UNSW | BUSINESS SCHOOL | SCHOOL OF ECONOMICS Calling the shots Experimental 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: $80 B: $20 A: $0 B: $0 A: $50 B: $50 A: $0 B: $0

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: 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

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

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: € 6.40 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%

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)

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 ~

≥ 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

> 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

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

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: € 12.0 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%

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

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%

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.

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)

 Thank you.

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

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”

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