Motivation

• Many "bargaining" contexts exist in which a less-informed (about preferences) party must decide what to offer to a more-informed party.
• For the proposers, offering more flexibility may result in the other party selecting a less favorable outcome... although not as bad as when their proposal is outright rejected.

Motivation

• Many "bargaining" contexts exist in which a less-informed (about preferences) party must decide what to offer to a more-informed party.
• For the proposers, offering more flexibility may result in the other party selecting a less favorable outcome... although not as bad as when their proposal is outright rejected.
• This bargaining environment takes many forms:

Motivation

Motivation

Manager prefers more work from office

Could enforce this as policy

Do they risk poor alignment with employees?

Motivation

Employee prefers to work from home

What leverage do they have?

Outside option?

Motivation

Manager can propose

• Range of options: "You can work from home up to 4 days a month."
  • Fully deferential: "Employees can choose how often they work from home."
• Take-it-or-leave-it: "Our policy is that everyone works from home on Fridays."
  • Fully restrictive: "We do not allow employees to work from home."

Motivation

Motivation

Employee can

• Accept from the range of options
• Accept the take-it-or-leave-it

• Veto these choices and seek an outside option: "I quit!"

Motivation

Motivation

???

Manager bargains without knowing existing alignment

Motivation

Manager bargains without knowing existing alignment

Employee can always veto (very bad for the manager)

Literature

Literature

Literature

Theory

Theory

0

1

Theory

Proposer

0

1

Theory

v

Vetoer

0

1

Theory

v

???

0

1

Theory

v

???

0

1

Theory

v

Status quo

Theory

v

Status quo

Theory

v

Status quo

Theory

Status quo

Full Delegation

v

Theory

Status quo

No Compromise

v

Theory

Status quo

Interval Delegation

v

Theory

Status quo

Interval Delegation

v

Theory

Status quo

Interval Delegation

v

Theory

Theory

The vetoer is drawn from a distribution on the interval

Theory

The vetoer is drawn from a distribution on the interval

Theory

Status quo

v

Theory

Status quo

v

Theory

Status quo

v

Full Delegation

Optimal if:

• Sufficiently risk-averse
• Density type is decreasing

Theory

Status quo

v

No Compromise

Optimal if:

• Vetoer density increasing

Theory

Status quo

v

Interval Delegation

Optimal if:

• Unimodal distribution and linear loss utility

Theory

Status quo

v

Interval Delegation

Comparative statics

c*

Theory

Status quo

v

Interval Delegation

Comparative statics

• Discretion ↑ in risk aversion

c*

Theory

Status quo

v

Interval Delegation

Comparative statics

• Discretion ↑ in risk aversion
• Discretion ↓ in ex ante alignment

c*

Theory

Status quo

v

Interval Delegation

c*

Theory

Status quo

v

Take-it-or-leave-it

c*

Theory

Status quo

v

Take-it-or-leave-it

c*

Strictly worse off

Theory

Status quo

v

Take-it-or-leave-it

c*

Strictly worse off

May be worse off

Theory

Status quo

v

Take-it-or-leave-it

c*

Strictly worse off

May be worse off

or better off

Theory

Status quo

v

Interval Delegation

c*

Theory

Status quo

v

Interval Delegation

c*

Acquiesce

Veto Threat

Theory

Status quo

v

Interval Delegation

c*

Acquiesce

Veto Threat

Theory

Status quo

v

Interval Delegation

c*

Acquiesce

Veto Threat

Optimal delegation allows for fewer veto results for the proposer than under cheap talk

Theory

Status quo

v

c*

Acquiesce

Veto Threat

Take-it-or-leave-it

Theory

Status quo

v

c*

Acquiesce

Veto Threat

Take-it-or-leave-it

Under take-it-or-leave-it, closer alignment can be achieved with cheap talk

Theory

• Full delegation optimal if proposer is sufficiently risk-averse and/or distribution of vetoer is decreasing on the interval

Theory

• Full delegation optimal if proposer is sufficiently risk-averse and/or distribution of vetoer is decreasing on the interval
• No delegation optimal if distribution of vetoer is increasing on the interval

Theory

• Full delegation optimal if proposer is sufficiently risk-averse and/or distribution of vetoer is decreasing on the interval
• No delegation optimal if distribution of vetoer is increasing on the interval
• The optimal interval is increasing in risk aversion and decreasing in higher ex-ante alignment

Theory

• Full delegation optimal if proposer is sufficiently risk-averse and/or distribution of vetoer is decreasing on the interval
• No delegation optimal if distribution of vetoer is increasing on the interval
• The optimal interval is increasing in risk aversion and decreasing in higher ex-ante alignment
• Take-it-or-leave-it is strictly worse for proposer and often worse for both

Theory

• Full delegation optimal if proposer is sufficiently risk-averse and/or distribution of vetoer is decreasing on the interval
• No delegation optimal if distribution of vetoer is increasing on the interval
  
• The optimal interval is increasing in risk aversion and decreasing in higher ex-ante alignment
• Take-it-or-leave-it is strictly worse for proposer and often worse for both
• Cheap talk does little for interval delegation but generates efficiency gains for take-it-or-leave-it

Experimental Design

• Constructed environment that models the veto bargaining framework

Experimental Design

• Constructed environment that models the veto bargaining framework

0

Experimental Design

• Constructed environment that models the veto bargaining framework
  • Fix Proposer's optimal point at 25 (max of the domain)

25

0

Experimental Design

• Constructed environment that models the veto bargaining framework
  • Fix Proposer's optimal point at 25 (max of the domain)
  • Linear loss and raise all payoffs by $5

25

30

0

Experimental Design

• Constructed environment that models the veto bargaining framework
  • Fix Proposer's optimal point at 25 (max of the domain)
  • Linear loss and raise all payoffs by $5

25

30

5

0

Experimental Design

• Constructed environment that models the veto bargaining framework
  • Give vetoer linear loss

25

0

25

10

Experimental Design

• Constructed environment that models the veto bargaining framework
  • Give vetoer linear loss
  • Always have the option to reject (select the "0" option)

25

0

25

10

15

Experimental Design

• Constructed environment that models the veto bargaining framework
  • Give vetoer linear loss
  • Always have the option to reject (select the "0" option)
  • Vary the optimal point

25

0

25

5

20

Experimental Design

• Constructed environment that models the veto bargaining framework
  • Give vetoer linear loss
  • Always have the option to reject (select the "0" option)
  • Vary the optimal point

25

0

25

20

5

Experimental Design

• Constructed environment that models the veto bargaining framework
  • Give vetoer linear loss
  • Always have the option to reject (select the "0" option)
  • Vary the optimal point

25

0

25

10

15

Experimental Design

• Within-subject
  • Varying distributions for the vetoer

Experimental Design

• Within-subject
  • Varying distributions for the vetoer

6

11

17

Experimental Design

• Within-subject
  • Varying distributions for the vetoer

6

11

17

Experimental Design

• Within-subject
  • Varying distributions for the vetoer

6

11

17

Experimental Design

• Within-subject
  • Varying distributions for the vetoer

6

11

17

Experimental Design

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Experimental Design

• Between-subject

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Experimental Design

Experimental Design

• Proposer can make a single point offer
• Vetoer must decide to accept or veto

Experimental Design

• Proposer can make a single point offer
• Vetoer must decide to accept or veto
• Participants can coordinate in advance of decisions

Experimental Design

• Proposer can offer a range of choices for the vetoer to consider
• Vetoer can accept any of the options, or veto

Experimental Design

• Proposer can offer a range of choices for the vetoer to consider
• Vetoer can accept any of the options, or veto
• Participants can coordinate in advance of decisions

Experimental Design

• Between-subject

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Experimental Design

• Between-subject

Chat should bring meaningful improvement to coordination

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Experimental Design

• Between-subject

Chat should bring meaningful improvement to coordination

           Over-revealing vetoers?

           Over-credulous proposers?

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Experimental Design

• Between-subject

Chat shouldn't have much effect, but behaviorally uncertain

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Experimental Design

• Between-subject

Chat shouldn't have much effect, but behaviorally uncertain

          High types see no benefit

       Appeals to other regarding?

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Experimental Design

• Between-subject

Can chat create efficiency gains enough to reach delegation?

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Experimental Design

• Between-subject

• Design captures
  • Alignment with qualitative predictions
  • Efficiencies
  • Delegation leniency
  • Differences across distributions

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Experimental Design

• Between-subject

• Design captures
  • Alignment with qualitative predictions
  • Efficiencies
  • Delegation leniency
  • Differences across distributions

• Other information to collect
  • Other regarding behavior (dictator game)
  • Cognitive abilities
  • Risk aversion

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles (more on this later)

Design Challenges

Design Challenges

Five phases of the current design

1. 10 rounds repeated in one role
2. Switch to other role and play 10 more
3. Play 3 rounds against a robot player
4. Lotteries within the same domain as the game
5. Dictator, cognition, and questionnaire

Design Challenges

1. 10 rounds repeated in one role
2. Switch to other role and play 10 more
3. Play 3 rounds against a robot player
4. Lotteries within the same domain as the game
5. Dictator, cognition, and questionnaire

Design Challenges

• Key area of focus is the single or range offer made by the Proposer
• Learning effects
• Is there a difference between AB and BA players?

1. 10 rounds repeated in one role
2. Switch to other role and play 10 more
3. Play 3 rounds against a robot player
4. Lotteries within the same domain as the game
5. Dictator, cognition, and questionnaire

Design Challenges

1. 10 rounds repeated in one role
2. Switch to other role and play 10 more
3. Play 3 rounds against a robot player
4. Lotteries within the same domain as the game
5. Dictator, cognition, and questionnaire

Design Challenges

• All players take the role of proposer
• Vetoer will respond by simple best response rule
• Proposer no longer needs to consider vetoer as another player

1. 10 rounds repeated in one role
2. Switch to other role and play 10 more
3. Play 3 rounds against a robot player
4. Lotteries within the same domain as the game
5. Dictator, cognition, and questionnaire

Design Challenges

1. 10 rounds repeated in one role
2. Switch to other role and play 10 more
3. Play 3 rounds against a robot player
4. Lotteries within the same domain as the game
5. Dictator, cognition, and questionnaire

Design Challenges

• Players continue to face a robotic response rule
• Fix the delegation cutoff at 10
• Vary the 3 distributions and give players the probability of non-veto result
• Elicit certainty equivalent to not play against the robot

1. 10 rounds repeated in one role
2. Switch to other role and play 10 more
3. Play 3 rounds against a robot player
4. Lotteries within the same domain as the game
5. Dictator, cognition, and questionnaire