Bargaining, Public Goods, and Social Preferences

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Bargaining, Public Goods, and Social Preferences
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Psychological Games

• Rabin
• Intentions of kindness and equity norms
• Game of chicken

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Beliefs and intentions

• Play Chicken in response to Chicken or Dare
• Play Dare in response to Chicken or Dare
• Row believes Col will play Dare
• Row believes Col believes Row will play Chicken
• Col plays Dare even though he believes Row will
  play Chicken
• Psychological value to Row?
• Psychological value to Col?

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Intentions and kindness

• If row believes that col takes a kind act
• Row gets additional utility from reciprocating
• Row gets negative utility from responding with an
  unkind act - guilt

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Dufwenbergs game

• B gets negative utility from not living up to
  expectations
• If A chooses In B may see him as kind and get
  positive utility from reciprocating

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Sequential trust game

• B have expectations on whether A will play In
  or not
• B can be surprised when A plays In if his
  probability is low enough
• Will not work in strategic form games

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Social Preferences Other regarding behavior

• Not necessarily related to beliefs or norms
• Altruism
• Reciprocity
• Inequality aversion

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• Charness and Rabin QJE 2002
• Fehr and Gachter AER
• Ostrom, Walker and Gardner APSR
• Berg, Dickhaut and McCabe
• Andreoni Warm Glow

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• Bargaining
• Unstructured Bargaining
• Sequential Bargaining
• Dictator and Ultimatum Games
• Social Preferences altruism, inequality
  aversion
• Public Goods and Sanctioning
• Trust and Reciprocity
• Equity

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Unstructured Bargaining

• Roth and Malouf (1979)
• Roth and Murnighan (1982)
• Induced risk neutrality by using binary lottery
  payments
• probability of winning the lottery is increasing
  in payoff of bargaining game
• assumes independence is not violated
• Nash Solution
• Maximize the product of the utility gains
• Fairness and efficiency compromise
• Pareto Optimality
• Symmetry
• Independence of irrelevant alternatives
• Invariance to linear transformations of utility
• Utility frontier over money payoffs can be
  normalized to (0, 100)

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• Maximize the product of the utility gains

If you win the lottery you get U100 If you lose
the lottery you get U0 Nash Solution is 50/50
split of the lottery ticket, giving each player
the same probability of winning the lottery and
an EU50
100
50
100
50
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Predictions

• Nash Solution prediction is independent of the
  payoff from winning lottery
• Invariance axiom
• No disagreements are predicted since that would
  result in inefficiencies
• Pareto optimality
• Computerized, anonymous bargaining over division
  of lottery tickets
• High prize 20, Low prize 5
• Information effect
• No information about other partys payoffs lead
  to 50/50 split of lottery tickets
• Information about other partys payoffs lead to
  50/50 split in payoffs
• Rejection of Invariance Axiom of Nash Solution

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Conclusions

• Low prize player knowing the prizes matter to
  bargaining outcome
• Violates invariance to linear transformations of
  utility
• Is this fairness?
• Disagreements are common in all information
  treatments
• Violates pareto optimality

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Structured sequential bargaining

• Alternating offers
• Division of amount of money k
• Odd number periods player 1 makes offer
• Even number periods player 2 makes offer
• If offer is accepted the game ends
• Y1dt-1x
• Y2 dt-1(k-x)
• d is the cost of delay (like discounting)
• Subgame perfect Nash Equilibrium
• Rules out incredible threats
• Backwards induction
• Multiple Nash Equilibria but only one Subgame
  Perfect NE

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Prediction

• 2 periods
• Last period dk remains of the pie
• Player 2 offers e to player 1 and dk- e for
  himself
• Player 1 accepts since e0, the disagreement
  outcome
• First period player 1 wants to make an offer so
  that player 2 will accept rather than go into
  period 2
• The whole pie k is on the table and player 1
  offers dk to player 2 and (1- d)k for himself
• Player 2 will accept

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• Binmore, Shaked, and Sutton (1985)
• Guth and Tietz (1988)
• Neelin, Sonnenschein, and Spiegel (1988)
• Ochs and Roth (1989)
• Harrison and McCabe (1996 IJGT) Expectations and
  fairness in a simple bargaining experiment

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Ultimatum Bargaining

• First mover/proposer given an initial endowment
• 10
• First mover makes a take it or leave it offer of
  division
• Second mover can either accept the offered split
  or reject, in which case neither player gets
  anything
• Backward induction prediction
• Subgame perfect Nash Equilibrium
• Multiple Nash Equilibria
• Guth, Schmittberger and Schwarz (1982)

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Subgame Perfection?

• Point predictions are rejected
• Some type of experience make subjects play the
  SPNE point prediction
• Experience in the second player role
• Look at figures 4.2 p 262-263 Handbook
• Example cell1 vs cell5
• Prediction shifts down from 12 to 7
• Choices do not change
• Equal division has attraction power

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Ultimatum Findings

• Offers are multi-modal
• 0 or e offers
• 25-30 offers
• 50 offers

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Fairness?

• What is fairness?
• Altruism UU(y, a) where a is warm-glow
• warm glow is independent of the level of y
• Inequality aversion Uy-a(y-y-i) if yy-i
• guilt
• Uy- b(y-i-y) if y
• envy
• Envy is stronger than guilt so ba
• Test of fairness in sequential and ultimatum
  bargaining are confounded with propensity to
  backward induct
• Reciprocity preferences
• Reward good deeds (kindness) and punish bad deeds
  (unkindness)

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Cox Triadic Games

• Identification and isolation of testable
  hypotheses
• Avoiding confounds
• Standard choice theory
• Utility maximization over consumption of goods or
  over income or wealth
• Behavioral extensions
• Psychological values and social preferences
• Utility arguments include other peoples utility
  or income, consumption, wealth
• Social norms
• Trust and Reciprocity

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The investment game

• 2 person game Investor and contractor
• Investor cannot enforce rate of return payment
  from contractor
• Incomplete contracts
• Investor and contractor both get 10
• Investor can send some of that to contractor
• Money sent triples (this is the return on the
  investment)
• Contractor can send some back or not no
  penalties

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Predictions

• Standard assertion of utility maximization
• Contractor will never return any money
• So investor will never send
• Alternative assertion 1 Trust and Reciprocity
• Recognition of efficiency gain if investor trusts
  and contractor reciprocates
• Alternative assertion 2 Equity preferences
  altruism
• Investor beliefs that contractor has inequality
  averse preferences

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Confounding influences

• Observations of sending and returning are not
  proof of Trust and Reciprocity
• Confounded by the possibility that preferences
  reflect inequality aversion
• Triadic game structure to test this
• Remove incentives to trust and test if giving
  still occurs
• Remove incentives to reciprocate and test if
  returning still occurs
• Finds evidence of both

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Dictator and Ultimatum Games

• Dictator games have no second stage
• A direct test of fairness
• Forsythe, Horowitz, Savin, and Sefton (1994)
• Ultimatum modal response at 50
• Dictator modal responses 0, 20 and 50

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Best shot games

• Harrison and Hirshleifer (1989)
• Prasnikar and Roth (1989)
• Public goods provision game
• Sequential provision
• Player 1 proposes q1 as his provision
• Player 2 sees proposal and subsequently makes his
  q2 provision proposal
• The maximum of q1 and q2 determines provision,
  but cost is q1 and q2
• Prediction q10 (profit 3.70) and q20 (profit
  0.42)
• Extreme payoff prediction is confirmed no
  fairness consideration?
• With incomplete information about payoffs play is
  close to subgame perfect equilibrium prediction
  HH experiment

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Off equilibrium payoffs

• Prasnikar and Roth (1989, 1992)
• Why do we see apparent fairness in Ultimatum
  games but not in (partial information) Best shot
  games?
• Learning
• Ultimatum offers increase after first movers
  experience rejections
• Best shot quantities (i.e. offers) decline after
  first movers experience lack of cooperation
• Off equilibrium payoffs
• Off-equilibrium rejections of small or zero
  offers in ultimatum leads to a large loss in
  income
• Off-equilibrium quantity offers lead to
  increasing losses in payoff
• Moving closer to equilibrium results in payoff
  increases in best shot but moving further from
  equilibrium results in payoff increases in
  ultimatum

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Culture, nationality and demographics

• Roth, Prasnikar, Okuno-Fujiwara and Zamir (1991)
• Israel, Yugoslavia, Japan and the US
• Nationality effect in ultimatum bargaining
  behavior
• Many studies claim also that there is a gender
  effect
• Botelho, Harrison, Hirsch and Rutstrom
  demonstrate interaction effects between
  nationality and other demographics
• Identifying culture is problematic

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Ultimatum in LDCs

• Henrich, Boyd, Bowles, Camerer, Fehr, Gintis
  (2004), Foundations of Human Sociality
• Study of 11 groups in small-scale societies
• Different degrees of market integration
• Ultimatum games (and others)
• Culture as characteristics of normal group
  interactions
• Payoffs to cooperation in daily economic life
• Family oriented societies no value of cooperating
  outside family
• Whale hunters high value of cooperating in large
  groups
• Market integration
• Frequency of market exchange
• Offers increase in both of these
• 47 of variation among societies in offers is
  explained by these two characteristics

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Designing experiments with rural LDC participants

• Non-monetary payoffs
• Goats?
• Instructions
• Anonymity
• Distrust of strangers

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Public Goods games and VCM

• What improves cooperation?
• Thresholds (provision points)
• Continuous contribution game is like PD
• Threshold game is like chicken
• Coordination game
• Pure and Mixed Strategy NE

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Value if one contributes 7 Value if both
contribute 10 Cost of provision 4
Value of Public Good 10 Cost of provision 4
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Findings

• Increases in thresholds increase average
  contributions
• But increase the probability that target will not
  be reach and public good will not be provided

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Factors that affect contributions in standard VCM

• Marginal payoffs
• Contributions increase with the return to the
  public good
• Number of group members
• Altruists stronger incentive to contribute
• Harder to detect free riders cooperation breaks
  down more easily
• Groups of 4 and 10 find no significant effect
  from group size
• Groups of 40 and 100 find higher contributions
  with the higher N
• Paid in extra-credit instead of cash
• Multi-day sessions
• Communications cheap talk
• Has a positive effect on contributions

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Common Pool Resource games

• Ostrom, Walker, Gardner (1992)
• Covenants without a sword Self-governance is
  possible
• Common Pool Resource Game
• Public resource
• Private incentives for use of public resource
  leads to over use

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Theory

• Group return to investment in CPR
• F(?xi) F(0)0 F(0)0 F(ne)
• n number of participants
• e initial endowment
• u(xi)w(e- xi)(xi/ ?xi)F(?xi)
• Symmetric Nash Equilibrium, each player chooses
  x
• -w (1/n)F(nx)F(nx)(n-1)/xn2
• Social optimum (max group payoffs)
• -wF(?xi)0
• Communications cheap talk does not change
  equilibrium prediction
• Costly voluntary sanctions
• u(x, s) u(x) f1 ?sij - f2 ?sji
• Costly voluntary sanctions do not change subgame
  perfect equilibrium predictions
• Imperfect equilibrium predictions
• Trigger strategies

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Experimental Design

• Parametric (numeric) version of CPR game
• Baseline no communications, no sanctions
• High and low endowments
• Changes off-equilibrium incentives
• Subjects experienced in CPR
• 20 rounds
• Treatments
• One time communications only (verbal
  face-to-face) after 10 rounds (3 groups of 8)
• Repeated communications every two rounds after 10
  rounds
• Sanctions only available after 10 round (8 groups
  of 8)
• One time communications and sanctions
• Imposed availability but voluntary use (3 groups
  of 8)
• One time communications and vote for or against
  sanctions
• Vote over availability of voluntary sanctions
  option (4 groups of 8)

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Analysis

• Descriptive mostly in-text
• Average yield of CPR by block of rounds
• Percent of social optimum
• 8 subjects in each group
• Small numbers of groups for each condition (in
  most cases 3 groups)
• Anecdotal discussion of communications and
  sanctions

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Findings

• Establish a social dilemma
• Communications alone lead to higher average
  yields
• High endowment environment is less effective
• Sanctions alone overuse of sanctions
• Low efficiency due to cost of sanctions
• No support for trigger strategies
• No over investment in CPR at the individual level
  in response to defections
• Covenants with our without a sword have force
• Swords without a covenant may be worse than the
  state of nature