*ROBERT V. DODGE*

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199857203
- eISBN:
- 9780199932597
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199857203.003.0005
- Subject:
- Economics and Finance, Behavioural Economics

This chapter introduces the most basic game theory tool—the two-by-two matrix—and looks at how to read, construct, and illustrate real-life situations with the simple four-cell box. It uses Sugden's ...
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This chapter introduces the most basic game theory tool—the two-by-two matrix—and looks at how to read, construct, and illustrate real-life situations with the simple four-cell box. It uses Sugden's “banknote game” to demonstrate basic interaction at the simplest level, with two players each having one choice. It shows how the outcome of player's choices can be ranked in order by utility and the simple matrix yields a surprisingly large number of different outcomes, representing many different situations. Sequential and simultaneous plays are also discussed. The chapter introduces Schelling's “staggered” payoffs, then simple instructions teach how to determine the results of games, looking at “dominance” and finding “natural outcomes.” There is a brief introduction to randomization for games without natural outcomes. Pareto efficiency as an evaluation of a game's result is discussed, followed by the construction of a matrix to evaluate a situation. The final two matrix constructions are real life ones: one involving the decision to require hockey helmets in the National Hockey League and the other being the arms race between the U.S. and the Soviet Union. The supplement to this section is a column by Pulitzer Prize winning humorist Dave Barry, presenting his own version of strategy, entitled “How to Win Arguments.”Less

This chapter introduces the most basic game theory tool—the two-by-two matrix—and looks at how to read, construct, and illustrate real-life situations with the simple four-cell box. It uses Sugden's “banknote game” to demonstrate basic interaction at the simplest level, with two players each having one choice. It shows how the outcome of player's choices can be ranked in order by utility and the simple matrix yields a surprisingly large number of different outcomes, representing many different situations. Sequential and simultaneous plays are also discussed. The chapter introduces Schelling's “staggered” payoffs, then simple instructions teach how to determine the results of games, looking at “dominance” and finding “natural outcomes.” There is a brief introduction to randomization for games without natural outcomes. Pareto efficiency as an evaluation of a game's result is discussed, followed by the construction of a matrix to evaluate a situation. The final two matrix constructions are real life ones: one involving the decision to require hockey helmets in the National Hockey League and the other being the arms race between the U.S. and the Soviet Union. The supplement to this section is a column by Pulitzer Prize winning humorist Dave Barry, presenting his own version of strategy, entitled “How to Win Arguments.”

*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.