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Small Decision-Making under Uncertainty and Risk

Takemi Fujikawa University of Western Sydney,

Australia

Agenda

- Introduction
- Experimental Design
- Experiment 1
- Experiment 2
- Conclusion

Introduction

- This presentation attempts to
- examine behavioural tendency in Small

Decision-Making (SDM) problems - present results of two experiments on SDM

problems - introduce the search-assessment model
- introduce EU model for SDM problems

What are SDM problems?

Introduction

- SDM problems involve repeated tasks The decision

makers (DMs) face repeated-play choice problems. - Each single choice is trivial It has very

similar but fairly small EV. - Little time and effort is typically invested in

SDM problems - The DMs have to rely on the feedback obtained in

the past decisions.

Experimental Design

Experimental Design

- Search treatment (Experiment 1)
- Experiment 1 was conducted without giving

subjects prior information on payoff structure. - To construct the search-assessment model
- Choice treatment (Experiment 2)
- Experiment 2 was conducted with giving subjects

prior information on payoff structure. - To construct EU model

Experimental Design

Experimental Design

- Experiment 1 and Experiment 2 were conducted in

order at Kyoto Sangyo University Experimental

Economics Laboratory (KEEL). - Forty-two undergraduates at KSU served as paid

subjects and participated in both experiments. - Subjects received cash contingent upon

performance (i.e., points they earned). - Exchange rate 1 point 0.3 Yen (0.25 US cent).

Choice Problems

Experimental Design

- Each experiment consists of Problem 1, 2 and 3.
- Each problem consists of 400 rounds.
- Subjects are asked to choose either H or L 400

times. - In each round t (t1, 2, , 400), subjects are

asked to choose either H or L.

Problem 1 H 4 (0.8) 0 (0.2) L 3 (1)

Problem 2 H 4 (0.2) 0 (0.8) L 3

(0.25) 0 (0.75)

Problem 3 H 32 (0.1) 0 (0.9) L 3 (1)

Experiment 1 Search in SDM problems

- Subjects in Experiment 1 are NOT informed of

payoff structure.

Experimental screen

Experiment 1

Problem 1 H 4 (0.8) 0 (0.2) L 3 (1)

Problem 2 H 4 (0.2) 0 (0.8) L 3

(0.25) 0 (0.75)

Problem 3 H 32 (0.1) 0 (0.9) L 3 (1)

Basic task in each problem was a binary choice

between two buttons for 400 times without giving

subjects prior information on payoff structure.

Results of Experiment 1

Experiment 1

- choiceH The mean proportions of H choices. For

example, if she has chosen H 100 out of 400

times, then choiceH is 0.25. - posteriorH The posterior average points of H.

For example, if she chose H 10 times in Problem 1

and unluckily has got 24 pts, then posteriorH is

2.4 (24/10). Note that posteriorH may or may not

be the same as EV(H).

Problem 1 H 4 (0.8) 0 (0.2) L 3 (1)

Experiment 1

Results choiceH

Problem 1 (choiceH0.48) H 4 (0.8) 0 (0.2)

L 3 (1)

Problem 2 (choiceH0.55) H 4 (0.2) 0 (0.8)

L 3 (0.25) 0 (0.75)

Problem 3 (choiceH0.22) H 32 (0.1) 0 (0.9)

L 3 (1)

Experiment 1

The tendency to select best reply to past outcomes

Problem 3 (choiceH0.22) H 32 (0.1) 0 (0.9)

L 3 (1)

- After the first 100 trials, posteriorH has become

around 1.6. - Then, subjects may have judged subjectively that

EV(H)?1.6 and EV(H)ltEV(L)

Analysis

Experiment 1

- Subjects are undisclosed payoff structure in

Experiment 1. - In Experiment 1, the information available to

subjects is limited to feedback about outcomes of

their previous decisions. - Subjects are required to discover payoff

structure by trying both alternatives as they are

undisclosed payoff distribution.

The search-assessment model

Experiment 1

- Recall that only one alternative includes

uncertain prospect Problem 1 and 3. - To investigate Problem 1 and 3, the following

Problem A is examined. - Suppose each DM in Problem A is asked to choose

either H or L at each round t (t1,2, , 400).

Problem A H x (p) 0 (1-p) L 1 (1) where

0ltplt1, pxgt1.

Problem 1 (choiceH0.48) H 4 (0.8) 0 (0.2)

L 3 (1)

Problem 3 (choiceH0.22) H 32 (0.1) 0 (0.9)

L 3 (1)

Experiment 1

- If she chooses H m times and gets an outcome of

x k times, then her posteriorH is greater than

or equal to 1, which is EV(L), with the

probability P(Hm) - This allows us to analyse the number of H choices

required for judging that EV(H)gtEV(L).

Problem A H x (p) 0 (1-p) L 1 (1) where

0ltplt1, pxgt1.

Problem 1 (choiceH0.48) H 4 (0.8) 0 (0.2)

L 3 (1)

Problem 3 (choiceH0.22) H 32 (0.1) 0 (0.9)

L 3 (1)

P(Hm) for Problem 3

Experiment 1

- P(Hm) is calibrated by setting p0.1 and x32/3.
- Calibration implies the probability that

posteriorHgt3 does not exceed 0.98 until H is

chosen 10,000 times in Problem 3.

Problem 3 (choiceH0.22) H 32 (0.1) 0 (0.9)

L 3 (1)

Problem A H x (p) 0 (1-p) L 1 (1) where

0ltplt1, pxgt1.

Experiment 2 Choice in SDM problems

- Subjects in Experiment 2 are clearly disclosed

payoff structure.

Experiment 2

Experimental screen

Problem 1 H 4 (0.8) 0 (0.2) L 3 (1)

Problem 2 H 4 (0.2) 0 (0.8) L 3

(0.25) 0 (0.75)

Problem 3 H 32 (0.1) 0 (0.9) L 3 (1)

Basic task in each problem was a binary choice

between two buttons for 400 times with prior

information on payoff structure.

Results choiceH

Experiment 2

Problem 1 (choiceH0.63) H 4 (0.8) 0 (0.2)

L 3 (1)

Problem 2 (choiceH0.69) H 4 (0.2) 0 (0.8)

L 3 (0.25) 0 (0.75)

Problem 3 (choiceH0.4) H 32 (0.1) 0 (0.9)

L 3 (1)

Analysis

Experiment 2

- Is it a optimal decision for risk-averse DM to

choose both H and L within 400 trials? - Results of Experiment 2 can be analysed within

the framework of EUT since subjects are disclosed

the payoff structure. - Making objective probabilities available to

subjects allows direct evaluation of EUT. - In analysing the results, this paper presumes

that subjects are asked how many times of 400

rounds they are willing to choose H once for all.

Experiment 2

- The utility function, u(x), is considered
- To investigate an optimal behaviour in Problem 1

and 3, we employ the risk-averse utility function

with

Problem 1 (choiceH0.63) H 4 (0.8) 0 (0.2)

L 3 (1)

Problem 3 (choiceH0.4) H 32 (0.1) 0 (0.9)

L 3 (1)

The EU model for Problem 1

Experiment 2

- Let V1(m) be EU she acquires when choosing H m

(?400) times in Problem 1 - where k is the number for the realised highest

payoff of H in Problem 1 (i.e., 4 points). - How many times out of 400 times should DM choose

H to maximise V1(m)?

Problem 1 (choiceH0.63) H 4 (0.8) 0 (0.2)

L 3 (1)

Analysis of Problem 1

Experiment 2

- V1(m) has its maximum at m252.
- An theoretically-optimal number of H choices is

252 out of 400 times. - DM can maximise EU by choosing H 252 out of 400

times. - This coincides exactly results of Experiment 2

that H was chosen 252 times.

Problem 1 (choiceH0.63) H 4 (0.8) 0 (0.2)

L 3 (1)

Conclusion Experiment 1 (search in SDM problem)

- Experiment 1 includes simple binary choice

problems without giving subjects any information

on payoff structure. - I have presented the search-assessment model,

which - shows that the probability that subjects

misestimate the payoff structure is large with

only 400 times, even in simple and SDM problems. - implies that subjects are likely to misunderstand

in such a way that EV(H)ltEV(L).

Conclusion Experiment 2 (choice in SDM problem)

- Experiment 2 is conducted with giving subjects

prior information on payoff structure. - Hence, the results can be analysed within the

framework of EUT. - In Experiment 2, subjects choose both H and L in

each choice problem. - This paper presents the EU models, which reveal

that it is theoretically-optimal to choose H

often but not all the time within given trials,

to maximise EU.

References

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