Nash Equilibrium and The Problem of Indeterminacy

Question 1

Define: Nash Equilibrium

Answer 1

a set of strategies, one for each player, such that each player’s strategy is a best response to the strategies being played by the other players in the game

Question 2

What are the two features of a Nash Equilibrium set of strategies?

Answer 2

these are strategically stable and self-enforcing

Question 3

Can games reach an outcome that is not Nash equilibria?

Answer 3

It is very rare, it would involve at least one player choosing a strategy which did not maximise his/her payoffs, given what is/her opponents are doing. Rational players do not normally do this. It could happen if a player has a clear incentive to select a different strategy.

Question 4

What do you need to do to find the Nash equilibrium?

Answer 4

Assess each cell to see if combination of strategies which generates that outcome is strategically stable and self-enforcing. Remember that Each player must not want to move to another cell, and if they did move their payoffs would be reduced.

Question 5

What is the dominant strategy in a PD Game?

Answer 5

It is not to confess. This can be equated to other defecting strategies in games that have the same structure as a PD game.

Question 6

What is a dominant strategy Nash Equilibrium?

Answer 6

An outcome as the outcome in a PD game. It is a dominant strategy, the strategy that a player would always choose because it always yields higher pay offs regardless of what the other person picks. (Happens in this case because strategies opened to each player are identical). They are also the Nash equilibrium, set of strategies for each player that is best outcome when a player picks this particular strategy. it is a sub concept of Nash Equilibrium.

Question 7

What are the three essential features of a PD Game?

Answer 7

It has 1) two strategies, 2) each player has a dominant strategy which is the same 3) the Nash equilibrium that emerges when both players play their dominant strategy is Pareto inefficient.

Question 8

Give examples of the PD Game in other situations than the two prisoner model

Answer 8

1) Cartel
2) Public Goods
3) Tragedy of the Commons
4) Training

Question 9

Why is a Cartel like a PD game?

Answer 9

Both firms have a dominant strategy which is producing high output. Yet both firms would earn greater profits if they formed a cartel. Neither firm can credibly commit to producing a low level of output. Each firm recognises that ‘High’ is a dominant strategy for its rival.

Question 10

Define: A public good

Answer 10

A public good is a good that is non rivalrous and non excludable, such as street lights.

Question 11

why is providing a public good like a PD game?

Answer 11

Each person’s dominant strategy is to play ‘Don’t contribute’. there exists a dominant strategy Nash equilibrium, namely ‘Don’t contribute, Don’t contribute’. Pareto inefficient outcome in which the public good is under-provided. Free markets will tend to under-provide public goods: rational individuals will attempt to free ride on other people’s contributions to the funding of the public good

Question 12

Define: collective action problem

Answer 12

the aims of an entire society or collective are best served if its members take a particular action, but that action is not in the best private interests of those individuals.

Question 13

Define: The tragedy of the commons

Answer 13

the problem of the over-use of common property resources (e.g. communal grazing lands and lakes, inshore fisheries, the oceans and the internet).

Question 14

Define: Common Property Resource

Answer 14

CPRs are resources whose property rights are held in common and exercised collectively by a group of people. No legal specification on how to use it or maintain it. CPRs are rivalrous.

Question 15

What is externality from over consumption, ie fish stocks?

what is the externality from underinvestment, ie fish stocks?

Answer 15

People ignore fact that their use of a CPR reduces the amount of the resource available for use by others (negative externality). The issue. Marginal Social Cost of using a CPR is greater than the Marginal Private Cost of using a CPR. this results in over-consumption.
people who undertake such investment ignore the external or social benefits of their activities (positive externality) . Marginal Social Benefit of investment is greater than Marginal Private Benefit of investment . this leads to under-investment in CPRs.

Question 16

where is the socially optimum level of consumption? what are the cost of going under or over?

Answer 16

Where the marginal social cost and the marginal social benefit are in equilibrium. going under or over would mean a deadweight loss triangle which represents the welfare loss.

Question 17

How is a common property resource akin to a PD

Answer 17

Each person’s dominant strategy is to play ‘Defect’. This includes over utilizing the resource and failing to invest to upkeep maintenance. There exists a dominant strategy Nash equilibrium, namely ‘Defect, Defect’. Pareto inefficient outcome in which the tragedy of the commons happens.

Question 18

How is training like a PD Game?

Answer 18

If game played only once, both firms have a dominant strategy, namely ‘Don’t train’. there is conflict between individual rationality and collective rationality, with outcome being Pareto inefficient.

Question 19

What is there a problem in regards to the creation of an asset when it comes to training?

Answer 19

This is because the asset created is a skilled workers whom it is impossible to have a property right over. this means other firms can poach the asset without having incurred the costs of training the asset. This fear will mean employers making the investment will discount the return it expects to ear from the investment.

Question 20

Explain the game with two Nash equilibria

Answer 20

Superpower relations after ww2 can be represented by the assurance game. There is no dominant strategy but there is two Nash equilibrium, Refrain,Refrain and Build,Build. The former is Pareto efficient and the other Pareto inferior.

Question 21

explain why is it that there can be multiple nash equilibira to arrive at the problem of indeterminacy

Answer 21

Remember that A Nash equilibrium is a set of strategies that is ‘self-enforcing’ in the sense that, if the players of a game are playing Nash equilibrium strategies, then they have no incentive to change their choice of strategy. Strategically stable because changing the strategy would only reduce the pay off given the strategy picked by the other player. BUT there is no implication that starting from a place of disequilibrium one will emerge as the outcome of the game.

Question 22

Explain the circumstances of a Dominant strategy Nash equilibria.

Answer 22

Dominant strategy Nash equilibria arise when each player of a game play a dominant strategy. single strategy which is a best response to every possible strategy. special case of Nash equilibria. They are a sub set of the concept.

Question 23

what are the main two ways to coordinate players choices so that they can arrive at the same equilibrium?

Answer 23

1. a pre-emptive or strategic move designed to ensure that their preferred equilibrium is achieved (e.g. US could simply pass a constitutional amendment which prohibited it from building nuclear weapons.
2. An equilibrium is a focal point if there is a common understanding amongst the players that, out of all the possible equilibria of a game, it is the obvious one to aim for. There needs to a unique reason why it is obvious and this mutual recognition must be common knowledge.

Question 24

How can focal points arise? Give multiple reasons

Answer 24

A) Narrowly economic reasons, ie the payoffs are clearly greater
B) Social
C) Cultural
D) Historic

Question 25

What is a clear example that focal points in empirical games do occur?

Answer 25

The Paris game. A pure coordination game like the ‘Paris’ game has an infinite number of Nash equilibria, all of which yield the same payoff to each player. The values of the payoffs do not help the players to identify a focal point. Players have the incentive to coordinate and pick the most common place. This is based on common knowledge.

Question 26

What are two examples of pre-emptive moves for the Chicken Game?

Answer 26

1) Cultivating a reputation for toughness that will intimidate rivals into playing ‘Swerve’.
2) Making an irreversible commitment to going on straight. i.e throw the steering wheel out of the window so the other can see, thus restricting ones strategies, and forcing the other, an assumed rational player into a preferred outcome.

Question 27

What are the Two Nash Equilibria if the Chicken Game?

Answer 27

Two Nash equilibria: ‘Swerve, Straight’ (preferred by Dean) and ‘Straight, Swerve’ (preferred by James) – there is a problem of indeterminacy but there is a difference in preference. Their interests are in conflict.

Question 28

Can we always get over the problem of indeterminacy?

Answer 28

No. The battle of the sexes game shows that. It is a one shot game, with no previous communication possible in which the couple wants to watch a film Art or Action. They have to go see it together but one mildly prefers the other. Given the info at our disposable we just don’t know. It may be easier if it was repeated, or if there was specific historical context

Question 29

What is shown by the battle of the sexes pt.2?

Answer 29

This is a dispute between the DVD+RW Alliance who want the DVD+RW standard and the DVD Forum who want the Forum standard as the format. This happened in 2002. They have a preferred format but will make a product so all can handle it. Two Nash equilibria in this game: ‘Forum standard. Forum standard’; and ‘DVD+RW standard, DVD+RW standard’. This is solved by first move advantage. the first who introduces their format onto the market will do better.