Jurnal PA Ztree

Institute for Empirical Research in EconomicsUniversity of Zurich

Working Paper SeriesISSN 1424-0459

forthcoming in: Experimental Economics

Working Paper No. 18

Efficient Contracting and Fair Play in a Simple

Principal-Agent Experiment

Vital Anderhub, Simon Gächter and Manfred Königstein

September 2000

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Figures

Figure 1: Marginal return function and marginal cost function as well asconditionally rational e¤ort choices for s = 60%, respectively s = 100%.

28

Figure 2a: Distribution of o¤ered …xed wages

Figure 2b: Distribution of o¤ered return shares

Figure 2c: Distribution of suggested e¤ort

29

Figure 3: Combinations of return share and …xed wageas o¤ered by the principals

Figure 4: Surplus share o¤ered to the agent(for e ¢ cient contract o¤ers)

30

Figure 5: Predicted acceptance rate (probability of ± = 1) conditionalon the surplus share o¤ered to the agent according

to logit regressions for RG1, respectively RG2

Figure 6: Frequency distribution of agents’ actual e¤ort choicesin both sequences of the repeated games (RG1 and RG2)

31

Figure 7: Conditionally rational e¤ort choices

32

Figure 8: The number of individuals who deviated from rationale¤ort (e ¡ be) for a given surplus share is indicated above the respective bar

33

Appendix: Experimental instructionsThese instructions were originally written in German. Both the principal and the agent received

- except for some role-specific minor details - the same instructions.

General information

The experiment you participate today is joint research with the Humboldt-University Berlin. It is financed by severalscience foundations. For your participation you will receive 15 Swiss Francs. Dependent on your decisions you canearn additional money. It is possible that some of your decisions lead to losses. You will have to finance them out ofthe gains from your other decisions, or, if necessary out of your show-up fee. However, you can always makedecisions that avoid any losses.

During the experiment you income will be calculated in points. The exchange rate of points into Swiss Francs is

1 point = 1.3 Rappen.

At the end of the experiment all points you have earned will be summed up, exchanged into Swiss Francs and paidout to you in cash immediately.

Please note that during the experiment communication is not allowed. If you do have questions please raiseyou hand. We will answer you questions in private.

Instructions1. IntroductionIn this experiment you will learn about a decision problem that involves two persons. We will call them participantsX and Y. All participants in this experiment are allocated in two groups: the group of participants X and thegroup of participants Y.

You belong to the group of participants X!

Thus, you will decide during the whole experiment in the role of a participant X.

The experiment consists of 6 periods. At the beginning you will be randomly matched with a participant of group Y.You will be paired with this participant in all 6 periods. You will make your decisions at the computer. The usage ofthe computer will be explained to you if necessary. Your decisions will be transmitted via the computer to participantY. This participant will only get informed about your decision. He will never learn your name or your participantnumber, i.e., your decisions remain anonymous.

2. An overview of the experimentThe experiment consists of 6 periods. It may help you to understand the decision situation if you think about thefollowing scenario. Participant X decides in the role of a "firm". The "firm" has an employee (participant Y), whosework effort produces some period return. Y can choose his work effort freely in each period. Below we will explainwhat work effort means and how the period return comes about. However, it is true that a higher work effort leads toa higher period return, but it also causes costs that Y has to bear.

Y's payment is determined in an employment contract and can take place in two forms, with a fixed wage and/or areturn share. The fixed wage has to be paid by participant X to participant Y independently of the period return. A

return share means that Y receives an agreed share (in percent) of the return. In the following we will call thesepercentage share "return share Y". In consequence, the "return share X" is just the rest (i.e., 100 percent minus"return share Y").

Thus, each period consists of three stages:

1. X makes, in accordance with the rules, up to two contract proposals.2. Y chooses one contract among the possible contracts.3. Y makes his work effort choice.

Afterwards X and Y will be paid according to the rules.

3. The experimental details

3.1 Employment contract: The proposals of participant X

At the beginning of each period, first an employment contract will be determined. For the contract design thefollowing holds:

• In each period there is a so-called "status quo"-contract that becomes effective if there is no agreement about anew contract. The "status quo"-contract consists of a fixed payment of 0 and a "return share Y" of 0. This "statusquo"-contract is the same in each period.

• In addition to the "status quo"-contract in each period X can - in the first period make up to two new contract proposals - in each of the later periods make one new contract proposal.

Y decides whether he accepts the new contract proposal (or which of the new proposals he accepts, respectively), or

whether the "status quo"-contract shall become valid.

• Each contract proposal by X also contains a desired work effort that, however, is not binding for Y.

A contract proposal consists of three components: a fixed wage, a "return share Y" and a desired work effort.Participant X is in the bounds of the rules given below completely free in the design of the contract proposals.

• It is possible to agree on a positive or a negative fixed wage. If the fixed wage is positive, this means thatparticipant Y gets this wage from participant X, regardless of the period return. A negative fixed wage means thatY has to pay that amount to X, regardless of the period return.

• The "return share Y" is expressed in percentage points. It says how large Y's share - in percent - of the totalperiod return is. Participant X gets the rest ("return share X" = 100 percent minus "return share Y").

• X's desired work effort is not binding for Y.

For the contract design the following rules hold:

−700 ≤ fixed wage ≤ 700

0 ≤ "return share Y" ≤ 100 (in percent)

0 ≤ desired work effort ≤ 20

Only integer numbers are possible!

In designing the contracts ALL combinations that are compatible with these rules are possible!

To make the rules clear to you, we depict the screen that will be shown to X at the beginning of period 1:

On this screen (as well as in all other screens in which you have to make a decision) you see the current periodnumber at the top left and at the top right the remaining time. Participant X now has the possibility to make up to twocontract proposals by just entering them into the corresponding boxes. The screen for the subsequent periods is verysimilar except that participant X can only propose one new contract.

3.2 Employment contract: The choice by participant Y

Participant Y chooses among the available contracts. In period 1 Y can choose between the "status quo"-contract(„fixed wage of 0 ["Festgehalt"], return share Y ["Erlösanteil von Y"] of 0 %“) and contract 1 or contract 2, and inall other periods between the "status quo"-contract or a new contract.

3.3 Work effort of participant Y

After Y has chosen a contract, he determines his work effort. The desired work effort ["gewünschterArbeitseinsatz"] stated by participant X in the contract is not binding for participant Y. The work effort is expressedas a number. In the enclosed table all possible work efforts (all integer numbers between 0 and 20) as well as theproduced returns are given. The table also contains the costs of the work effort that Y has to bear. The higher thework effort, the higher is the return but the higher are also the costs of the work effort.

3.4 Period payoffs and end of period

After participant Y has entered his work effort into the computer, the period gains will be calculated according to theformulas stated on the enclosed table.

Afterwards both participants will be informed about the decisions (work effort, fixed wages, "return share Y"), ownperiod payoff and the sum of the own payoffs so far. This ends a period and the next one starts.

4. Control questionnaire

The following control questions are only designed to test your understanding of the payoff calculations. You shouldlearn - with the help of some arbitrary examples - how the payoffs of X and Y change if the terms of the contract, orthe work effort changes. In the experiments you are in no way bound by these examples!

1. Y accepts the following contract: fixed wage: 580, return share Y: 10 %. Calculate the payoffs of X and Y if Ychooses a work effort of 2.Payoff X: Payoff Y:

2. The same as 1., but Y chooses a work effort of 18.Payoff X: Payoff Y:



5. Y accepts the following contract: fixed wage: -580, return share Y: 10 %. Calculate the payoffs of X and Y if Ychooses a work effort of 2.Payoff X: Payoff Y:






11. Y accepts the "status quo"-contract: fixed wage: 120, return share Y: 0 %. Calculate the payoffs if Y chooses awork effort of 0.Payoff X: Payoff Y:

Work effort, return of the work effort and costs of the work effort for Y:

Work effort:Total period return from work

effort

costs of work effort for Y

0 0 0

1 35 5

2 70 10

3 105 15

4 140 20

5 175 30

6 210 40

7 245 50

8 280 60

9 315 75

10 350 90

11 385 105

12 420 120

13 455 140

14 490 160

15 525 180

16 560 200

17 595 225

18 630 250

19 665 275

20 700 300

Period payoff Y: return share Y [= "return share Y"/100 ⋅ return]

+ fixed wage

− costs of work effort

Period payoff X: return share X [=((100 − "return share Y")/100) . return]

− fixed wage

Please note: the return share is given in percentages and shares the period return between X and Y.

Jurnal PA Ztree

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