Abstract
The chapter discusses the extensive form of a game when sequences of moves may matter. In general, the game tree is an adequate representation of the sequential structure of a game. Using the game tree representation, the implications of missing recall, solutions to sharing a cake, and a sequential form of the Battle of Sexes are analysed. Moves can also be ingredients of thought experiments and backward induction can stabilize strategy choices which do not constitute a Nash equilibrium. This is the message of the Theory of Moves discussed in the concluding section of the chapter.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Holler (2018) contains a larger chapter on second-mover advantages—including theoretical analysis and a bundle of historical cases.
- 2.
The expected value of 1.5 was reached as follows: Considering each of the four events corresponding to the various strategy combinations as equally probable, we multiply the utility values 0, 1, 2, and 3 by the probability ¼ = 0.25 and add the results. Here, we apply the Laplace principle or the “Principle of Insufficient Reason.” The theoretical concept behind such procedure is the expected utility hypothesis which we will study more closely in Chap. 8.
- 3.
Choosing craziness, this is how Hamlet (in the first version of the play) escaped the life-threatening persecution of his father´s murderer.
- 4.
In fact, move is what we see—an action—strategy is the plan.
- 5.
There are many versions of this story. Our version even entered the world of (German language) literature in the form of a quote. See the fiction “Der Egoist” by Helmut Eisendle.
- 6.
Translated and paraphrased by the authors.
- 7.
For a formal analysis of the divide-and-choose mechanism, see van Damme (1987:130ff).
- 8.
There is a recent discussion in Frahm (2019: 314–326).
References
Brams, S. J. (1994). Theory of moves. Cambridge: Cambridge University Press.
Brams, S. J. (2011). Game theory and the humanities: Bridging two worlds. Cambridge, Mass., and London: MIT Press.
Brams, S. J., & Wittman, D. (1981). Nonmyopic equilibria in 2×2 games, conflict. Management and Peace Science,6, 39–62.
Camus, A. (1982 [1942]). The outsider. Harmondsworth: Penguin.
Frahm, G. (2019). Rational choice and strategic conflict: The subjectivistic approach to game and decision theory. Berlin and Boston: De Gruyter.
Holler, M. J. (2018). The economics of the good, the bad, and the ugly: Secrets, desires, and second-mover advantages. London and New York: Routledge.
Strouhal, E. (2000). Schach. Die Kunst des Schachspiels, Hamburg: Nikol Verlagsgesellschaft. An unauthorized reprint of E. Strouhal (1996), 8x8. Die Kunst des Schachspiels, Wien: Springer.
van Damme, E. (1987). Stability and perfection of Nash equilibrium. Heidelberg: Springer.
Zagare, F. (1984). Limited move equilibria in 2×2 games. Theory and Decision,16, 1–19.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Holler, M.J., Klose-Ullmann, B. (2020). Sequence of Moves and the Extensive Form. In: Scissors and Rock. Springer, Cham. https://doi.org/10.1007/978-3-030-44823-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-44823-3_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44822-6
Online ISBN: 978-3-030-44823-3
eBook Packages: Economics and FinanceEconomics and Finance (R0)