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ON THE RELATION BETWEEN PERFECT EQUILIBRIA IN EXTENSIVE FORM GAMES AND PROPER EQUILIBRIA IN NORMAL FORM GAMES

John Hillas

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Abstract

This paper examines the question of the extent to which it is true that any equilibrium that is quasi-perfect in any extensive form game having a given normal form is necessarily proper. If one fixes not only the equilibrium in question but also a sequence of completely mixed strategies converging to that equilibrium then indeed the notions are equivalent. However the stronger result is not true. An example of a normal form game is given in which there is an equilibrium that is quasi-perfect in any extensive form game having that normal form but

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What this paper is about

This paper examines the question of the extent to which it is true that any equilibrium that is quasi-perfect in any extensive form game having a given normal form is necessarily proper. If one fixes not only the equilibrium in question but also a sequence of completely mixed strategies converging to that equilibrium then indeed the notions are equivalent. However the stronger result is not true. An example of a normal form game is given in which there is an equilibrium that is quasi-perfect in any extensive form game having that normal form but

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper examines the question of the extent to which it is true that any equilibrium that is quasi-perfect in any extensive form game having a given normal form is necessarily proper. If one fixes not only the equilibrium in question but also a sequence of completely mixed strategies converging to that equilibrium then indeed the notions are equivalent. However the stronger result is not true. An example of a normal form game is given in which there is an equilibrium that is quasi-perfect in any extensive form game having that normal form but

Key concepts: Mathematical economics, Extensive-form game, Sequential equilibrium, Relation (database), Mathematics, Repeated game, Markov perfect equilibrium, Sequence (biology)

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ON THE RELATION BETWEEN PERFECT EQUILIBRIA IN EXTENSIVE FORM GAMES AND PROPER EQUILIBRIA IN NORMAL FORM GAMES — Research Paper | ScholarLens