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

• 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:

Experimental Design

• Constructed environment that models the veto bargaining framework: buyers and sellers
• Sellers want to sell as many widgets as possible
• Buyers have an ideal point X that determines the optimal purchase number of widgets
  • The seller is unaware of the ideal point
  • Both know the distribution from which the ideal point was determined
• Buyer can always "walk away" and not buy anything

Experimental Design

Experimental Design

Experimental Design

Experimental Design

• The buyer's optimal point is drawn from an urn, and the possible draws from the urn are known to both

Experimental Design

• The buyer's optimal point is drawn from an urn, and the possible draws from the urn are known to both

Experimental Design

• The buyer's optimal point is drawn from an urn, and the possible draws from the urn are known to both

Experimental Design

• The buyer's optimal point is drawn from an urn, and the possible draws from the urn are known to both

Experimental Design

• The buyer's optimal point is drawn from an urn, and the possible draws from the urn are known to both

Experimental Design

• The seller is tasked with making an offer that maximizes their payoff, which is contingent on the buyer accepting the offer
  • In delegation treatment, the buyer can offer a menu range of options to buy
  • In take-it-or-leave-it treatment, the buyer can only offer a single point

Experimental Design

• Within-subject
  • Varying distributions for the vetoer

Experimental Design

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles

Experimental Design

• Between-subject

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles

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

Experimental Design

• Between-subject

Chat should bring meaningful improvement to coordination

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles

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

Experimental Design

• Between-subject

Chat shouldn't have much effect, but behaviorally uncertain

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles

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

Experimental Design

• Between-subject

Can chat create efficiency gains enough to reach delegation?

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles

Experimental Design

• Between-subject
• After 15 rounds, instead play against a robot player who simply optimizes response
• Lotteries over the same domain

• Within-subject
  • Varying distributions for the vetoer
  • Changing roles

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

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

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