Trembling Hand Perfect Equilibrium - Definition
Written by Jason Gordon
Updated at December 19th, 2020
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Trembling Hand Perfect Equilibrium Definition
The trembling hand perfect equilibrium, as defined in game theory, is a situation or state that takes into consideration the possibility of an unintended move by a player by mistake. The probability of this type of play occurring is very small, and the decision on using this concept in such a case could be inconclusive. This concept was gotten from a refinement of the Nash equilibrium which was created by German economist Rienhard Selten, and was proposed by John Forbes Nash, Jr, a Nobel Memorial Prize winner in Economic Sciences.
A Little More on What is the Trembling Hand Perfect Equilibrium
This concept, when used in a game of cards, can refer to a playing unintentionally playing the wrong card through error (popularly known as tremble). If a player acknowledges the possibility of an error occurring, they can choose a trembling hand perfect equilibrium that will protect them in case their opponent makes a mistake. Trembling Hand Equilibrium can only be chosen before a move is made, and not after the mistake might have occurred. This concept has many uses in different areas, especially in the macroeconomic theory for economic policy.
References for Trembling Hand Perfect Equilibrium
https://en.wikipedia.org/wiki/Trembling_hand_perfect_equilibriumhttps://www.investopedia.com Economy Economics Behavioral Economicshttps://math.stackexchange.com/questions/.../trembling-hand-perfect-equilibrium
Academic research for Trembling Hand Perfect Equilibrium
The complexity of approximating a trembling hand perfect equilibrium of a multi-player game in strategic form, Etessami, K., Hansen, K. A., Miltersen, P. B., & Srensen, T. B. (2014, September). The complexity of approximating a trembling hand perfect equilibrium of a multi-player game in strategic form. In International Symposium on Algorithmic Game Theory (pp. 231-243). Springer, Berlin, Heidelberg.
Application of trembling-hand perfect equilibrium to Nash nonlinear Grey Bernoulli model: an example of BRIC's GDP forecasting, Hsin, P. H., & Chen, C. I. (2017). Application of trembling-hand perfect equilibrium to Nash nonlinear Grey Bernoulli model: an example of BRICs GDP forecasting. Neural Computing and Applications, 28(1), 269-274.
Multiagent planning with trembling-hand perfect equilibrium in multiagent POMDPs, Yabu, Y., Yokoo, M., & Iwasaki, A. (2007, November). Multiagent planning with trembling-hand perfect equilibrium in multiagent POMDPs. In Pacific Rim International Conference on Multi-Agents (pp. 13-24). Springer, Berlin, Heidelberg.
Forecasting Taiwan's GDP by the novel nash nonlinear grey Bernoulli model with trembling-hand perfect equilibrium, Hsin, P. H. (2013, September). Forecasting Taiwan's GDP by the novel nash nonlinear grey Bernoulli model with trembling-hand perfect equilibrium. In AIP Conference Proceedings (Vol. 1557, No. 1, pp. 224-228). AIP.
Irrational Bidders, the First-price Sealed Auction and Trembling-hand Perfect Equilibrium, Han, Z. G., Wang, W. J., & Qing, L. R. (2013). Irrational Bidders, the First-price Sealed Auction and Trembling-hand Perfect Equilibrium. In Advanced Materials Research (Vol. 601, pp. 432-436). Trans Tech Publications.
The computational complexity of trembling hand perfection and other equilibrium refinements, Hansen, K. A., Miltersen, P. B., & Srensen, T. B. (2010, October). The computational complexity of trembling hand perfection and other equilibrium refinements. In International Symposium on Algorithmic Game Theory (pp. 198-209). Springer, Berlin, Heidelberg.
On the existence of pure-strategy perfect equilibrium in discontinuous games, Carbonell-Nicolau, O. (2011). On the existence of pure-strategy perfect equilibrium in discontinuous games. Games and Economic Behavior, 71(1), 23-48.
The existence of perfect equilibrium in discontinuous games, Carbonell-Nicolau, O. (2011). The existence of perfect equilibrium in discontinuous games. Games, 2(3), 235-256.
The algebraic geometry of perfect and sequential equilibrium, Blume, L. E., & Zame, W. R. (1994). The algebraic geometry of perfect and sequential equilibrium. Econometrica: Journal of the Econometric Society, 783-794.
Are game theoretic concepts suitable negotiation support tools? From Nash equilibrium refinements toward a cognitive concept of rationality, Munier, B. R., & Rullire, J. L. (1993). Are game theoretic concepts suitable negotiation support tools? From Nash equilibrium refinements toward a cognitive concept of rationality. Theory and decision, 34(3), 235-253.