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 ...
More
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.
