Abstract
We present a discrete n-person model of a dynamic strategic market game. We show that for some values of the discount factor the game possesses a stationary equilibrium where all the players make high bids. Within the class of all the high-bidding strategies we distinguish between two classes of more and less aggressive ones. We show that the set of discount factors for which these more aggressive strategies form equilibria shrinks as n goes to infinity. On the other hand, the analogous set for the less aggressive strategies grows to the whole interval (0,1) as n grows to infinity. Further we analyze the properties of the value function corresponding to these high-bidding equilibria. We also give some numerical examples contradicting some other properties that seem intuitive.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Federgruen, A.: On n-person stochastic games with denumerable state space. Adv. Appl. Probab. 10, 452–471 (1978)
Geanakoplos, J., Karatzas, I., Shubik, M., Sudderth, W.D.: A strategic market game with active bankrupcy. J. Math. Econ. 34, 359–396 (2000)
Kakutani, S.: A generalization of Brouwer’s fixed point theorem. Duke Math. J. 8(3), 457–459 (1941)
Karatzas, I., Shubik, M., Sudderth, W.D.: Construction of stationary Markov equilibria in a strategic market game. Math. Oper. Res. 19(4), 975–1006 (1992)
Karatzas, I., Shubik, M., Sudderth, W.D.: A strategic market with secured lending. J. Math. Econ. 28, 207–247 (1997)
Pontiggia, L.: Topics in stochastic games. Ph.D. dissertation, University of Minnesota, United States (2004)
Ross, S.: Introduction to Stochastic Dynamic Programming. Academic Press, New York (1983)
Schäl, M.: Conditions for optimality in dynamic programming and for the limit of n-stage optimal policies to be optimal. Z. Wahrscheinlichkeitstheor. Verw. Geb. 32, 179–196 (1975)
Secchi, P., Sudderth, W.D.: A two-person strategic market game. Quaderni di Dipartamento 83(6-98), Dipart. di Econ. Polit. e Met. Quant., Università di Pavia (1998)
Secchi, P., Sudderth, W.D.: A simple two-person stochastic game with money. In: Nowak, A.S., Szajowski, K. (eds.) Advances in Dynamic Games. Applications to Economics, Finance, Optimization, and Stochastic Control. Ann. of ISDG, vol. 7, pp. 39–66. Birkhäuser, Boston (2005)
Shubik, M., Whitt, W.: Fiat money in an economy with one nondurable good and no credit. A noncooperative sequential game. In: Blaquiere, A. (ed.) Topics in Differential Games, pp. 401–449. North-Holland, Amsterdam (1973)
Więcek, P.: Pure equilibria in a simple dynamic model of strategic market game. Math. Methods Oper. Res. 69, 59–79 (2009)
Więcek, P., Radzik, T.: On a continuous dynamic strategic market game. In: Petrosjan, L., Mazalov, V.V. (eds.) Game Theory and Applications, vol. 11, pp. 187–196. Nova Science Publishers, New York (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Więcek, P. n-Person Dynamic Strategic Market Games. Appl Math Optim 65, 147–173 (2012). https://doi.org/10.1007/s00245-011-9147-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00245-011-9147-8