Behavioural Economics Final Exam

Nash Equilibrium

A list of strategies (one for each player for each possible decision) which has the property that no player can unilaterally change his strategy to get a better payoff

Nash Equilibrium in the Beauty Contest Game

= 0

Pure Coordination Game

Only focus is on coordination, it doesn’t matter on what you coordinate

Coordination Game with Pareto-Ranked Nash Equilibrium

It is better for everyone of you coordinate on a specific equilibria

Dominated Strategies

Choices that are always worse than another choice, regardless of what others do i.e. you would never play a dominated strategy

Iterated Elimination of Dominated Strategies

A method to simplify games by repeatedly removing strategies that are strictly worse for a rational player until no strategies can be removed, revealing potential equilibria

D-k

A way of classifying Types (Strategies)

A person is D-0 if they never play a dominated strategy but sometimes play a one-step eliminated strategy

A person in D-k if they never play a D-k strategy but sometimes play a D-k+1 strategy

Level-k

Behavioural Types

Type L-0 chooses naively and randomly

Type L-1 thinks that all others will be type L-0

Type L-k thinks that all others will be L-k-1

D-k vs Level-k

Different Behavioural Assumptions

D-k is more about eliminating “dumb” moves whereas L-k is more about how best to respond to beliefs about others behaviour

Cognitive hierarchy

Similar to level-k but allows for distribution of lower levels

Sophisticated beliefs

A level-k thinker is naive in believing that everyone is one level lower than them

A sophisticated type has correct beliefs about what others will do including other sophisticated types

Coordination and multiple equilibria

Focal points may help to coordinate

Context dependent

Many possible answers to coordinate = multiple equilibria

Primary Salience Hypothesis

We all choose out favourite answer and coordinate by ‘accident’

Secondary Salience Hypothesis

People expect others to use primary salience and so coordinate by choosing what they think will be others’ favourite answers

Schelling Salience Hypothesis

We ignore what is favourite and focus on uncovering the clue how to coordinate

Multiple Nash Equilibria

Which focal point to choose?

Equilibrium Refinement

A ways of Eli igniting equilibria that seem unintuitive

Many or no equilibria may pass the refinement

Equilibrium Selection

A way of selecting unique equilibria

May rule out ‘sensible’ equilibria

Pareto Dominant Nash Equilibria

Gives everyone a higher payoff than any other equilibrium

Risk Dominant Nash Equilibria

Each person chooses the strategy that maximises their payoff given maximal uncertainty about what others will do

Battle-of-the-Sexes

A coordination game with conflict of interest

Different people have different preferences over which equilibria they want to coordinate on

Backward Induction

In the battle-of-the-sexes game, when played sequentially, only one equilibrium survives - revealing a unique subgame-perfect Nash equilibrium

Weakest-link / minimum effort game

Everyone chooses an effort level, and the lowest effort of anyone in the group determines the outcome

Nash Equilibria in the Weakest-link game

There are multiple Nash equilibria in this game, where the best strategy for an individual is to match the minimum effort of the group

The Turnaround Game (of the weakest-link game)

Incentives, communication and growing the group overtime improves outcomes in the weakest link game

Threshold Public Good Games

A public good will be provided if and only if people collectively give enough to finance the good

Nash Equilibria in Public Goods Games

Multiple Nash Equilibria

e.g. £125 needed to finance a TV for a group of 5

Nash Equilibrium when all pay £25

Also when one pays £5 and four pay £30 each

Can create conflict of interest in the group

Problems in Public Good Games

Conflicts of interest due to multiple Nash equilibria

Frequent failures of coordination

The institution matters for the success rate

Decision-making in teams

Games within teams and between teams

Teams are better at coordination

Teams can outperform individuals and be more sophisticated

Teams are no better at simple/complex tasks

Teams are no better at judgemental tasks

Auctions

Common way to sell goods at individual, company and government levels

English Auctions

Private

Start low and bud up until only one bidder is left

Dutch Auction

Public Auction

Start with high price and lower until a bidder offers to buy at that price

First Price Sealed Bid

Bidders simultaneously submit private bids

The highest bidder wins

Second Price Sealed Bid

Bidders simultaneously submit private bids. The highest bidder wins but pays at the price of the second highest bidder

Independent Private Value Auctions

Most Simple Auction model

Independent: One person’s valuation of the item is independent from another’s

Private Value: People value the item differently; a person knows their own value, not that of others

Revenue Equivalence

In an IPV auction, the expected revenue for the auctioneer is the same for all four auction formats

Failures of Revenue Equivalence

In the sale of ‘magic cards’ revenue equivalence fails

Common Value Auctions

Common Value Auctions

All bidders value the item the same

But the bidders do not know this value precisely

They only have an imperfect private signal of the value

The Winner’s Curse

The winner likely has the highest estimate of the value, which will be too optimistic

Therefore, the person who wins the auction often pays more than the value of the item

Acquiring a Company/Bike Game

Equation to calculate expected profit of acquiring an item based on how much you value the item, the actual value of the item and the price you offer

Empirically, bidders will overbid and lose money

Due to failures of contingent reasoning

The Dictator Game

£10 with proposer, who is asked how much they want to give to the receiver

Receiver gets what they are given by the proposer

Advantages of the Dictator Game

Simple, intuitive, non-strategic

Disadvantages of the Dictator Game

When do people give in this way?

Data from the Dictator Gam e

Consistent with social-preferences rather than self-interest

The Trust Game

£10 with proposer who is asked how much they would give to the receiver

This amount is triples and given to the receiver

Receiver decides how much to give back to the proper and keeps the rest

Advantages of the Trust Game

Simple, strategic interaction about trust

Data from the Trust Game

Lots of trust i.e. substantial amounts given to the receiver and given back to the sender

The Ultimatum Game

£10 with proposer who is asked how much they wish to give to the receiver

The receiver can wither accept or reject the offer

If rejected, both get £0

Advantages of the Ultimatum Game

Stylised bargaining

Data from Ultimatum Games

Unfair offers frequently rejected

Many fair offers

Ultimatum Games with Competition

Many proposers have £10

The receiver sees the best offer and then either accepts or rejects

Advantages of Ultimatum games with competition

Shows the effect of competition on pro-social behaviour

Data from Ultimatum Games with Competition

Offers are much more favourable to the receiver with competition

Receiver’s don’t mind accepting “unfair” offers

Gift Exchange Games

£10 with proposer who sends a wage to receivers

Receiver decides how much effort to put in

Effort is costly to the receiver but beneficial to the proposer, increasing profits more than it costs to the receiver

Advantages of Gift Exchange

Stylised labour market

Data from gift exchange game

High wages = high effort

Repeated interaction increases effort

Dictator Game with Punishment

£10 to proposer who is asked how much they would like to give to the receiver

Receiver gets this amount and the proposer keeps the rest

A third party observers how much the proposer gives to the receiver and for every £1 the punisher pays, they can reduce the payoff of the proposer by £3

Advantages of the Dictator Game with Punishment

The punisher can enforce social norms

Disadvantages of the Dictator Game with Punishment

Punishment is costly to the punisher

Who punishes the punisher?

Data from Dictator Games with Punishment

Lots of punishment - unfair offers are costly for the proposer

Public Goods Games with Punishment

Each member of the group is given £20

Any contribution is x1.6 and then split every between the group

Each member sees the contribution of others and for every £1 they spend they can reduce the payoff of another by £3

Advantages of Public Good Games with Punishment

Is cooperation sustainable in larger groups?

Is punishment needed and helpful?

Data from Public Good Games with Punishment

Individuals have an incentive to stop contributing as their own return from the public good is always less than the cost of contributing

Contributions decrease over time but punishment can sustain cooperation

Partner Matching increases contributions

The Moonlighting Game

Proposer and receiver are given £10 each

The proposer can invest money with the receiver or take money from the receiver

Amount sent to the receiver is tripled

Receiver can return money to the proposer or punish the proposer by taking money away

Advantages of the moonlighting game

Most flexible game format - Trust, punishment and reward in one format

Data from the Moonlighting Game

Reciprocity - trusting behaviour rewarded and betrayal was punished

Intentions matter - if the proposers choices are generated randomly, the receivers do not respond

Teams in Trust and Ultimatum Games

Teams offer, invest and return less in all game formats

Summary of Evidence

Some social preferences rather than self-interest

Strategic concerns matter

• Receiver effect in ultimatum games

• Punishment increases cooperation

• Repeated interaction increases cooperation

Reciprocity Matters

• Positive reciprocity

• Negative reciprocity

• Strong reciprocity - many are both positive and negatively reciprocal

• Indirect reciprocity - 3rd parties punish non-cooperation

Rational but not selfish behaviour

Self Interest

U_i = U_i(u_i)

Simple Altruism

U_i = U_i(u_i, u_-i)

Where does Simple Altruism Model Hold?

Dictator Games

Fehr-Schmidt Model

A way of modelling inequality aversion that takes into account how a person may dislike earning more or less than others

Fehr-Schmidt Equation

U_i = u_i - amax(u_j - u_i, 0) - bmax(u_i - u_j, 0)

Intentions and Social Norms

Models of inequality aversion simply assumes people do not like inequality

But people care about the source of inequality i.e. intentions matter

Intentions are judges relative to something - social reference points and social norms

Mini Ultimatum Game

Restricts the prospers choice to two options

This changes the acceptance rate of lower offers

Property Rights and Fairness

Framing and the generation of endowment matters for dictators giving

Plausible Deniability and Audience Effects

If there is a chance that the dictator is forces to give 0, many dictators will choose to give 0

Moral wiggle Room

When one offer out of a choice between two is hidden, proposers will choose to keep the second hidden and choose the higher payoff for them

Reciprocity and intentions are …

Important for pro-social behaviour

Gift exchange in the labour market