Rewards and Punishments in Bargaining

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Rewards and Punishments in Bargaining

• Svetlana Pevnitskaya and Dmitry Ryvkin
• Florida State University
• June 5, 2009
• Moscow

2
Introduction

• Economic and social activity is usually preceded
  by bargaining between the interested parties
• Bargaining fails when participants do not reach
  an agreement despite an opportunity for Pareto
  improvement
• Bargaining positions are often asymmetric
• The deal still hinges on a decision of voluntary
  engagement from the other party
• Can the acceptance decision be facilitated?

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In this paper

• asymmetric bargaining with two parties employing
  the setting of ultimatum games
• acceptance decision is required for positive
  payoffs
• extensively studied (robust and well understood
  behavior)
• most responders do not agree to low offers
  resulting in monetary efficiency losses
• review of early ultimatum experiments e.g., Guth
  1995, Roth 1995, Camerer and Thaler 1995

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IntroductionIn this paper

• augment the mechanism to adjust behavior
• rewards and punishments
• reward desirable and sanction undesirable actions
  by changing payoffs
• feedback and emotional expressions (see e.g.
  Xiao, et al., 2005, Brandts and Cooper, 2007,
  Casari and Luini, 2008)
• Punishment decrease in payoff that a
  second-stage player imposes on a first stage
  player
• Reward increase in payoff to a first stage
  player imposed by a second stage player.
• (Andreoni et al, 2003)

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IntroductionPrevious studies of rewards and
punishments

• provision of public goods (e.g. Fehr and
  Gachter, 2000, Sefton et al., 2007, Nikiforakis
  and Normann, 2008)
• common pool resources (e.g. Ostrom et al., 1992)
• dictator games (e.g. Ahlert et al., 1999,
  Andreoni et al., 2003b),
• investment games (e.g. Abbink et al., 2000,
  Houser et al., 2008)
• general result that they are, to various degrees,
  effective in increasing contributions and
  promoting cooperation.

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Implementation of rewards and punishments

• one-to-one application
• both instruments
• fixed cost (or inverse effectiveness) of reward
  or punishment that is equal to one
• Key findings
• availability of instruments promotes the
  acceptance decision
• proposers are most generous when responders can
  reward and punish, and offer least when
  responders can only reward
• for a population of proposers where a significant
  number of low offers is present, punishment only
  leads to greater efficiency

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Experimental Design

• The first-stage player (proposer) chooses amount
  x such that he gets (500-x) cents and the
  second-stage player (responder) gets x.
• x offer
• U second-stage player can reject or accept the
  offer resulting in payoffs (0,0) and (500-x, x)
  respectively.
• UR second-stage player can reject or accept the
  offer. In the former case payoffs are (0,0). In
  the latter case responder chooses transfer
• 0 y x such that resulting payoffs are
  (500-xy, x-y)
• UP second-stage player can reject or accept the
  offer. In the former case payoffs are (0,0). In
  the latter case responder chooses reduction
• 0 z minx, 500-x such that resulting payoffs
  are (500-x-z, x-z)
• UPR second-stage player can reject or accept the
  offer. In the former case payoffs are (0,0). In
  the latter case responder chooses either
  transfer, y, or a reduction, z, such that the
  payoffs are as specified above for corresponding
  option.

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Theoretical Considerations
Individual payoff maximization framework (U,
UR, UP and UPR) responders accept any x gt 0, and
yz0. Experimental evidence U low offers are
likely to be rejected, and many proposers offer
0.5S. RP in other mechanisms substantial demand
even when costly
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Theoretical Considerations choice of parameters
Effectiveness of reward and punishment, k and
l Reward reward spending of 1 increases
proposers payoff by k Punishment punishment
spending of 1 decreases proposers payoff by
l (possibility for efficiency enhancement) Model
s of other-regarding preferences (Rabin 1993,
Fehr and Schmidt 1999, Bolton and Ockenfels 2000,
etc.) relative payoffs
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Theoretical Considerations
Using Fehr and Schmidt (1999) model with
inequality aversion
This study k l 1 Separate the effect of
reward from efficiency enhancement
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Hypotheses

• Proposers increase their offers in the UR, UP and
  UPR games compared to the U game.
• Responders likelihood of accepting a given offer
  is larger in the UR, UP and UPR games compared to
  the U game.
• Responders reward (in UR and UPR) and punish (in
  UP and UPR) mostly by symbolic amounts.
• Proposers adjust their offers to maximize their
  expected payoff given the behavior of responders.

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Experimental Design
Treatment U UR UP UPR
Sessions 2 2 2 2
Subjects 36 40 34 34
Procedures Subjects FSU undergraduate
students Z-tree (Fischbacher, 2007) Session
60-90 minutes Zipper matching Payment based on 2
randomly chosen rounds 10 show up fee, approx.
20 average total payment
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ProposersAverage offer
Responders Acceptance rate
U UR
206.7 (5.0) 183.8 (10.3)
205.8 (12.7) 219.7 (7.5)
UP UPR
U UR
.83 (.04) .75 (.05)
.83 (.04) .88 (.04)
UP UPR






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Frequency of Reward/Punishment Instruments Use
U UR UP UPR
transfergt0/all (std. error) .13 (.04) .10 (.04)
reductgt0/all (std. error) .12 (.04) .14 (.05)
reject/all (std. error) .17 (.04) .25 (.05) .17 (.04) .12 (.04)
accept/all (std.error) .83 (.04) .75 (.05) .83 (.04) .88 (.04)
UP smaller rejection frequency than UR supports
the explanation that use P as a feedback,
correspondingly in R greater frequency of
rejection since this is the only way to send
negative feedback
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Proposers Distributions of Offers by Treatment
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Proposers Cumulative Distributions of Offers
Result 1. The empirical distributions of offers
are different. Offers in all treatments FOS
dominate those in UR and offers in the UPR
treatment FOS dominate offers in all other
treatments.
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Responders
Prob(accept) Prob(accept) U UR UP UPR
offer Coeff. .058 .028 .008 .036
offer Intercept -9.4 -3.5 -0.54 -4.7
Marginal Effect Marginal Effect .023 .011 .003 .014
(Random Effects Probit regressions) All pairwise
comparisons except UR-UPR are significant
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Responders Probability to Accept
Result 2. The presence of rewards and/or
punishments facilitates acceptance of offers. The
most dramatic difference is observed in UP where
even very low offers have a good likelihood of
being accepted.
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Responders Probability of Reward
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Responders Probability of Punishment
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Responders Reward and Punishment
Result 3. The probability of using rewards and
punishments depends asymmetrically on the
presence of the other instrument. Rewards are
less likely in the presence of punishment than
without it, but punishments are more likely in
the presence of reward than without it. Result
4. (i) Rewards are statistically significant and
larger in magnitude in the presence of punishment
than without it. (ii) Punishments are
statistically significant in the presence of
reward but are essentially zero without reward,
indicating they are used as feedback.
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Responders Estimated Update (conditional on
acceptance)
Updatetransferprob(transfergt0)
reductionprob(reductiongt0)
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Proposers Expected Payoff (and average offers)
Result 5. Proposers average offers are
consistent with the expected payoff maximization
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Total expected payoff
Consider population of proposers with offers
distributed uniformly over 0, 250. Total
expected payoffs (proposers payoff, responders
payoff) 332.8 (235.4, 97.4) in UP 251.4 (159.8,
91.6) in UR 242.0 (151.8, 90.2) in UPR 177.1
(104.8, 72.3) in U Result 6. In
environments with substantial presence of low
offers (i) introducing the costly reward and/or
punishment options increases efficiency (ii) a
punishment-only scheme leads to the largest gain
in efficiency.
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Proposers Dynamics of Offers
Offer const accept_lag offer_lag
U 167.7 -20.1 .26
UR 75.8 -21.4 .68
UP 146.3 -4.2 .31
UPR 192.1 -55.1 .36
plt0.01, plt0.05, plt0.10 const
UPRgtUR, plt0.01 UgtUR, plt0.01 accept_lag
UPgtUPR, p0.02, UgtUPR, plt0.08 offer_lag
URgtUPR, plt0.08 URgtU, plt0.03
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Dynamics
Result 7. Responders do not exhibit
(statistically significant) adjustment in our
setting. Result 8. Proposers adjustment depends
on the availability of the reward and punishment
options to responders. In U and UPR, proposers
react to past acceptance decisions, while in UR
they ignore past acceptances but reciprocate past
rewards. In UP, neither acceptances nor
punishments affect proposers decisions.
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Conclusions

• Conducted conservative test of the effect of
  rewards and punishments in bargaining
• The likelihood of agreement is increasing if the
  responding party has an option to apply a costly
  reward and/or punishment after accepting the
  offer.
• The least generous terms, which typically lead to
  lost opportunities due to rejection, have the
  highest chance to be accepted in the presence of
  punishment only.
• Proposers make more generous offers when the
  responders can reward and punish, and offer least
  (even compared to the baseline) when responders
  can only reward.
• The presence of the symbolic amounts of both
  suggests feedback from the responding to the
  proposing party.

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Conclusions

• Did not observe adjustment in responders
  behavior.
• Proposers adjust behavior in U, UR and UPR. based
  on acceptance (decrease) in U, UPR and reward
  (increase) in UR

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Proposers Average Offer (over time)
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Responders Probability to Accept (over time)
31
Responders Probability of Positive Transfer
(over time)
32
Responders Probability of Positive Reduction
(over time)
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Feasible Payoffs
Responders payoff
500
Proposers payoff
0
500