Correlated equilibria in competitive staff selection problem

Ramsey, David M. and Szajowski, Krzysztof (2004): Correlated equilibria in competitive staff selection problem. Published in: Banach Center Publications , Vol. 71, (2006): pp. 253-265.

Abstract

This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The idea of this paper was presented at Game Theory and Mathematical Economics, International Conference in Memory of Jerzy Łoś (1920 - 1998), Warsaw, September 2004. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players' decisions. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the staff selection competition in the case of two departments are given. Utilitarian, egalitarian, republican and libertarian concepts of correlated equilibria selection are used.

• Item Type: MPRA Paper
• Language: English
• Keywords: correlated equilibria, Nash equilibria, non-zero sum game, secretary problem
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C68 - Computable General Equilibrium Models; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D58 - Computable and Other Applied General Equilibrium Models; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium

References

Aumann, R.J. (1974) Subjectivity and correlation in randomized strategies. J.Math. Economics, 1:67-96.

Baston, V.J., Garnaev,A.Y. (2005) Competition for staff between two departments. Game Theory and Applications, X:27-36.

Bruss, F.T., Louchard, G. 1998) Sharp bounds for winning probabilities in the competitive rank selection problem. J.Appl. Prob., 35:1007-1011.

Calvó-Armengol, A. (2004) The set of correlated equilibria of 2x2 games. \href{http://selene.uab.es/acalvo/correlated.pdf}.

Chen, R.W., Rosenberg, B., Shepp, L.A. (1997) A secretary problem with two decision makers. J. Appl. Probab., 34(4):1068-1074.

Chun, Y.H. (2000) Sequential search and selection problem under uncertainty. Decision Sciences, 31:627-648.

Chun,Y.H., Platt, M. (1992) On the sequential selection problem. Decision Sciences, 23:1251--1262.

Chun, Y.H. (1999) Selecting the best choice in the full information group interview problem. Eur. J. Oper. Res., 119(3):635-651.

Chun, Y.H. (1996) Selecting the best choice in the weighted secretary problem. Eur. J. Oper. Res., 92(1):135-147.

Enns, E.G., Ferenstein, E. (1985) The horse game. J. Oper. Res. Soc. Jap., 28:51-62.

Enns, E.G., Ferenstein, E.Z., Sheahan, J.N. (1986) A curious recursion arising in game theory. Utilitas Math., 30:219-228.

Ferguson, T.S. (1989) Who solved the secretary problem? Statistical Science, 4:282-296.

Forges, F. (1986) An approach to communication equilibria. Econometrica, 54:1375-1385.

Freeman,P.R. (1983) The secretary problem and its extensions: a review. Int. Statist. Rev., 51:189-206.

Fushimi, M. (1981) The secretary problem in a competitive situation. J. Oper. Res. Soc. Jap., 24:350-358.

Garnaev, A.Y. (2004) A game-theoretical model of competition for staff between two departments. In: Game Theory and Mathematical Economics. International Conference in Memory of Jerzy Łoś(1920 - 1998), Warsaw, vol. 71, 137-145.

Gerard-Varet, L.A., Moulin, H. (1978) Correlation and duopoly. J.~Econom. Theory, 19:123-149.

Greenwald, A., Hall, K. (2003) Correlated {Q}-learning. In: Tom Fawcett & Nina Mishra, eds, Proc. Twentieth International Conf. on Machine Learning (ICML-2003), August 21-24, 2003, 242-249. The AAAI Press, Washington DC.

Moulin, H. (1986) Game Theory for the Social Sciences. New York University Press, New York.

Nowak, A.S. (1993) Correlated equilibria in nonzero-sum differential games. J. Math. Analysis and Appl., 174(2):539-549.

Peeters, R., Potters, J. (1999) On the structure of the set of correlated equilibria in two-by-two bimatrix games. http://econpapers.hhs.se/paper/fthtilbur/9945.htm.

Ramsey, D., Szajowski, K. (2001) Random assignment and uncertain employment in optimal stopping of Markov processes. In: L.~A. Petrosjan et~al., eds, Game theory and applications, vol. 7, 147-157. Nova Science Publishers, Huntington, New York.

Ramsey, D., Szajowski, K. (2003) Correlated equilibria in Markov stopping games. Technical report, Institute of Mathematics, TU Wrocław.

Ramsey, D., Szajowski, K. (2005) Bilateral approach to the secretary problem. In: K. Szajowski & A.S. Nowak, eds, Advances in Dynamic Games: Applications to Economics, Finance, Optimization, and stochastic Control, Annals of the International Society of Dynamic Games, vol. 7, 271-284, Birkhaser, Boston.

Ramsey, D.M., Szajowski, K. (2004) Correlated equilibria in Markov stopping games. The main characterizations. In: Game Theory and Mathematical Economics. International Conference in Memory of Jerzy Łoś (1920 - 1998), Warsaw, September.

Ramsey, D.M., Szajowski, K. (2004) Correlated equilibria in Markov stopping games. The numerical methods and examples. In: Game Theory and Mathematical Economics. International Conference in Memory of Jerzy Łoś (1920 - 1998), Warsaw, September.

Rose, J.S. (1982) Twenty years of secretary problems: a survey of developments in the theory of optimal choice. Management Studies, 1:53-64.

Sakaguchi, M. (1989) Multiperson multilateral secretary problem. Math. Japonica, 35:459-473.

Sakaguchi, M. (1995) Optimal stopping games - a review. Math. Japonica, 42:343-351.

Samuels, S.M. (1991) Secretary problems. In: B.K. Ghosh & P.K. Sen, eds, Handbook of Sequential Analysis, 381-405. Marcel Dekker, Inc., New York, Basel, Hong Kong.

Seale, D.A., Rapoport, A. (1997) Sequential decision making with relative ranks: An experimental investigation of the ''secretary problem''. Organizational Behaviour and Human Decision Processes, 69:221-236.

Seale, D.A., Rapoport, A. (2000) Optimal stopping behavior with relative ranks: The secretary problem with unknown population size. J. Behavioral Decision Making, 13:391-411.

Solan, E., Vieille, N. (2002) Correlated equilibrium in stochastic games. Games and Econ. Behavior, 38:362-399.

Solan, E. (2001) Characterization of correlated equilibria in stochastic games. Int. J. Game Theory, 30(2):259-277.

Stein, W.E., Seale, D.A., Rapoport, A. (2003) Analysis of heuristic solutions to the best choice problem. Eur. J. Oper. Res., 151(1):140-152.

Szajowski, K. (1994) Markov stopping games with random priority. Zeitschrift fuer Operations Research, 37(3):69-84.

Thomson, W. (1994) Cooperative models of bargaining. In: R.J. Aumann et al., eds, Handbook of game theory with economic applications. Handbooks in Economics., vol. 2, 1237-1284, Elsevier, Amsterdam.

Tolwiński, B., Haurie, A., Leitmann, G. (1986) Cooperative equilibria in differential games. J.Math. Anal. Appl., 119:182-202.