UNSW | BUSINESS SCHOOL | SCHOOL OF ECONOMICS

Calling the shotsExperimental evidence on significant aversion

to non-existing strategic risk

Ben Greiner

Strategic Risk “Regular” risk:

• Uncertainty about an outcome of a random event• Known or unknown (guessed, subjective) probabilities

Strategic risk:• Uncertainty about strategies/actions other people are

going to choose• Subjective probabilities

In (standard) game theory there is no strategic uncertainty• Beliefs are correct in equilibrium, and equilibrium

strategies are best responses to beliefs

An experiment

A

B

B

A: $??B: $??

A: $??B: $??

A: $??B: $??

A: $??B: $??

A

B

B

A: $80B: $20

A: $0B: $0

A: $50B: $50

A: $0B: $0

A

B

B

A: $80B: $20

A: $0B: $0

A: $50B: $50

A: $50B: $0

A

B

B

A: 80B: 20

A: 0B: 0

A: 50B: 50

A: 50B: 0

A

B

B

A: 80B: 20

A: 0B: 0

A: 50B: 50

A: 0B: 0

Ultimatum Game Reverse Impunity Game

A

B

B

A: € 6.40B: € 1.60

A: € 0.00B: € 0.00

A: € 4.00B: € 4.00

A: € 4.00B: € 0.00

A

B

B

A: € 6.40B: € 1.60

A: € 0.00B: € 0.00

A: € 4.00B: € 4.00

A: € 4.00B: € 4.00

Ultimatum Game Reverse Impunity Game

Experiment 1

Experiment 1: Procedures One-shot experiment, pie size € 8, 145 participants Conducted in foyer of student restaurant:

• Students participant before lunch• Get paid after lunch

Participants decided in all (altogether 5) games and both roles (strategy method)

Payoff: 10-sided dice, thrown for 2 randomly matched subjects, each number implies a particular game and role assignment, game played out and paid out

A

B

B

A: € 6.40B: € 1.60

A: € 0.00B: € 0.00

A: € 4.00B: € 4.00

A: € 4.00B: € 0.00

A

B

B

A: € 6.40B: € 1.60

A: € 0.00B: € 0.00

A: € 4.00B: € 4.00

A: € 4.00B: € 4.00

Ultimatum Game Reverse Impunity Game

Experiment 1

55% 28%

99.3% 99.3%

91.0% 93.8%

Experiment 2: Beliefs 2 years after first experiment in large classroom

135 subjects were asked to predict frequencies of choices in 1st experiment

Instructions included all procedural information and original instructions of 1st experiment

Incentive compatible payment (step-function approximately following quadratic scoring rule)

≥98.8% 96.6%99.3% 99.3%

Guessed Acceptance Rates of Equal Split ProposalsExperiment 2: Beliefs

Exp 1 observedExp 2 Average Guess

100% 100%Exp 2 Median Guess

~ Ultimatum Game Reverse Impunity Game

>79.0% 51.6%55.2% 28.3%

Guessed Share of Unequal Split ProposalsExperiment 2: Beliefs

Exp 1 observedExp 2 Average Guess

89.5% 48.1%Exp 2 Median Guess

>

Ultimatum Game Reverse Impunity Game

A

B

B

A: € 12.0B: € 3.0

A: € 0.0B: € 0.0

A: € 7.5B: € 7.5

A: € 7.5B: € 0.0

A

B

B

A: € 12.0B: € 3.0

A: € 0.0B: € 0.0

A: € 7.5B: € 7.5

A: € 0.0B: € 0.0

Ultimatum Game Reverse Impunity Game

Experiment 3

Experiment 3: Play method

214 participants invited to laboratory

Role lottery Responders leave lab to next room

56 / 51 proposer-responder pairs in UG / RIG

Pen & paper

A

B

B

A: € 12.0B: € 3.0

A: € 0.0B: € 0.0

A: € 7.5B: € 7.5

A: € 7.5B: € 0.0

A

B

B

A: € 12.0B: € 3.0

A: € 0.0B: € 0.0

A: € 7.5B: € 7.5

A: € 0.0B: € 0.0

Ultimatum Game Reverse Impunity Game

Experiment 3

64% 39%

94% 100%

70% 87%55% 28%

A

B

B

A: $ 31B: $ 15

A: $ 10B: $ 10

A: $ 23B: $ 23

A: $ 23B: $ 23

A

B

B

A: $ 31B: $ 15

A: $ 10B: $ 10

A: $ 23B: $ 23

A: $ 0B: $ 0

Ultimatum Game Reverse Impunity Game

Experiment 4: Enter or not

ENTER THE GAME or STAY OUT?

Both ENTER: roles assigned 50/50; Both OUT: $20, $20 One enters, other stays out: ENTER= proposer, OUT= responder

Experiment 4: Procedures 66 / 52 participants in Ultimatum / Reverse Impunity Computerized, all decisions at computer screen, zTree

Pairs of 2 participants anonymously • decided simultaneously about entering• dropped out or not• were informed about random move, if necessary• proceeded and played Ultimatum / Rev. Impunity• got paid in cash

Experiment 4: Results

72%77%

89%75%

100%

83%56%

96%79%

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 0B: 0

Ultimatum Game Reverse Impunity Game

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 50B: 0

Although• equal splits are almost never rejected• equal splits are not expected to be rejected

a non-neglible share of people behaves as if there is a non-neglible chance that an equal split will be rejected.

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 0B: 0

Ultimatum Game Reverse Impunity Game

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 50B: 0

Behavior • is not compatible with a consistency between

strategies and rational beliefs• implies extreme risk aversion / pessimism when dealing

with people (strategic risk), as opposed to lotteries (regular risk)

Thank you.

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 0B: 0

Ultimatum Game Reverse Impunity Game

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 50B: 0

Behavior is not compatible with a consistency between strategies and rational beliefs Social preferences Errors Risk Aversion

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 0B: 0

Ultimatum Game Reverse Impunity Game

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 50B: 0

Maximin *behavior*? Von Neumann & Morgenstern: “...the rules of rational behaviour

must provide definitely for the possibility of irrational conduct on the part of others”

Selten (2001): vNM “do not pin down what to be expected from other players”, in vNM’s pre-Nash concept “players concentrate on what can be assured in a game”

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 0B: 0

Ultimatum Game Reverse Impunity Game

AB

B

A: 80B: 20A: 0B: 0A: 50B: 50A: 50B: 0

Strategic ambiguity aversion• Gilboa, Schmeidler – non-additive beliefs / capacities• Chateauneuf, Eichberger & Grant (2007) –

non-extreme-outcome additive capacities

• Eichberger, Kelsey (, Schipper) (2010, 2008, 2009) – compare to empirical / experimental data

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