Ken Binmore
- Published in print:
- 2007
- Published Online:
- May 2007
- ISBN:
- 9780195300574
- eISBN:
- 9780199783748
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195300574.003.0005
- Subject:
- Economics and Finance, Microeconomics
This chapter consolidates the ideas necessary to understand the strategic form of a game. Payoff functions are introduced, and strategic forms of versions of Duel and Russian Roulette illustrate the ...
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This chapter consolidates the ideas necessary to understand the strategic form of a game. Payoff functions are introduced, and strategic forms of versions of Duel and Russian Roulette illustrate the idea. Matrices and vectors are reviewed because of their use with payoff matrices. Strong and weak domination are defined. The iterated deletion of dominated strategies is illustrated using the game of Duel. The iterated deletion of dominated strategies is related to backward induction. Problems of credibility and commitment are discussed in the context of subgame-perfect equilibria in simple Cournot and Stackelberg games. The application of subgame-perfect equilibria is discussed when players may only be boundedly rational.Less
This chapter consolidates the ideas necessary to understand the strategic form of a game. Payoff functions are introduced, and strategic forms of versions of Duel and Russian Roulette illustrate the idea. Matrices and vectors are reviewed because of their use with payoff matrices. Strong and weak domination are defined. The iterated deletion of dominated strategies is illustrated using the game of Duel. The iterated deletion of dominated strategies is related to backward induction. Problems of credibility and commitment are discussed in the context of subgame-perfect equilibria in simple Cournot and Stackelberg games. The application of subgame-perfect equilibria is discussed when players may only be boundedly rational.
João P. Hespanha
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175218
- eISBN:
- 9781400885442
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175218.003.0009
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter defines a number of key concepts for non-zero-sum games involving two players. It begins by considering a two-player game G in which two players P₁ and P₂ are allowed to select policies ...
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This chapter defines a number of key concepts for non-zero-sum games involving two players. It begins by considering a two-player game G in which two players P₁ and P₂ are allowed to select policies within action spaces Γ₁ and Γ₂, respectively. Each player wants to minimize their own outcome, and does not care about the outcome of the other player. The chapter proceeds by discussing the security policy and Nash equilibrium for two-player non-zero-sum games, bimatrix games, admissible Nash equilibrium, and mixed policy. It also explores the order interchangeability property for Nash equilibria in best-response equivalent games before concluding with practice exercises and their corresponding solutions, along with additional exercises.Less
This chapter defines a number of key concepts for non-zero-sum games involving two players. It begins by considering a two-player game G in which two players P₁ and P₂ are allowed to select policies within action spaces Γ₁ and Γ₂, respectively. Each player wants to minimize their own outcome, and does not care about the outcome of the other player. The chapter proceeds by discussing the security policy and Nash equilibrium for two-player non-zero-sum games, bimatrix games, admissible Nash equilibrium, and mixed policy. It also explores the order interchangeability property for Nash equilibria in best-response equivalent games before concluding with practice exercises and their corresponding solutions, along with additional exercises.
João P. Hespanha
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175218
- eISBN:
- 9781400885442
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175218.003.0010
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter discusses the computation of the Nash equilibrium for bimatrix games. It begins by considering a different version of the battle of the sexes game introduced in Chapter 9, in which ...
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This chapter discusses the computation of the Nash equilibrium for bimatrix games. It begins by considering a different version of the battle of the sexes game introduced in Chapter 9, in which action 1 corresponds to going to the baby shower and action 2 to the football game. In this new version no one really wants to go to the football game alone (cost of 3), but going to the baby shower alone is a little better (cost of 0). After finding the mixed Nash equilibrium for this case, the chapter describes the computation of a completely mixed Nash equilibrium and the numerical computation of a mixed Nash equilibrium. It concludes with a practice exercise and the corresponding solution, along with an additional exercise.Less
This chapter discusses the computation of the Nash equilibrium for bimatrix games. It begins by considering a different version of the battle of the sexes game introduced in Chapter 9, in which action 1 corresponds to going to the baby shower and action 2 to the football game. In this new version no one really wants to go to the football game alone (cost of 3), but going to the baby shower alone is a little better (cost of 0). After finding the mixed Nash equilibrium for this case, the chapter describes the computation of a completely mixed Nash equilibrium and the numerical computation of a mixed Nash equilibrium. It concludes with a practice exercise and the corresponding solution, along with an additional exercise.
