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Stay-in-a-set games
Secchi, Piercesare; Sudderth, William D. - In: International Journal of Game Theory 30 (2002) 4, pp. 479-490
There exists a Nash equilibrium (-Nash equilibrium) for every n-person stochastic game with a finite (countable) state space and finite action sets for the players if the payoff to each player i is one when the process of states remains in a given set of states Gi and is zero otherwise.
Persistent link: https://www.econbiz.de/10005598527
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Decision making in dynamic stochastic Cournot games
Kebriaei, Hamed; Rahimi-Kian, Ashkan - In: Mathematics and Computers in Simulation (MATCOM) 81 (2011) 6, pp. 1202-1217
In this paper, the Cournot competition is modeled as a stochastic dynamic game. In the proposed model, a stochastic market price function and stochastic dynamic decision functions of the rivals are considered. Since the optimal decision of a player needs the estimation of the unknown parameters...
Persistent link: https://www.econbiz.de/10011051165
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Understanding Fixed Point Theorems
Arnold, Lutz G. - Wirtschaftswissenschaftliche Fakultät, Universität … - 2003
Fixed point theorems are the standard tool used to prove the existence of equilibria in mathematical economics. This paper shows how to prove a slight generalization of Brouwer's and Kakutani's fixed point theorems using the familiar techniques of drawing and shifting curves in the plane and is,...
Persistent link: https://www.econbiz.de/10005607526
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Classical, Modern, and New Garne Theory
Holler, Manfred J. - In: Journal of Economics and Statistics (Jahrbuecher fuer … 222 (2002) 5, pp. 556-583
This paper is a brief history of game theory with its main theme being the nature of the decision makers assumed in the … what many believe to be progress in game theory. The first stage, classical game theory, is defined by John von Neumann …'s and Oskar Morgenstern's pioneering book "Game Theory and Economic Behaviour" which introduced the concept of individual …
Persistent link: https://www.econbiz.de/10008633413
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Subgame perfect equilibria in stopping games
Mashiah-Yaakovi, Ayala - In: International Journal of Game Theory 43 (2014) 1, pp. 89-135
Stopping games (without simultaneous stopping) are multi-player sequential games in which at every stage one of the players is chosen according to a stochastic process, and that player decides whether to continue the interaction or to stop it, whereby the terminal payoff vector is obtained by...
Persistent link: https://www.econbiz.de/10010993356
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Perfect information two-person zero-sum markov games with imprecise transition probabilities
Chang, Hyeong - In: Computational Statistics 64 (2006) 2, pp. 335-351
Based on an extension of the controlled Markov set-chain model by Kurano et al. (in J Appl Prob 35:293–302, 1998) into competitive two-player game setting, we provide a model of perfect information two-person zero-sum Markov games with imprecise transition probabilities. We define an...
Persistent link: https://www.econbiz.de/10010847476
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Perturbation of linear quadratic systems with jump parameters and hybrid controls
Azouzi, Rachid El; Abbad, Mohammed; Altman, Eitan - In: Computational Statistics 51 (2000) 3, pp. 399-417
We consider the problem of the perturbation of a class of linear-quadratic differential games with piecewise deterministic dynamics, where the changes from one structure (for the dynamics) to another are governed by a finite-state Markov process. Player 1 controls the continuous dynamics,...
Persistent link: https://www.econbiz.de/10010847587
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Pure equilibria in a simple dynamic model of strategic market game
Więcek, Piotr - In: Mathematical Methods of Operations Research 69 (2009) 1, pp. 59-79
We present a discrete model of two-person constant-sum dynamic strategic market game. We show that for every value of discount factor the game with discounted rewards possesses a pure stationary strategy equilibrium. Optimal strategies have some useful properties, such as Lipschitz property and...
Persistent link: https://www.econbiz.de/10010999710
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Perfect information two-person zero-sum markov games with imprecise transition probabilities
Chang, Hyeong - In: Mathematical Methods of Operations Research 64 (2006) 2, pp. 335-351
Based on an extension of the controlled Markov set-chain model by Kurano et al. (in J Appl Prob 35:293–302, 1998) into competitive two-player game setting, we provide a model of perfect information two-person zero-sum Markov games with imprecise transition probabilities. We define an...
Persistent link: https://www.econbiz.de/10010949918
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Perturbation of linear quadratic systems with jump parameters and hybrid controls
Azouzi, Rachid El; Abbad, Mohammed; Altman, Eitan - In: Mathematical Methods of Operations Research 51 (2000) 3, pp. 399-417
We consider the problem of the perturbation of a class of linear-quadratic differential games with piecewise deterministic dynamics, where the changes from one structure (for the dynamics) to another are governed by a finite-state Markov process. Player 1 controls the continuous dynamics,...
Persistent link: https://www.econbiz.de/10010950019