*The Business Professor*, updated September 20, 2019, last accessed June 4, 2020, https://thebusinessprofessor.com/lesson/trembling-hand-perfect-equilibrium-definition/.

Back to: ECONOMICS, FINANCE, & ACCOUNTING

### 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 E****quilibrium”**

https://en.wikipedia.org/wiki/Trembling_hand_perfect_equilibrium

https://www.investopedia.com › Economy › Economics › Behavioral Economics

https://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., & Sørensen, 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.**

*International Symposium on Algorithmic Game Theory*

### 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 BRIC’s GDP forecasting. ***Neural Computing and Applications***, ***28***(1), 269-274.**

*Neural Computing and Applications*

*28*

### 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.**

*Pacific Rim International Conference on Multi-Agents*

### 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.**

*AIP Conference Proceedings*

### 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.**

*Advanced Materials Research*

### The computational complexity of trembling hand perfection and other equilibrium refinements, **Hansen, K. A., Miltersen, P. B., & Sørensen, 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.**

*International Symposium on Algorithmic Game Theory*

### 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.**

*Games and Economic Behavior*

*71*

### 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.**

*Games*

*2*

### 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.**

*Econometrica: Journal of the Econometric Society*

Are game theoretic concepts suitable negotiation support tools? From Nash equilibrium refinements toward a cognitive concept of rationality, Munier, B. R., & Rullière, 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.