Paper Info
Title
New Results on the Existence of Open Loop Nash Equilibria in Discrete Time Dynamic Games
Abstract
We address the problem of finding conditions which guarantee the existence of open-loop Nash equilibria in discrete time dynamic games (DTDGs). The classical approach to DTDGs involves analyzing the problem using optimal control theory which yields results mainly limited to linear-quadratic games. We show the existence of equilibria for a class of DTDGs where the cost function of players admits a quasi-potential function which leads to new results and, in some cases, a generalization of similar results from linear-quadratic games. Our results are obtained by introducing a new formulation for analysing DTDGs using the concept of a conjectured state by the players. In this formulation, the state of the game is modelled as dependent on players. Using this formulation we show that there is an optimisation problem such that the solution of this problem gives an equilibrium of the DTDG. To extend the result for more general games, we modify the DTDG with an additional constraint of consistency of the conjectured state. Any equilibrium of the original game is also an equilibrium of this modified game with consistent conjectures. In the modified game, we show the existence of equilibria for DTDGs where the cost function of players admits a potential function. We end with conditions under which an equilibrium of the game with consistent conjectures is an $\epsilon$-Nash equilibria of the original game.
Year
Venue
Field
2015
CoRR
Mathematical optimization,Mathematical economics,Best response,Repeated game,Equilibrium selection,Game theory,Normal-form game,Symmetric game,Sequential game,Mathematics,Stochastic game
DocType
Volume
Citations 
Journal
abs/1509.03597
0
PageRank 
References 
Authors
0.34
5
2
Name
Order
Citations
PageRank
mathew p abraham100.34
Ankur A. Kulkarni210620.95