Veto Power, Delegation and Mechanism Design

Brandon Williams

Alistair Wilson

Richard Van Weelden

Demand for Bad Policy Workshop

Bolzano

July 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:
    • Can make simple take it or leave it offers
    • Or, they can offer a range of options to the informed party, conceding some of their agenda-setting power

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: Take-it-or-leave-it

0

1

Proposer

  • Proposer has:
    • Increasing payoff \(\pi(z)\) over the outcome \(z\), for simplicity we'll assume this is linear 
    • Makes take-it-or-leave it offer \(y\)
  • Vetoer has:
    • ideal point \(\theta\) which is private information, \(\theta\sim F(\theta)\)
    • Chooses \(z\in\left\{0,y\right\}\), either the veto threat point (here \(0\)) or the offer

\(y\)

\(\theta\)

Vetoer

Theory: Take-it-or-leave-it

\(\theta\)

Vetoer

0

1

Proposer

  • Proposer has:
    • Increasing payoff \(\pi(z)\) over the outcome \(z\), for simplicity we'll assume this is linear 
    • Makes take-it-or-leave it offer \(y\)
  • Vetoer has:
    • ideal point \(\theta\) which is private information, \(\theta\sim F(\theta)\)
    • Chooses \(z\in\left\{0,y\right\}\), either the veto threat point (here \(0\)) or the offer

Theory: Offer Realization

0

1

Proposer, ideal

\(\tfrac{y}{2}\)

Offer \(y\)

These types veto

These types choose \(y\)

Theory: Offer Realization

0

1

Proposer, ideal

\(\tfrac{y}{2}\)

Offer \(y\)

These \(\theta\)-types veto

These \(\theta\)-types choose offer

\(z=y\)

\(z=0\)

Theory: TIOLI Realization

0

1

Proposer, ideal

\(\tfrac{y}{2}\)

Offer \(y\)

Suboptimal: Inefficient outcome, as \(\theta>y\), so higher outcome preferred by both

Breakdown: Inefficient  as \(\theta>0\) preferred by both

Theory: TIOLI equilibrium

0

1

\(\tfrac{y}{2}\)

  • Proposer increasing the offer \(y\) leads to:
    • Marginal gain of \(\pi'(y)\cdot(1-F(\tfrac{y}{2}))\)
    • Marginal loss of \(\left(\pi(y)-\pi(0)\right)\cdot \tfrac{1}{2}f(\tfrac{y}{2})\)

\(z=0\)

\(z=y\)

\(y\)

\(f(\theta)\)

Theory: TIOLI equilibrium

0

1

\(\tfrac{y}{2}\)

  • Proposer increasing the offer \(y\) leads to:
    • Marginal gain of \((1-F(\tfrac{y}{2}))\)
    • Marginal loss of \(\tfrac{y}{2}\cdot f(\tfrac{y}{2})\)

\(z=0\)

\(z=y\)

\(y\)

\(f(\theta)\)

Theory: Delegation

\(\theta\)

Vetoer

0

1

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 Realization

0

1

\(\tfrac{y}{2}\)

Offer \(\left[y,1\right]\)

These types veto \(z=0\)

These types choose \(z=y\)

These types choose \(z=\theta\)

\(y\)

Theory: Delegation Realization

0

1

\(\tfrac{y}{2}\)

Offer \(\left[y,1\right]\)

\(y\)

No Suboptimality: Delegation option ensures this

Breakdown: Inefficient  as \(\theta>0\) preferred by both, but smaller region than TIOLI

Theory: Delegation Equilibrium

0

1

\(\tfrac{y}{2}\)

\(y\)

\(f(\theta)\)

  • Proposer increasing the minimal offer \(y\) leads to:
    • Marginal gain of \(\pi'(y)\cdot(F(y)-F(\tfrac{y}{2}))\)
    • Marginal loss of \(\left(\pi(y)-\pi(0)\right)\cdot \tfrac{1}{2}f(\tfrac{y}{2})\)

Theory: Delegation Equilibrium

0

1

\(\tfrac{y}{2}\)

\(y\)

\(f(\theta)\)

  • Proposer increasing the offer \(y\) leads to:
    • Marginal gain of \((F(y)-F(\tfrac{y}{2}))\)
    • Marginal loss of \(\tfrac{y}{2}\cdot f(\tfrac{y}{2})\)

Theory: Delegation Equilibrium

0

1

\(\tfrac{y}{2}\)

\(y\)

\(f(\theta)\)

  • With increasing density we get a corner solution:
    • coincide with TIOLI solution, \(y^\star=1\)

Theory: Delegation Equilibrium

0

1

\(\tfrac{y}{2}\)

\(y\)

\(f(\theta)\)

  • Or if we allow for offers above the maximum state we can get a solution

Theory: Delegation Equilibrium

  • With decreasing density we get the other corner solution:
    • Full delegation, with \(Y^\star=\Theta\) and \(z^\star=\theta\)

0

1

\(\tfrac{y}{2}\)

\(y\)

\(f(\theta)\)

Theory: Communication

  • Communication is predicted to:
    • Improve coordination in the take-it-or-leave it case (Matthews 1989)
  • Do nothing in the delegation case (Kartik et al. 2021)

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?
  • To make the experiment tractable we:
    • Discretize the state-space to 6 states with three distributions:
      • Low (decreasing)
      • Middle (modal distribution)
      • High (increasing)
    • Frame the decision as a Buyer/Seller problem:
      • State is the Buyer's ideal demand
      • Delegation is choice of a menu to offer

State introduced via an Urn

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
  • 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

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
TIOLI N=66 N=60
Delegation N=64 N=66

Predictions: Seller outcome

Dist. TIOLI Delegation
Low -12% 0%
Middle 7% 10%
High 18% 18%

Relative to full delegation:

So we should see a decreasing gain to seller as the distribution shifts

Predictions

Dist. Breakdown Suboptimal Breakdown Suboptimal
Low 55% 5% 0% 0%
Middle 25% 10% 25% 0%
High 25% 0% 25% 0%

TIOLI

Delegation

So we a decrease in efficiency between TIOLI and Delegation, and the disappearance of suboptimal positive outcomes

Results

  • Buyer behavior is almost always self-maximizing:
    • 90% in TIOLI, 88% in Delegation
    • Of the remainder \(\sim\)75% is Generous to the Seller

Results: Seller offers in TIOLI

Low

Middle

High

Results: Seller offers in TIOLI

Results: Seller offers in Delegation

Low

Middle

High

Minimal offer in interval:

Results: What else is included in interval?

Results: Seller offer Comparison

TIOLI

Delegation

Results: Offer comparison over Mechanisms

Low

Middle

High

In the No Communication games we find that:

  • Well-ordered behavior across the distributions
  • More spread across than the point prediction
  • Lower minimal offers in Delegation, more than expected in High

General behavior

Results: Inefficiency (Theory)

TIOLI

Delegation

Results: Inefficiency (Data)

TIOLI

Delegation

Results: Outcomes

Dist. TIOLI Delegation
Low -12% 0%
Middle 7% 10%
High 18% 18%

Theory relative to full delegation:

Dist. TIOLI Delegation
Low -14% 1%
Middle -7% 4%
High 3% -7%

Actual:

Effect of Delegation: Theory

Effect of Delegation: Empirical Payoffs

We find that:

  • Delegation \(\succ\) TIOLI
  • We find this for all distributions:
    • even increasing!
  • Most of the efficiency gains are captured by the Responder
  • ​Best improvement for Proposer in decreasing distribution

Efficiency

Results: Inefficiency (Data with No Comm)

TIOLI

Delegation

Results: Inefficiency (Data with Comm)

TIOLI

Delegation

Results: Communication Offers (TIOLI)

Low

Middle

High

Chat

No Chat

Results: Offers (Delegation)

Low

Middle

High

Chat

No Chat

Results: Outcome \(z\), relative to Full deleg

Dist. TIOLI Delegation
Low -14% +1%
Middle -7% +4%
High +3% -7%

Without Chat:

Dist. TIOLI Delegation
Low +20% +13%
Middle +13% 0%
High +8% +5%

With Chat:

We find that:

  • Communication substantially improves bargaining efficiency in both mechanisms
  • Proposers do worse in the Delegation case

Communication

Diagnosing the Failures

At the end of the experiment the participants make choices across a number of decision problems:

  1. A pure optimization problem
  2. A lottery choice
  3. An other regarding choice

Diagnosing the Failures: Pure Optimization

Diagnosing the Failures: Lotteries

Diagnosing the Failures: Distribution

Diagnosing the Failures: Results

Using the decision problems we can begin to understand where deviations are coming from:

  • Risk preferences
  • Other-regardingness
  • Optimization failure

So far the results are only preliminary but:

  • Main reason sellers  don't extract more of the delegation gain is optimization failure
    • Lottery choices indicate less delegation
    • Robot choices match behavior in the Delegation game

 

Conclusion

  • Test delegation bargaining with veto power in a lab setting 
  • Sellers respond to key distribution parameters
  • Clear efficiency gains from the delegation mechanism over take-it-or-leave-it offers
    • But more of the surplus goes to the responder
  • Both mechanisms are highly efficient with open communication, but proposers do better here without the delegation option
  • Optimization failures in understanding the mechanism action space underly the proposer's failure to extract more. 
    • However, this doesn't lead to inefficiency as they over-delegate

Thank you!

Questions or Comments?