17 - coordination and equilibrium selection

Question 1

what are coordination games

Answer 1

coordination games represnt situations where group of independent agents have common interest in coordinating their actions.

these are games with multiple nash equilibria, where if attained there would be no incentive to deviate

• but challenge is how to coordinate to mutually benefit without communication, it would also require trust

Question 2

what are the 3 types of coordination games

Answer 2

1. pure coordination game
2. mixed motive coordination game
3. coordination game with pareto rankable equilibria

Question 3

what is a pure coordination game

Answer 3

• 2 NE - each is a coordination equilibrium
  both players are indifferent about how to coordinate - both the NE give the same payoffs to each player (1,1)

both players are also indifferent between the discoordination outcomes - both (0,0)

Question 4

what is a mixed motive coordination

Answer 4

• 2 NE (2,1) and (1,2)
• players have opposed preferences over how to coordinate
• but both have a common interest in coordinating
• one player would prefer to cood on left the other would prefer to cood on right
• players have 2 incentives

Question 5

what is a coordination game with pareto rankable equilibria

Answer 5

• 2 pure NE
• both players rank the cood equilibria the same way
  (1,1) or (2,2)
• all players have same view on which equilibria is the best

Question 6

what is the challenge with coordination games

Answer 6

how can they coordinate amongst the multiple equilibria
- how they choose the best one
- no communication

• what e will be reached

Question 7

what does game theory expect from pareto rankable equilibria

Answer 7

• all players have the same view on which of the equilibria are the best
• players should play the pareto dominating equilibria - both maximise payoffs

Question 8

what does game theory expect from pure coordination games

Answer 8

• all players are indifferent between all the equilibria
• game theory provide no reason to choose 1 strategy over another - wont be able to coordinate

Question 9

Cooper et al (1992)

Answer 9

• subjects grouped in cohorts of 11
• each subject players a 2-player game agaisnt every other player in the cohort in random order
• in second phase this process is repeated - so players gain experience

Question 10

cooper et al 1992
coordination game set up

Answer 10

left left righ right
(L,L) and (R,R) = both coordination equilibria

RR is preferred by both players
- but RR is riskier
- by choosing left you are always guaranteed 800, but choosing right when other person chooses left you get 0

Question 11

Cooper et al 1992
findings

Answer 11

• by second phase an equilibrium is always player 0 but L,L not R,R like game theory suggests
• 97% of second phase play L,Lwh

Question 12

what is the aim of
Cooper et al 1992

Answer 12

do disequilibium payoffs matter for which equilirbia is reached

• will subjects choose pareto dominating/pareto inferioir/ not reach an equibrium at all

Question 13

Van Huyck et al 1990
name of game

Answer 13

weakest link game

Question 14

what is a weakest link game

Answer 14

• team
• players choose simultaenously choose effort levels
• output depends on lowest effort of any team member

Question 15

explain Van Huyck
game design

Answer 15

• each player chooses effort level from 1-7
• variable payoff is determined by the lowest effort number chosen by any player in the group
• game played 10 times in constant groups with lowest effort number being announced at the end of each round

Question 16

what is the strat to maximise your own payoff in weakest link game

Answer 16

• match the person that is has the lowest effort levels
• no incentive to put in more effort - because this is costly
• no incentive to put in less than the weakest link - because payoff will decrease
• max payoff by being join weakest link

Question 17

what are the possible equibria in the weakest link game

Answer 17

if choosing effort 1-7
* 7 pure NE - in each all players choose same number as each other
* the E are pareto rankable
* 7,7 dominates - but is risky if the lowest effort in the group in 1

Question 18

Van Huyck aim
1990

Answer 18

• if game repeated which equilibrium will be reached
• will the pareto dominant outcome be reached?

Question 19

Van Huyck

results how are they displayed

Answer 19

• displays the total number of subjects choosing each effort level
• and number of groups (out of 7) in which minimum effort is 1

Question 20

Van Huyck findings

Answer 20

• NE NE not usually attained - because not all group members make the same choice
• as rounds are played - the direction of behaviour change is away from the pareto superior equilibrium and towards the inferior equilibrium
• presence of pareto superiod - doesnt mean it will always be played
• by round 10 - most people put in lowest effort

Question 21

pure coordination
can you coordinate

Answer 21

payoffs dont give a guide on how to coordinate
because players are indifferent between the payoffs
and indifferent between the disequilibrium outcomes

Question 22

what is Schellings hypothesis

Answer 22

labels can facilitate coordination - by making particular ways to play more focal/salient
- draws attention to certain options

hypothesis = people can coordinate with higher frequency than randomising independently

Question 23

what does game theory suggest about labelling

Answer 23

relabelling strategies or presenting them in a different way will not make a difference to how the game is played
- it will not make coordination easier - because coordination determined by payoffs and in this case indifferent between payoffs

Question 24

Mehta, Starmer & Sugden

aim
what did they expect to find

Answer 24

to test schellings hypothesis
* to distinguish between primary salience and reflective salience

Question 25

what is primary salience

Answer 25

• labels make some strategies stand out to individuals even when not trying to coordinate
• unintended coordination in coordination games?

Question 26

what is reflective salience

Answer 26

players use labels deliberately as a tool for coordination
- choose what they think the aggregate will choose

Question 27

Mehta, Starmer & Sugden (1994)

Answer 27

20 questions
- randomly allocated to 1 of 2 groups
* group P = each individual asked all the questions, no game is played, no rewards = get what people will say if they werent trying to coordinate
* group C = each individual asked questions
- each paired at random with another in group C
- score 1 point if your answers match - incentive to coordinate
- at the end get a reward

• calculated and compared coordination index - compare against 1/k

Question 28

why is group
P
C
used for

Answer 28

P = distribution of primarily salient responses
- how successful you would be at coordinating without trying - answer that naturally comes to head

C = coordination game

Question 29

what is the coordination index used in
Mehta Starmer Sugden

Answer 29

= proportion of all possible pairings that subjects gave the same answer

c=1 = all subjects gave same answer
c=0 = none gave the same answer
c = 1/k = every subject chooses each of k possible answers with equal probability

Question 30

how to MSS test schelling hypothesis

Answer 30

• compare c to 1/k in group C = schelling
• compare c to 1/k in group p = unintended coordination
• compare c of groups P and C

Question 31

MSS
findings

Answer 31

• value of c is always greater than 1/k (giving all possible options at equal probability)
• coordination occuring in P
• higher coordination occuring in C

Question 32

MSS
conclusion

Answer 32

• evidence of deliberate use of salient lablels as coordinating devices
• P doesnt explain all of C - labelling plays a part