Introducing Game Theory: A Graphic Guide (Graphic Guides)

by Ivan Pastine

simply do the best he could from then on.

subgame-perfect Nash equilibrium: players have best responses to each other in each subgame of the original game. Subgame perfection implies that players are forward-looking. They do the best they can at each decision node they encounter without either holding grudges or developing goodwill for past actions.

There are many games where making an early commitment puts a player at a disadvantage.

time-inconsistency problem: the decision maker does not find it optimal to follow the original action plan.

Financial markets often use collateral as a commitment device.

Due to the difficulty of coming up with a commitment device, the poor stay poor, while the rich get richer. Lack of access to credit markets can prevent poor people from being upwardly mobile,

delegate

proliferation solution.

In practice, both delegation and proliferation are used to make retaliation credible and, hence, to ensure that no initial attack is part of a subgame-perfect equilibrium.

a Doomsday Device is only useful as a deterrent if the potential attacker knows of its existence. As soon as it needs to be used, it has already failed its purpose. Hence, there is no reason to keep the existence of such a device secret and every reason to publicize it. Therefore, we can be pretty sure that this is not yet an approach the major superpowers have taken.

players have imperfect information about the game tree:

A manager may have imperfect information about an employee’s habits. If the employee doesn’t make progress in a task, the manager doesn’t know whether to blame the employee or to believe that it’s a particularly difficult task.

scale economic patterns and effects, often study the problem of persistent unemployment, a situation in which there are people who are willing to work but who cannot find a job.

It seems like wages should eventually adjust downward to the point where the number of people who want to work equals the number jobs.

hidden action at the workplace -where the actions of workers are not perfectly observable.

monitor him imperfectly,

In order to encourage workers to work hard, a firm has to give them something to lose if they get caught shirking. It can do this by offering higher wages than workers could get elsewhere. These high efficiency wages can induce efficient output from the workforce.

Since more people will be willing to work at those higher wages and the number of jobs has not gone up, this will result in unemployment.

games of incomplete information, where players are uncertain about the characteristics of the other player and so are uncertain about the payoffs from the possible outcomes of the game.

separating equilibrium, a firm’s choice of warranty depends on the type of its product (high-quality or low-quality). A firm with a high-quality product chooses to offer warranty, but a firm with low-quality product chooses not to.

Advertising works as a signalling device because of a simple cost-benefit analysis. The cost of advertising is the same no matter what quality of product the firm sells. But the benefit from advertising is much higher for a firm producing a high-quality product since new customers will make repeat purchases.

Since membership of the community provides some material benefits, non-believers have an incentive to pretend to be true believers.

the group as a whole may seem irrational even when each member of the group is rational.

Rational decision makers have transitive preferences.

However, even when all group members are rational, group preferences can be non-transitive.

each council member votes for the option that he or she actually prefers, which is referred to as sincere voting.

Every person on the committee has transitive preferences and votes sincerely. But when acting as a group the committee’s preferences are non-transitive – whatever it chooses, the group will always think that another option is better.

“Arrow’s Impossibility Theorem”. It shows that, for groups which are not run by a dictator, there will always be the possibility of some situations where group preferences are non-transitive, where we reject a choice that may be better for everybody or where irrelevant options change our choice. These problems are inherent in group decision making.

Arrow’s Impossibility Theorem shows that, other than autocracy, whatever system we use to decide our best choice as a group, there is always the possibility that the group behaves inconsistently.