7. Quantal Response Equilibrium

Question 1

Describe the travellers dilemma

Answer 1

-two travellers have lost their baggage
-airline asks then to simultaneously name its value between 80-200
-both get compensated by lower amount of the two amounts
-the one with higher value is assumed to lie and pays fine of R>1 to other traveller

Question 2

What is the standard prediction of the travellers dilemma?

Answer 2

Both choose 80

Question 3

How does a greater fine effect the results of the travellers dilemma in the literature?

Answer 3

-Capri Et al 1999 finds higher R causes people to choose lower values. When R is higher people reduce their valuation in repeated rounds

Question 4

Possible explanations for why people choose low numbers when fine is high in travellers dilemma

Answer 4

-Fairness. If inequality aversion is strong, all equal numbers can be equilibria
-if fine is low it’s not expensive to choose high number but it is expensive to choose low number

Question 5

Quantal response equilibrium

Answer 5

The assumption that rationality is common knowledge is replaced with the assumption that a specific form of bounded rationality is common knowledge.
A QRE is a statistical version of NE where players’ utility for each action is subject to a random error

Question 6

What are the two types of monotonicity that reaction functions display?

Answer 6

1. Choice probabilities of an action increase in expected payoffs to the action
2. For any player and any pair of that players strategies, the strategy with the higher expected payoff is chosen with higher probability.
   This implies that better actions are more likely to be chosen than worse ones

Question 7

How is lambda related to the level of error?

Answer 7

It is inversely related to the level of error. If lambda=0 the action only consists of error and if lambda= infinity there is no error

Question 8

How can the set of LQRE be characterised as a function of lambda?

Answer 8

When lambda=0 the unique solution has each action being chosen with equal probability. When lambda= infinity the LQRE converges to NE

Question 9

What is the own payoff effect?

Answer 9

The fact that chosen probabilities are dependent on the probabilities chosen by the other player. This shouldn’t occur but it does

Question 10

In the public good games what does an increase in m or w or a decrease in lambda lead to?

Answer 10

Stochastic increase in contributions

Question 11

In public goods game how does an increase in number of players affect contributions?

Answer 11

Doesn’t affect contributions

Question 12

How is the predicted effect of m and n on contributions supported by experimental evidence?

Answer 12

M is supported by experimental evidence. Prediction for n is less supoorted

Question 13

If players display altruism and warm glow what does an increase in n do?

Answer 13

Altruism leads to a stochastic increase in contributions. No effect of n with warm glow alone. Other effects quantitatively unaffected

Question 14

Summary and limits of QRE?

Answer 14

-fits data well in many experiments
-however, how informative is fit? Varying the error distribution gives considerable flexibility to QRE and allows for almost any prediction
-in LQRE the parameter lambda plays a crucial role in determining predictions. What determines lambda? Is it stable across games? Over time?
-QRE reasoning cognitively taxing (Crawford Et al 2013): is it a plausible model of limited strategic thinking?

Question 15

Findings of Isaac & Walker 1988

Answer 15

Group size doesn’t matter much to contributions but marginal returns (size of m) does determine contributions to public good. Holds over 10 rounds.