If both keep their mouth shut, they would both serve 6 months for a minor crime. Obviously, the optimal choice for both of them would be to keep silent and serve the 6 months. But since they don't know what the other person intends to do, they will both fear that the other one might confess, leaving them to suffer the 10 years. However, the opposing interests is that the wife prefers to go to the ballet while her husband prefers to go to the boxing match.
It is conventional belief that the ability to communicate could never work to a player's disadvantage since a player can always refuse to exercise his right to communicate.
However, refusing to communicate is different from an inability to communicate. The inability to communicate may work to a player's advantage in many cases. An experiment performed by Luce and Raiffa compares what happends when player can communicate and when players cannot communicate.
Luce and Raiffa devised the following game:. If Susan and Bob cannot communicate, then there is no possiblity of threats being made. Both prefer to go to a movie together rather than to go alone. We can represent the situation with the payoff matrix in Table 4.
Not zero-sum. Explain why this is not a zero-sum game. In zero-sum games it is never advantageous to let your opponent know you strategy. Does that property still apply for games like Battle of the Sexes? Announcing a strategy.
Could it be advantageous for a player to announce his or her strategy? Could it be harmful to announce his or her strategy? If possible, describe a scenario in which it would be advantageous to announce a strategy.
If possible, describe a scenario in which it would be harmful to announce a strategy. We might first try to analyze Battle of the Sexes using the same techniques as we used for zero-sum games, For example, we might start as we would in zero-sum games by looking for any equilibrium points. Are there any strategy pairs where players would not want to switch?
Values of equilibrium points. Are the equilibrium points the same in other words, does each player get the same payoff at each equilibrium point? Compare this to what must happen for zero-sum games. Now that we know Battle of the Sexes has two equilibrium points, we should try to find actual strategies for Alice and Bob. Is there a good strategy for each if they play the game only once? What if they repeat the game?
Recall that with zero-sum games, if there was an equilibrium, rational players always want to play it, even if the game is repeated. Does that still seem to work here? Also, how might the ability to communicate change what the players do?
Repeating the game. Suppose the game is played repeatedly. For example, Alice and Bob have movie night once a month. Suggest a strategy for Alice and for Bob. Feel free to play the game with someone from class. Try a playing several times without communicating about your strategy before each game. How could communication affect the choice of strategy?
Now play several times where you are allowed to communicate about your strategy. Does this change your strategy? In the business world, the non-zero sum game concept often reflects expanding markets where individual companies may grow even while losing market share.
Non-zero sum games are best identified on a case-by-case basis. It appears that most complex, real-life interactions are non-zero. Zero sum games seem too exact, symmetrical and simplistic to have dominated modern civilization that has seen so many wide-ranging, positive-sum improvements.
Even the poorest in many lands today enjoy indoor plumbing and refrigeration — provisions absent from royal palaces just a few generations ago!
Since uncertainties in the stock market connote gambling in the minds of some, shareholder transactions have often been viewed as win-lose propositions. Consider this counterexample. Suppose a shareholder sells at a capital gain and has a better use for the funds.
0コメント