*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/9780691175218.003.0003
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses a number of key concepts for zero-sum matrix games. A zero-sum matrix game is played by two players, each with a finite set of actions. Player 1 wants to minimize the outcome ...
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This chapter discusses a number of key concepts for zero-sum matrix games. A zero-sum matrix game is played by two players, each with a finite set of actions. Player 1 wants to minimize the outcome and Player 2 wants to maximize it. After providing an overview of how zero-sum matrix games are played, the chapter considers the security levels and policies involved and how they can be computed using MATLAB. It then examines the case of a matrix game with alternate play and one with simultaneous play to determine whether rational players will regret their decision to play a security policy. It also describes the saddle-point equilibrium and its relation to the security levels for the two players, as well as the order interchangeability property and computational complexity of a matrix game before concluding with a practice exercise with the corresponding solution and an additional exercise.Less

This chapter discusses a number of key concepts for zero-sum matrix games. A zero-sum matrix game is played by two players, each with a finite set of actions. Player 1 wants to minimize the outcome and Player 2 wants to maximize it. After providing an overview of how zero-sum matrix games are played, the chapter considers the security levels and policies involved and how they can be computed using MATLAB. It then examines the case of a matrix game with alternate play and one with simultaneous play to determine whether rational players will regret their decision to play a security policy. It also describes the saddle-point equilibrium and its relation to the security levels for the two players, as well as the order interchangeability property and computational complexity of a matrix game before concluding with a practice exercise with the corresponding solution and an additional exercise.

*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 ...
More

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.