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UNSW | BUSINESS SCHOOL | SCHOOL OF ECONOMICS Calling the shots Experimental evidence on significant aversion to non-existing strategic risk Ben Greiner
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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
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An experiment
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A B B A: $?? B: $?? A: $?? B: $?? A: $?? B: $?? A: $?? B: $??
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A B B A: $80 B: $20 A: $0 B: $0 A: $50 B: $50 A: $0 B: $0
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A B B A: $80 B: $20 A: $0 B: $0 A: $50 B: $50 A: $50 B: $0
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A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 50 B: 0 A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 0 B: 0 Ultimatum Game Reverse Impunity Game
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A B B A: € 6.40 B: € 1.60 A: € 0.00 B: € 0.00 A: € 4.00 B: € 4.00 A: € 4.00 B: € 0.00 A B B A: € 6.40 B: € 1.60 A: € 0.00 B: € 0.00 A: € 4.00 B: € 4.00 A: € 4.00 B: € 4.00 Ultimatum Game Reverse Impunity Game Experiment 1
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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
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A B B A: € 6.40 B: € 1.60 A: € 0.00 B: € 0.00 A: € 4.00 B: € 4.00 A: € 4.00 B: € 0.00 A B B A: € 6.40 B: € 1.60 A: € 0.00 B: € 0.00 A: € 4.00 B: € 4.00 A: € 4.00 B: € 4.00 Ultimatum Game Reverse Impunity Game Experiment 1 55%28% 99.3% 91.0% 93.8%
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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)
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Guessed Acceptance Rates of Unequal Split Proposals Experiment 2: Beliefs Ultimatum Game Reverse Impunity Game ~ 94.4%92.8% 91.0%93.8% Exp 1 observed Exp 2 Average Guess 99% Exp 2 Median Guess ~
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≥ 98.8%96.6% 99.3% Guessed Acceptance Rates of Equal Split Proposals Experiment 2: Beliefs Exp 1 observed Exp 2 Average Guess 100% Exp 2 Median Guess ~ Ultimatum Game Reverse Impunity Game
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> 79.0%51.6% 55.2%28.3% Guessed Share of Unequal Split Proposals Experiment 2: Beliefs Exp 1 observed Exp 2 Average Guess 89.5%48.1%Exp 2 Median Guess > Ultimatum Game Reverse Impunity Game
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A B B A: € 12.0 B: € 3.0 A: € 0.0 B: € 0.0 A: € 7.5 B: € 7.5 A: € 7.5 B: € 0.0 A B B A: € 12.0 B: € 3.0 A: € 0.0 B: € 0.0 A: € 7.5 B: € 7.5 A: € 0.0 B: € 0.0 Ultimatum Game Reverse Impunity Game Experiment 3
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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
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A B B A: € 12.0 B: € 3.0 A: € 0.0 B: € 0.0 A: € 7.5 B: € 7.5 A: € 7.5 B: € 0.0 A B B A: € 12.0 B: € 3.0 A: € 0.0 B: € 0.0 A: € 7.5 B: € 7.5 A: € 0.0 B: € 0.0 Ultimatum Game Reverse Impunity Game Experiment 3 64%39% 94%100% 70% 87% 55%28%
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A B B A: $ 31 B: $ 15 A: $ 10 B: $ 10 A: $ 23 B: $ 23 A: $ 23 B: $ 23 A B B A: $ 31 B: $ 15 A: $ 10 B: $ 10 A: $ 23 B: $ 23 A: $ 0 B: $ 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
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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
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Experiment 4: Results 72% 77% 89% 75% 100% 83% 56% 96% 79%
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A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 0 B: 0 Ultimatum Game Reverse Impunity Game A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 50 B: 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.
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A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 0 B: 0 Ultimatum Game Reverse Impunity Game A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 50 B: 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)
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Thank you.
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A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 0 B: 0 Ultimatum Game Reverse Impunity Game A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 50 B: 0 Behavior is not compatible with a consistency between strategies and rational beliefs Social preferences Errors Risk Aversion
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A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 0 B: 0 Ultimatum Game Reverse Impunity Game A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 50 B: 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”
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A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 0 B: 0 Ultimatum Game Reverse Impunity Game A B B A: 80 B: 20 A: 0 B: 0 A: 50 B: 50 A: 50 B: 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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