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2020 | OriginalPaper | Buchkapitel

5. Sequence of Moves and the Extensive Form

verfasst von : Manfred J. Holler, Barbara Klose-Ullmann

Erschienen in: Scissors and Rock

Verlag: Springer International Publishing

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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.

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Fußnoten
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).
 
Literatur
Zurück zum Zitat Brams, S. J. (1994). Theory of moves. Cambridge: Cambridge University Press. Brams, S. J. (1994). Theory of moves. Cambridge: Cambridge University Press.
Zurück zum Zitat Brams, S. J. (2011). Game theory and the humanities: Bridging two worlds. Cambridge, Mass., and London: MIT Press. Brams, S. J. (2011). Game theory and the humanities: Bridging two worlds. Cambridge, Mass., and London: MIT Press.
Zurück zum Zitat Brams, S. J., & Wittman, D. (1981). Nonmyopic equilibria in 2×2 games, conflict. Management and Peace Science,6, 39–62. Brams, S. J., & Wittman, D. (1981). Nonmyopic equilibria in 2×2 games, conflict. Management and Peace Science,6, 39–62.
Zurück zum Zitat Camus, A. (1982 [1942]). The outsider. Harmondsworth: Penguin. Camus, A. (1982 [1942]). The outsider. Harmondsworth: Penguin.
Zurück zum Zitat Frahm, G. (2019). Rational choice and strategic conflict: The subjectivistic approach to game and decision theory. Berlin and Boston: De Gruyter.CrossRef Frahm, G. (2019). Rational choice and strategic conflict: The subjectivistic approach to game and decision theory. Berlin and Boston: De Gruyter.CrossRef
Zurück zum Zitat 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.CrossRef 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.CrossRef
Zurück zum Zitat 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. 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.
Zurück zum Zitat van Damme, E. (1987). Stability and perfection of Nash equilibrium. Heidelberg: Springer.CrossRef van Damme, E. (1987). Stability and perfection of Nash equilibrium. Heidelberg: Springer.CrossRef
Zurück zum Zitat Zagare, F. (1984). Limited move equilibria in 2×2 games. Theory and Decision,16, 1–19.CrossRef Zagare, F. (1984). Limited move equilibria in 2×2 games. Theory and Decision,16, 1–19.CrossRef
Metadaten
Titel
Sequence of Moves and the Extensive Form
verfasst von
Manfred J. Holler
Barbara Klose-Ullmann
Copyright-Jahr
2020
Verlag
Springer International Publishing
DOI
https://doi.org/10.1007/978-3-030-44823-3_5

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