Veto Power, Delegation and Mechanism Design

Brandon Williams

Alistair Wilson

Richard Van Weelden

Caltech Behavioral/Experimental Workshop

June 20, 2025

Motivation

  • Many "bargaining" contexts exist in which a less-informed party must decide what to offer to a more-informed party, who hold veto power

Motivation

  • Many "bargaining" contexts exist in which a less-informed party must decide what to offer to a more-informed party, who hold veto power

Motivation

  • Many "bargaining" contexts exist in which a less-informed party must decide what to offer to a more-informed party, who hold veto power

 

 

 

 

 

  • The proposers might have a choice:
    • Try to coordinate to gain information from the other party
    • Offer a range of options that concedes some agenda-setting power, but internalizes conflict in the mechanism

Literature

Models of similar bargaining forms have been proposed in theory...

  • Under complete information - Romer and Rosenthal (1978)   
  • Under cheap talk negotiation - Matthews (1989)
  • With valuable expertise involved - Holmström (1977)
  • More recently: Kartik, Kleiner, Van Weelden (2021)

 

And used in experiments...

  • Early bargaining - e.g. Roth and Murnighan (1980, 1982)
  • Vetoes within committees - Kagel, Sung, and Winter (2010)
  • Multiple rounds of bargaining - Nunnari (2021)

 

More recently: Kartik, Kleiner, Van Weelden (2021)

Theory

 

More recently: Kartik, Kleiner, Van Weelden (2021)

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

The vetoer differs in ex ante alignment, which changes bargaining power

Theory

The vetoer differs in ex ante alignment, which changes bargaining power

Theory

The vetoer differs in ex ante alignment, which changes bargaining power

Theory

Status quo

v

Theory

Status quo

v

Theory

Status quo

v

Full Delegation

Optimal if:

  • Sufficiently risk-averse
  • Lower bargaining power

Theory

Status quo

v

No Compromise

Optimal if:

  • Higher bargaining power

Theory

Status quo

v

Interval Delegation

Optimal if:

  • Bargaining power lies in between

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

  • Delegation ↑ in risk aversion
  • Delegation ↓ in bargaining power

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

a_I^*

Theory

Status quo

v

Interval Delegation

c*

Acquiesce

Veto Threat

a_I^*

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

Theory

Status quo

v

c*

Acquiesce

Veto Threat

a_I^*

Take-it-or-leave-it

Theory

Status quo

v

c*

Acquiesce

Veto Threat

a_I^*

Take-it-or-leave-it

Under take-it-or-leave-it, efficiency gains 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
  • One challenge: how to bring this abstract environment to a participants in a way that is easier to understand?

Experimental Design

  • Constructed environment that models the veto bargaining framework
  • One challenge: how to bring this abstract environment to a participants in a way that is easier to understand?

Experimental Design

  • Constructed environment that models the veto bargaining framework
  • One challenge: how to bring this abstract environment to a participants in a way that is easier to understand?

Experimental Design

  • Constructed environment that models the veto bargaining framework
  • One challenge: how to bring this abstract environment to a participants in a way that is easier to understand?
  • Buyers and Sellers framework bargaining over widgets to purchase:
    • Sellers (our proposers) want to sell as many widgets as possible
    • Buyers (our responders/vetoers) have an optimal number of widgets 

Delegation treatment:

offer a range

Take it or leave it:

single offer

Experimental Design

  • Within-subject variation:
    • Varying distributions (high, middle, low) for the Buyer           
    • Changing roles: 5 rounds in one role, 5 rounds in the other, and back to first role for 5 more rounds
  • Between subject 2x2

 

 

 

 

 

  • 12 sessions at the Pittsburgh Experimental Economics Laboratory
No Chat Chat
Take-it-or-leave-it N=66 N=60
Delegation N=64 N=66

Experimental Design

  • Within-subject variation:
    • Varying distributions (high, middle, low) for the Buyer           
    • Changing roles: 5 rounds in one role, 5 rounds in the other, and back to first role for 5 more rounds
  • Between subject 2x2
  • 12 sessions at the Pittsburgh Experimental Economics Laboratory
  • Collect other behavioral variables:                                                  
    • Optimizing ability while playing against a robot Buyer
    • Risk-aversion over the same domain
    • Other-regardingness also over the same domain

Results

  • Recall our theoretical predictions:
    • Sellers should adjust their offer according to the Buyer's distribution
    • We should expect efficiency gains from the delegation mechanism
    • Chat should generate more efficient outcomes for take-it-or-leave-it but not for delegation
    • Sellers (and potentially Buyers) worse off under take-it-or-leave it

Results

  • Sellers should adjust their offer according to the Buyer's distribution
  • No Chat condition:

Results

  • Sellers should adjust their offer according to the Buyer's distribution
  • No Chat condition:

Results

  • Sellers should adjust their offer according to the Buyer's distribution
  • No Chat condition:

Results

  • Sellers should adjust their offer according to the Buyer's distribution
  • No Chat condition:

Results

  • Sellers should adjust their offer according to the Buyer's distribution
  • No Chat condition:

Results

  • Sellers should adjust their offer according to the Buyer's distribution
  • No Chat condition:

Results

  • We should expect efficiency gains from the delegation mechanism                                                 
  • Chat should generate more efficient outcomes for take-it-or-leave-it but not for delegation
  • Define efficiency in a Pareto sense:
    • Inefficient: widgets purchased ≥ optimal Buyer amount
    • ​A breakdown (veto) is inefficient
    • A purchase less than the optimal quantity, which could have been increased and made both better off, is inefficient

Results

  • We should expect efficiency gains from the delegation mechanism                                                 
  • Chat should generate more efficient outcomes for take-it-or-leave-it but not for delegation

Results

  • We should expect efficiency gains from the delegation mechanism                                                 
  • Chat should generate more efficient outcomes for take-it-or-leave-it but not for delegation

Results

  • We should expect efficiency gains from the delegation mechanism                                                 
  • Chat should generate more efficient outcomes for take-it-or-leave-it but not for delegation

Results

  • We should expect efficiency gains from the delegation mechanism                                                 
  • Chat should generate more efficient outcomes for take-it-or-leave-it but not for delegation

Meaningful efficiency

gains through delegation

Results

  • We should expect efficiency gains from the delegation mechanism                                                 
  • Chat should generate more efficient outcomes for take-it-or-leave-it but not for delegation

Meaningful efficiency

gains through delegation

Meaningful efficiency

gains through chat

Results

  • We should expect efficiency gains from the delegation mechanism                                                 
  • Chat should generate more efficient outcomes for take-it-or-leave-it but not for delegation

Meaningful efficiency

gains through delegation

Meaningful efficiency

gains through chat

Limited efficiency

gains through chat

Delegation reduces

inefficient accepted offers

What types of inefficiency occur?

Delegation reduces

inefficient accepted offers

Delegation reduces

inefficient accepted offers

Results

  • Sellers (and potentially Buyers) worse off under take-it-or-leave it
  • Alternatively, who does better by treatment? 
  • Who does better by bargaining power?

Seller extracting more

Buyer extracting more

Conclusion

  • Modeled delegation bargaining with veto power in a lab setting using a Buyer-Seller framework
  • Sellers responded to the possible Buyer types, but left money on the table for both parties
  • Efficiency gains from the delegation mechanism were nearly as good as allowing open communication
  • Much still to do:
    • Identify those who optimize against robot Buyer but deviate behaviorally when interacting with participants
    • Analyze chat messages
    • Integrate measure risk-aversion and altruism

Thank you!

Questions or Comments?

Experimental Design

Results

  • How often do trades breakdown?                                                    
  • No Chat condition:

27% failure

23% failure

Results

  • How often do trades breakdown?                                                    
  • No Chat condition:

16% failure

19% failure

Results

  • How often do trades breakdown?                                                    
  • No Chat condition:

Evidence of

self-limiting