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Game Theory
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Erik G. Larsson, Eduard Jorswiec
for all strategies si of player i. It can be shown that all finite extensive form games with complete information have a subgame-perfect equilibrium. The proof works with backward induction. The subgame-perfect equilibrium is not necessarily unique. Clearly, all subgame-perfect equilibria are Nash equilibria. The condition in (19.34) reduces the set of Nash equilibria to the plausible outcomes.
Why do Low Cost Carriers Arise and How can they Survive the Competitive Responses of Established Airlines?: A Theoretical Explanation
Published in Peter Forsyth, David W. Gillen, Otto G. Mayer, Hans-Martin Niemeier, Competition versus Predation in Aviation Markets, 2018
In this section the equilibrium is derived. Since the game is dynamic (firms move sequentially) the equilibrium concept is subgame perfect Nash equilibrium.13 The idea is that each player has to play a best response after each possible action of the other player and not only after those which were actually played. This concept rules out incredible threats.14 The solution technique is backward induction.
Game Theory
Published in Robert H. Chen, Chelsea Chen, Artificial Intelligence, 2022
In game theory, a subgame is any subset of a game where all members of the subset belong to the subgame that has a single initial node and includes all of its own successor nodes (as shown schematically in the schematic figure at right where there are altogether six subgames, two of which contain two subgames each as enclosed by the ovals).
Online channel strategies under different offline channel power structures for the Belt and Road of China
Published in Maritime Policy & Management, 2020
Xujin Pu, Bowen Ji, Hongfeng Wang
We solve the subgame by using backward induction. For any given wholesale price and retail price , we first characterize the equilibrium foreign retailer margin that would maximize . Then, we determine the wholesale price and the retail price by maximizing . Lemma 2. A unique equilibrium exists for mode . The equilibrium prices and quantities are as follows: Based on the equilibrium solutions, the profit of each supply chain partner can be calculated. In this study, we focus on the Chinese manufacturer’s decisions; thus, we present the Chinese manufacturer’s profit by .
A review of game theory models of lane changing
Published in Transportmetrica A: Transport Science, 2020
Over several decades of exploration and discovery, game theory, especially the conventional two-player, non-cooperative game, has been experimentally tested and verified in a variety of cases (Von Neumann and Morgenstern 1944; Nisan et al. 2007; Camerer 2011). During this period, there have been many strategy solutions with different assumptions. Classic Nash Equilibrium is one of the widely-used methods to find the solution that maximizes individual benefits, which is fit for games with complete information. As people deepen their understanding of GT, some refined solutions were also proposed to solve particular problems. A Bayesian Nash Equilibrium can be applied to games with imperfect information (Harsanyi 1967). A ‘Subgame Perfect Equilibrium’ is usually deployed in sequential games with perfect information (Fudenberg and Levine 1983). A Perfect Bayesian Equilibrium solves for the best solutions in sequential games with imperfect information (Fudenberg and Tirole 1991). These progressive refinements extend conventional theory to adapt to both incomplete information and dynamic scenarios.
Enhancing cyber-physical security in manufacturing through game-theoretic analysis
Published in Cyber-Physical Systems, 2018
Zach DeSmit, Aditya U. Kulkarni, Christian Wernz
The backward induction procedure identifies the SPNE, which is the NE for sequential games. A subgame in an extensive-form game is any subset of the game tree that begins with a node which belongs to a singleton information set. That is, a subset of the game tree can qualify as a subgame only if the player who moves at the start of the subgame can identify the exact subgame they are going to play, and there is no other node in the game tree that belongs to the same information set as the starting node. An SPNE can be defined as follows [49]: