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Characteristic Function and Time Consistency for Two-Stage Games with Network Externalities

by Artem Sedakov 1,2,3
1
Department of Mathematical Game Theory and Statistical Decisions, Saint Petersburg State University,7/9 Universitetskaya nab., Saint Petersburg 199034, Russia
2
School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
3
Institute of Applied Mathematics of Shandong, Qingdao 266071, China
Mathematics 2020, 8(1), 38; https://doi.org/10.3390/math8010038
Received: 14 December 2019 / Revised: 24 December 2019 / Accepted: 26 December 2019 / Published: 1 January 2020
(This article belongs to the Special Issue Mathematical Game Theory 2019)
Time consistency is a property of the solution to a cooperative dynamic game which guarantees that this solution remains stable with respect to its revision by players over time. The fulfillment of this property is directly related to the characteristic function and its behavior with the course of the game as any solution is based on this function. In this paper, we will examine the characteristic functions for two economic models with network externalities represented by a two-stage network game using the theory developed for this class of games. For a network game with positive externalities represented by a public goods provision model, we demonstrate a sufficient condition for time consistency. For a network game with negative externalities represented by a market competition model, we show that the cooperative solution is always time consistent. View Full-Text
Keywords: network externalities; cooperation; public goods provision; market competition; time consistency network externalities; cooperation; public goods provision; market competition; time consistency
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Sedakov, A. Characteristic Function and Time Consistency for Two-Stage Games with Network Externalities. Mathematics 2020, 8, 38.

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