On forward induction and evolutionary and strategic stability
type: Item
instance of: scholarly article
title: On forward induction and evolutionary and strategic stability
zbMATH Open document ID: 1041.91005
author: Esther Hauk
author: Sjaak Hurkens
published in: Journal of Economic Theory
publication date: 2002-12-16T00:00:00Z
full work available at URL: http://hdl.handle.net/10230/737
review text: The authors study the following model. Let \(G = (E,F,u_1,u_2)\) be a two-person non-zero-sum game with finite players' strategy spaces \(E\) and \(F\), and with players' payoff functions \(u_1\) and \(u_2\), respectively. Let \(G^{0}\) be an {outside option game}, that is the following modification of \(G\): First Player 1 decides between two of his new strategies, ``out'' and ``in''. If he chooses ``out'' the game ends with a payoff vector \((x,y)\) to the players. If Player 1 chooses ``in'' the players play the game \(G\). It is assumed that there exists a {forward induction equilibrium} \(s^*\), which is Player 1's preferred Nash equilibrium in \(G\) satisfying \(u_1(s^*) > x > u_1(s)\) for any other equilibrium \(s\) in \(G\). The paper discusses three properties of the sets of Nash equilibria in outside option game \(G^{0}\). The first result is an example of the game \(G^{0}\) with zero index showing that the outside option component \(M\) for this game (the set of Nash equilibria \((s_1,s_2)\) in \(G^{0}\) with \(s_1(``\text{Out}")>0\)) can be essential. Next, it is shown for the same game that the set \(M\) do not have to be hyperstable. The last result says generally that if the outside option component is an equilibrium evolutionary stable set then the game \(G\) is nongeneric.
Mathematics Subject Classification ID: 91A10
zbMATH DE Number: 1845941
zbMATH Keywords: forward induction equilibrium
zbMATH Keywords: essential set
zbMATH Keywords: hyperstable set
zbMATH Keywords: strategic stability
zbMATH Keywords: EES sets
zbMATH Keywords: index theory
reviewed by: Tadeusz Radzik
MaRDI profile type: Publication
OpenAlex ID: W3121770234
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DOI: 10.1006/JETH.2001.2856
description: scientific article; zbMATH DE number 1845941