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/9780691175218.003.0002
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter explains the distinction between the concepts of “actions” and “policies,” along with the implications of this distinction. An action is defined as a possible move that is available to a ...
More
This chapter explains the distinction between the concepts of “actions” and “policies,” along with the implications of this distinction. An action is defined as a possible move that is available to a player during a game, whereas a policy is a decision rule that a player uses to select actions, based on available information. In game theory, the word “strategy” is commonly inferred to be synonymous to policy. The chapter first illustrates the actions vs. policies distinction by considering a game in marketing known as the advertising campaign game. It then discusses the war of attrition game as an example of a multi-stage game and an open-loop game called zebra in the lake game before concluding with practice exercises related to the Nash equilibrium and a chicken game with alternate play, with their corresponding solutions.Less
This chapter explains the distinction between the concepts of “actions” and “policies,” along with the implications of this distinction. An action is defined as a possible move that is available to a player during a game, whereas a policy is a decision rule that a player uses to select actions, based on available information. In game theory, the word “strategy” is commonly inferred to be synonymous to policy. The chapter first illustrates the actions vs. policies distinction by considering a game in marketing known as the advertising campaign game. It then discusses the war of attrition game as an example of a multi-stage game and an open-loop game called zebra in the lake game before concluding with practice exercises related to the Nash equilibrium and a chicken game with alternate play, with their corresponding solutions.