. (2005) Equality and priority. Utilitas 17: 299–309
Phelps R. R. (2001) Lectures on choquet’s theorem. Springer, New York
Potters J. A. M., Tijs S. H. (1992) The nucleolus of a matrix game and other nucleoli. Mathematics of Operations Research 17(1): 164–174
Rasmusen E. (1994) Games and information. Blackwell, Oxford
Sevast’janov S. (1991) On the compact summation of vectors. Diskretnaya Matematika 3(3): 66–72 (In Russian)
Stephen T., Tuncel L., Luss H. (1999) On equitable resource allocation problems: A lexicographic minimax approach. Operations Research 47(3): 361–376
Stirling D. S. G. (1997) Mathematical analysis and proof. Albion Publishing, Chichester
Temkin L. S. (2003) Equality, priority or what?. Economics and Philosophy 19: 61–87
Verbeeck K., Nowé A., Parent J., Tuyls K. (2006) Exploring selfish reinforcement learning in repeated games with stochastic rewards. Journal of Autonomous Agents and Multi-Agent Systems 14(3): 239–269
Verbeeck, K., Parent, J., & Nowé, A. (2003). Homo egualis reinforcement learning agents for load balancing. In Innovative concepts for agent-based systems: 1st international workshop on radical agent concepts, volume 2564 of lecture notes in computer Science (pp. 81–91).
Yager R. R. (1988) On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems Man and Cybernetics 18(1): 183–190
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A preliminary version of this paper was published in [2].
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Balan, G., Richards, D. & Luke, S. Long-term fairness with bounded worst-case losses. Auton Agent Multi-Agent Syst 22, 43–63 (2011). https://doi.org/10.1007/s10458-009-9106-9
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DOI: https://doi.org/10.1007/s10458-009-9106-9