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Principles of Game Theory

In: Workbook for Principles of Microeconomics

Author

Listed:
  • Martin Kolmar

    (University of St. Gallen)

  • Magnus Hoffmann

    (University of St. Gallen)

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. (No entry, Fight) is a Nash equilibrium. 2. (No entry, Concede) is a Nash equilibrium. 3. (Entry, Fight) is a Nash equilibrium. 4. (Entry, Concede) is a Nash equilibrium. Consider the following game in normal form (Table 11.1). 1. Strategy U is dominant for player 1. 2. $$(D,R)$$ ( D , R ) is a Nash equilibrium in this game. 3. $$(U,L)$$ ( U , L ) is a Nash equilibrium in this game. 4. $$(D,R)$$ ( D , R ) is an equilibrium in dominant strategies in this game. Consider the following game in extensive form (Fig. 11.2). 1. The strategy sets of the players are $$S_{1}=\{Y,X\}$$ S 1 = { Y , X } for player 1 and $$S_{2}=\{O,U\}$$ S 2 = { O , U } for player 2. 2. In order to maximize his utility, player 2 will never choose O. 3. This is a simultaneous-move game. 4. The following game in normal form (Table 11.2) has the same Nash equilibrium/equilibria as the former extensive-form game.

Suggested Citation

  • Martin Kolmar & Magnus Hoffmann, 2018. "Principles of Game Theory," Springer Texts in Business and Economics, in: Workbook for Principles of Microeconomics, chapter 11, pages 173-195, Springer.
    • Handle: RePEc:spr:sptchp:978-3-319-62662-8_11
    DOI: 10.1007/978-3-319-62662-8_11
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