Stationary State in a Multistage Auction Model

Authors

  • Aleksei Y. Kondratev Karelian Research Center of RAS

Abstract

We consider a game-theoretic multistage bargaining model with incomplete information related with deals between buyers and sellers. A player (buyer or seller) has private information about his reserved price. Reserved prices are random variables with known probability distributions. Each player declares a price which depends on his reserved price. If the bid price is above the ask price, the good is sold for the average of two prices. Otherwise, there is no deal. We investigate model with infinite time horizon and permanent distribution of reserved prices on each stage. Two types of Nash-Bayes equilibrium are derived. One of them is a threshold form, another one is a solution of a system of integro-differential equations.

Keywords:

multistage auction model, Nash equilibrium, integro-differential equations for equilibrium, threshold strategies

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References

Chatterjee, K. and Samuelson, W. (1983). Bargaining under incomplete informationg. Operations Research, 31(5), 835–851.

Mazalov, V. V. and Kondratyev, A. Y. (2012). Bargaining model with incomplete information. Vestnik St. Petersburg University. Ser. 10, 1, 33-Ű40.

Mazalov, V. V. and Kondratev, A. Y. (2013). Threshold strategies equilibrium in bargaining model. Game theory and applications, 5(2), 46–63.

Mazalov, V. V., Mentcher, A. E. and Tokareva, J. S. (2012). Negotiations. Mathematical theory. Lan. Saint-Petersburg. 304 P.

Mazalov, V. V. and Tokareva, J. S. (2011). Equilibrium in bargaining model with non-uniform distribution for reservation prices. Game theory and applications. 3(2), 37–49.

Myerson, R. and Satterthwait, M. A. (1983) Efficient mechanisms for Bilateral Trading. Journal of Economic Theory, 29, 265–281.

Myerson, R. (1984) Two-Person Bargaining Problems with Incomplete Information. Econometrica, 52, 461–487.

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Published

2022-08-09

How to Cite

Y. Kondratev, A. (2022). Stationary State in a Multistage Auction Model. Contributions to Game Theory and Management, 7. Retrieved from https://gametheory.spbu.ru/article/view/13599

Issue

Vol. 7 (2014)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.