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Bargaining with Absentmindedness

Cole Wittbrodt

Abstract

Delay is the norm in bargaining. I propose a novel source of bargaining delay: absentmindedness. Instead of interpreting absentmindedness as a literal memory friction, I use absentmindedness to represent a broader form of bounded rationality in dynamic games where players cannot perfectly track a game's progression. Bargainers unable to finely condition play on the stage of dynamic interaction can credibly refuse last-minute ultimatums. Other parties that anticipate this behavior are driven to offer preemptive concessions to avoid a breakdown in negotiations. Absentmindedness is thus a source of bargaining power, even for players who never make offers. This bargaining power comes at the cost of efficiency; I show that there can be equilibria where offers are rejected on the path of play.

Bargaining with Absentmindedness

Abstract

Delay is the norm in bargaining. I propose a novel source of bargaining delay: absentmindedness. Instead of interpreting absentmindedness as a literal memory friction, I use absentmindedness to represent a broader form of bounded rationality in dynamic games where players cannot perfectly track a game's progression. Bargainers unable to finely condition play on the stage of dynamic interaction can credibly refuse last-minute ultimatums. Other parties that anticipate this behavior are driven to offer preemptive concessions to avoid a breakdown in negotiations. Absentmindedness is thus a source of bargaining power, even for players who never make offers. This bargaining power comes at the cost of efficiency; I show that there can be equilibria where offers are rejected on the path of play.

Paper Structure

This paper contains 10 sections, 12 theorems, 91 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Model
  3. Analysis
  4. Ex-Ante Equilibrium
  5. Discussion
  6. Absentminded Proposer
  7. A Model with Side Payments
  8. Conclusion
  9. Sequential MBE
  10. Two Absentminded Players

Key Result

Theorem 1

There exists a threshold $u_P^R/u_R^R\leq\underline{\delta}(T)<1$ such that, if $T\geq2$ and $\delta\geq\underline{\delta}(T)$, the following cases exhaust all possibilities of strategy profiles $(\sigma^*,p^*)$ that can occur in MBE:

Figures (3)

  • Figure 1: Game tree when $T=2$. The nodes after receiving an offer $a_P$ are in the same information set. The nodes after receiving an offer $a_R$ are in the same information set. In each payoff pair, the first element represents the proposer's payoffs and the second element represents respondent payoffs.
  • Figure 2: Decision problems in the case of $T=3$ when $a_3=a_P$ and $a_3=a_R$.
  • Figure 3: The classic centipede game rosenthal81

Theorems & Definitions (35)

  • Definition : MBE
  • Theorem 1: Equilibrium Characterization
  • Corollary 1
  • Corollary 2
  • Definition : Ex-Ante Equilibrium
  • Theorem 2: Equivalence between MBE and Ex-Ante Equilibria
  • Definition : MBE --- Proposer Absentminded
  • Proposition 1
  • Definition : MBE --- With Side Payments
  • Definition : Markov Property
  • ...and 25 more