Veto Power, Delegation and Mechanism Design

Brandon Williams

Alistair Wilson

Richard Van Weelden

ESA North America

October 11, 2025

Setup

Setup

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

Setup

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

Setup

Constrained delegation can improve efficiency:
- Kartik, Kleiner, and Van Weelden (2021) show this mechanism is particularly useful in veto bargaining
- The proposer can offer a menu of options to the informed party, conceding some of their agenda-setting power in exchange for fewer bargaining breakdowns
- The responders can then choose from the menu, or veto
Experimentally, we find:
- Constrained delegation does increase efficiency
- Responders get most of the benefit
- Proposers fail to optimize over the menu design and generally provide more latitude to responders

Theory

Theory

Proposer

Theory

Proposer

Proposer has:
- Increasing payoff \( \pi (z) \) over the outcome \( z \) (for simplicity, we'll assume this is linear)
- Will make an offer to the vetoer

Theory

Vetoer

Proposer

\( \theta \)

Veteor has:
- Ideal point \( \theta \) which is private information, \( \theta \sim F(\theta) \)

Theory

???

\( \theta \)

Veteor has:
- Ideal point \( \theta \) which is private information, \( \theta \sim F(\theta) \)

Theory

???

Veteor has:
- Ideal point \( \theta \) which is private information, \( \theta \sim F(\theta) \)
- A choice \( z \in \{0,Y\} \), either the veto threat point (here 0) or in the offer

\( \theta \)

Theory

Veteor has:
- Ideal point \( \theta \) which is private information, \( \theta \sim F(\theta) \)
- A choice \( z \in \{0,Y\} \), either the veto threat point (here 0) or in the offer

Theory: Take it or Leave It

Proposer

Offer \( y \)

\( \frac{ y}{2} \)

These \( \theta \)-types veto

These \( \theta \)-types choose offer

\( z = 0 \)

\( z = y \)

Theory: Take it or Leave It

Proposer

Offer \( y \)

\( \frac{ y}{2} \)

Suboptimal:

inefficient as \( \theta > y \)

preferred by both

Breakdown:

inefficient as \( \theta > 0 \)

Theory: Delegation

\( \theta \)

Vetoer

Proposer

Proposer:
- Offers set of options \(Y\)
Vetoer has:
- Chooses \(z\in\left\{0\right\}\cup Y\), either the veto threat point (here \(0\)) or some offer in delegation set

Theory: Delegation

\( \frac{ y}{2} \)

These \( \theta \)-types veto

These \( \theta \)-types

choose minimum offer

\( z = 0 \)

\( z = y \)

Offer \( [y,1] \)

\( y \)

These \( \theta \)-types

choose their preferred

\( z = \theta \)

Theory: Delegation

\( \frac{ y}{2} \)

Offer \( [y,1] \)

\( y \)

No suboptimality:

The delegation mechanism ensures

these options are available

Breakdown:

inefficient as \( \theta > 0 \)

Theory: Summary

Delegation should capture a meaningful proportion of alignment failures, and therefore have more efficient outcomes than take it or leave it offers
In both cases, proposers should change their offer according to ex-ante alignment (i.e. bargaining power)
Theory informs the optimal offer, including when no delegation and full delegation are optimal
We test if these predictions hold and assess behavioral deviations (e.g. other regarding behavior, optimization failures, etc.)

Experiment

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

Proposer

Seller

Vetoer

Buyer

State

Ideal Demand

Offer

Widgets

Delegation

Widget Menu

Types

Urn Draws

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

	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
Collect other behavioral variables (identification through subtraction):
- Remove player: Optimizing ability while playing against a robot Buyer
- Remove mechanism complexity: Preferences over pure lotteries
- Remove uncertainty over both player payoffs: Pure allocation decisions

Results

Sanity check: Sellers respond to alignment

Low

Middle

High

Low

Middle

High

Sanity check: Sellers respond to alignment

Low

Middle

High

Minimal offer in interval:

Sanity check: Sellers respond to alignment

Low

Middle

High

Minimal offer in interval:

Sanity check: Sellers respond to alignment

Other quick results

Buyers overwhelmingly pick the best option available
- They pick the best number of widgets from the menu, and take the outside option when better
Sellers (mostly) keep offers higher than the minimum
- They do not constrain the upper bound of the delegation set

Sellers offer more latitude under delegation

Low

Middle

High

Low

Middle

High

Sellers offer more latitude under delegation

Delegation should increase efficiency

Take it or Leave It

Delegation

Delegation should increase efficiency

Take it or Leave It

Delegation

Take it or Leave It is inefficient

Take it or Leave It

Delegation

Inefficiency not eliminated under delegation

Take it or Leave It

Delegation

Delegation does increase efficiency

Take it or Leave It

Delegation

Take it or Leave It

Delegation

Delegation does increase efficiency

Who benefits from delegation?

Who benefits from delegation?

Buyers mostly benefit from delegation

What explains behavioral deviations?

Main reason sellers don't extract more of the delegation gain is optimization failure:

What explains behavioral deviations?

Main reason sellers don't extract more of the delegation gain is optimization failure:

Remove player: Robot choices closely match delegation choices

What explains behavioral deviations?

Main reason sellers don't extract more of the delegation gain is optimization failure:

Remove player: Robot choices closely match delegation choices
Remove mechanism complexity: Lottery choices indicate less delegation

Other Choices

Results: Key Points

Offers respond to the bargaining alignment of the types in a well-ordered manner
- Sellers offer more latitude than perfectly-optimized predictions
- Sellers in delegation offer more latitude
Delegation mechanism is more efficient than take it or leave it
Most of the "cost" of the mechanism falls on the Seller:
- More of the efficiency gains are captured by the Buyer
- Best improvements for the Seller is when alignment is low
- Data suggest that the optimization failures are the main reason for overly-permissive Sellers
Addendum: pre-play communication is just as efficient as delegation

Communication Efficiency

Communication Offers

Conclusion

Test delegation bargaining with veto power in a lab setting
Proposers respond to key distribution parameters and change their offers accordingly
Clear efficiency gains from the delegation mechanism over take-it-or-leave-it offers
- But more of the surplus goes to the responder
Optimization failures in understanding the mechanism action space explain some of the proposer's failure to extract more
- However, this doesn't lead to inefficiency as they over-delegate