[Paper Review] Sequential Veto Bargaining with Incomplete Information

S. Nageeb Ali, Navin Kartik+1 more|arXiv (Cornell University)|Feb 5, 2022

Auction Theory and Applications4 citations

TL;DR

This paper studies sequential veto bargaining with incomplete information, where a proposer makes repeated proposals to a veto player with unknown ideal point. Despite lacking commitment power, the proposer can achieve payoffs arbitrarily close to the commitment benchmark through 'leapfrogging'—targeting low-type vetoes early to credibly extract surplus from high types later, especially under patient behavior and single-peaked preferences.

ABSTRACT

We study sequential bargaining between a proposer and a veto player. Both have single-peaked preferences, but the proposer is uncertain about the veto player's ideal point. The proposer cannot commit to future proposals. When players are patient, there can be equilibria with Coasian dynamics: the veto player's private information can largely nullify proposer's bargaining power. Our main result, however, is that under some conditions there are also equilibria in which the proposer obtains the high payoff that he would with commitment power. The driving force is that the veto player's single-peaked preferences give the proposer an option to "leapfrog", i.e., to secure agreement from only low-surplus types early on to credibly extract surplus from high types later. Methodologically, we exploit the connection between sequential bargaining and static mechanism design.

Motivation & Objective

• To analyze sequential bargaining between a proposer and a veto player when the proposer lacks commitment power and is uncertain about the veto player’s ideal point.
• To investigate whether proposers can achieve payoffs close to those under commitment, despite incomplete information and sequential proposal dynamics.
• To explore the role of learning, signaling, and strategic rejection in shaping equilibrium outcomes under patient behavior.
• To examine conditions under which Coasian dynamics (where lack of commitment erodes proposer power) are overcome by strategic leapfrogging.
• To establish the existence of equilibria where proposers extract surplus from high-type vetoes by first securing agreement from low-type vetoes.

Proposed method

• Formalizes an infinite-horizon sequential bargaining model with single-peaked preferences and incomplete information about the veto player’s ideal point.
• Uses a dynamic programming approach to characterize equilibrium payoffs, defining continuation values $ R_v $ and proposal functions $ P_v $ for each type $ v $.
• Applies the generalized theorem of the maximum to ensure continuity and upper hemicontinuity of equilibrium correspondence, enabling recursive construction.
• Introduces the concept of 'leapfrogging'—where the proposer targets low-surplus types first to credibly commit to future concessions for high types.
• Constructs equilibria via backward induction and approximation techniques, extending solutions from finite to infinite type spaces.
• Leverages connections to static mechanism design to derive upper bounds on the commitment payoff and show when it can be achieved without commitment.

Experimental results

Research questions

• RQ1 Under what conditions can a proposer achieve a payoff arbitrarily close to the commitment benchmark in sequential veto bargaining with incomplete information?
• RQ2 How does the absence of commitment power affect proposers’ ability to extract surplus when the veto player’s ideal point is privately known?
• RQ3 What role does the veto player’s single-peaked preference structure play in enabling the proposer to credibly commit to future concessions?
• RQ4 Can strategic rejection by the veto player lead to Coasian dynamics, or can the proposer counteract this through leapfrogging?
• RQ5 Is leapfrogging a necessary mechanism for achieving the commitment payoff without commitment, or are alternative equilibrium structures possible?

Key findings

• When players are patient, there exist equilibria in which the proposer obtains a payoff arbitrarily close to the commitment benchmark, even without commitment power.
• The key mechanism enabling this outcome is 'leapfrogging', where the proposer secures early agreement from low-type vetoes to credibly commit to future concessions for high types.
• The proposer’s ability to leapfrog relies on the veto player’s single-peaked preferences, which allow the proposer to extract surplus from high types by first targeting low types.
• An upper bound on the commitment payoff is derived using static mechanism design techniques, and it is shown that this bound can be achieved in equilibrium without commitment.
• Equilibria exist where the proposer extracts surplus from high-type vetoes by making proposals that are initially far from their own ideal point but acceptable to low types.
• The existence of such equilibria is robust to the distribution of types and holds under general conditions, including when the type space is continuous and the discount factor approaches one.