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Principles of Game Theory

  • Martin Kolmar
  • Magnus Hoffmann
Chapter
Part of the Springer Texts in Business and Economics book series (STBE)

Abstract

Consider the following sequential game (Fig. 11.1).

Player 1 has the strategies {No entry, Entry}, while player 2 has the strategies {Fight, Concede}.
  1. 1.

    (No entry, Fight) is a Nash equilibrium.

     
  2. 2.

    (No entry, Concede) is a Nash equilibrium.

     
  3. 3.

    (Entry, Fight) is a Nash equilibrium.

     
  4. 4.

    (Entry, Concede) is a Nash equilibrium.

     

Consider the following game in normal form (Table 11.1).

  1. 1.

    Strategy U is dominant for player 1.

     
  2. 2.

    \((D,R)\) is a Nash equilibrium in this game.

     
  3. 3.

    \((U,L)\) is a Nash equilibrium in this game.

     
  4. 4.

    \((D,R)\) is an equilibrium in dominant strategies in this game.

     

Consider the following game in extensive form (Fig. 11.2).

  1. 1.

    The strategy sets of the players are \(S_{1}=\{Y,X\}\) for player 1 and \(S_{2}=\{O,U\}\) for player 2.

     
  2. 2.

    In order to maximize his utility, player 2 will never choose O.

     
  3. 3.

    This is a simultaneous-move game.

     
  4. 4.

    The following game in normal form (Table 11.2) has the same Nash equilibrium/equilibria as the former extensive-form game.

     

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Martin Kolmar
    • 1
  • Magnus Hoffmann
    • 1
  1. 1.School of EconomicsUniversity of St. GallenSt. GallenSwitzerland

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