Katz, Leonard

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University of Massachusetts AmherstScholarWorks@UMass AmherstMasters Theses 1911 - February 20141961Monetary incentive and range of payoffs asdeterminers of risk taking.Leonard KatzUniversity of Massachusetts AmherstFollow this and additional works at: https://scholarworks.umass.edu/thesesThis thesis is brought to you for free and open access by ScholarWorks@UMass Amherst. It has been accepted for inclusion in Masters Theses 1911 -February 2014 by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contactscholarworks@library.umass.edu.Katz, Leonard, "Monetary incentive and range of payoffs as determiners of risk taking." (1961). Masters Theses 1911 - February 2014.1655.Retrieved from https://scholarworks.umass.edu/theses/1655MONETARY INCENTIVE AND RANGE OF PAYOFFSAS DETERMINERS OF RISK TAKINGTilt • • : • ;.' \*:vi\"r .'ii.W;''.;^'.'^.* :V; -'.V;:;- ' V; ^•. ,.";iu;J^- —--^ .::*«.v.KATZ-1961Monetary Incentive and Range ofPayoffs as Determiners of Risk TakingLeonard KatzB. 3. University of MassachusettsThesis Submitted in Partial Fulfillmentof the Requirements for theMaster of Science DegreeAdvisor: J. L. Myers September, 196IUniversity of MassachusettsTabl-3 ox ContentsPageIntroduction2.Method 2Materials 2Procedure....... 3*Ratings 5Subjects 5Results 5Choices ...... 5Ratings 6Discussion 10Summary 16References 17Acknowledgments 19&5?:IntroductionThe few studies on the decision to gamble have beenprimarily concerned with measurement of utility (e.g.,Mosteller & Nogee, 1951; Royden. Supres, & Walsh, 1959)and. therefore, have provided no systematic data on vari-ables affecting this decision. In several studies gamb-ling behavior was related to distribution of payoffs(Edwards, 195^J Coombs & Pruitt, i960). Subjects chosebetween bets rather than between gambling and not gambling.Subsequently, Myers and associates have been concerned withthe effects of parameters of the payoff distribution uponthe choice between gambling and not gambling.Myers and Sadler (i960) varied the number of chipswhich might be won or lost on each gamble (range), theaverage payoff being zero. When the alternative to gamb-ling was the sure gain of one chip, gambling increased withincreases in range; when the alternative to gambling wasthe sure loss of one chip, gambling decreased with an in-crease in range.Had the chips been exchangeable for money, Myers andSadler 1 s results might have been different. Both monetaryincentive and range of payoffs increase the risk associatedwith e' ch gamble. The Implied hypothesis, which is the op-2posite of that generated by data on effects of incentive onsequential choices, is that Increased monetary incentive,like a wider range, should Increase gambling, where thealternative tc gambling ie the sure gain of one chip, and.decrease gambling when the alternative to gambling is thesure loss of one chip. To decide between these alternativeimplications, in the present study the decision tc gamblewas investigated as a function of monetary incentive andpayoff range. The chips were worth no money or 5 cents anda decision to gamble involved a narrow, medium, or widerange of unknown ray off.In addition to providing data on the effects of mone-tary incentive, the present study investigated the effectsof a payoff range greater than that used in the Myers &Sadler study. To control for any range effects due todifferences among ranges due to sequences of payoffs, onesequence was randomly generated, and the other two were de-rived from it in the manner described in the procedure sec-tion.MethodMaterials . Four decks of 100 3 x white cards wereprepared. In the known payoff deck $0 cards with *1 writtenon then alternated randomly with 50 cards with -1. The3three other decks of 100 cards eaoh provided differentranges of unknown payoffs. The narrow-range deck (N) hadIntegers randomly chosen from *2 to +6 and from -2 to -6.Thf? medium range deck (M) was constructed by adding 10 toevery positive nu iber of (N) and subtracting 10 from everynegative number Riving a range of +12 to *16 and -12 to -16.The wide range deck (W) was constructed by adding and sub-tracting 20 to the Integers In (N ) • Thus the ordinal posi-tions of the oardB were the same In all three decks,Pr ore dure . Eighteen j3s gambled only for poker chips(0^) and 18 others gambled for chips worth 5 cents apiece.On eaoh of three successive days, 3 was presented with theknown payoff deck, and a different one of the unknown pay-off decks. Order of use of the (N), (M), and (W) decks wagcounterbalanced In a 3 x 3 Latin Square with six 3s adminis-tered eaoh order. The main features of the experimentaldesign are shown on the left-hand side of Table 1.The 3s were run Individually. They were given fullInstructions at the beginning of the first session.Briefly, 3b were told to turn over the top card In the deckof known payoffa at th* beginning of eaoh trlsl. Vhey thenoho-^e between standing pat by aoceptlng the gain or loss ofone chip represented by the card f-nd gambling by drawingthe top cerd from the deck of unknown payoffs. It 812 ^ £c* c oHI c300aCDCOl-iaj«HU<P rHc eR 1H OOorHIIHOINOCMCcCO* -.o oc >>M asw p*a0) I V.a>£ o ^c* -a &ce o d Pi>>t>cd #»c oo cX MNO rH O<n,cMM> ONC^CMo>2CM HH CMG\rHrH CMNO CMnO Hcm cmH HH H•AOs vO (NvO OOn O*r\oomiocso o-*T\C00\0CO vr>NO INCM 00CO c~>CM HH CCM OnCVJ rHOn CMCM CMH CMO (V O (X)5 nCM H O CMr\cvNO^tU^{N-3* 00* CMC c\i^ NOON\rvr^CNONHoo ro^tooNO H3F«oo^tH HF~\rHCM OO N O ONO Hr\(M-3* CMCNi rHOnc^cmCM CMso cmC^CMONO HnOvtvOn•^€NCM NO-3- 00COo ONUNCO(NOON On^CN sn>aQ o00 XTv03 CM HCM1H§ OnoVAONO (NCNOnCM HNO rs-00 00CM H00 OnCM v\H H0N\TxH CMv\(NVT\CNCM CMO NOCM ONNO CNNO 00^ CO O00CO NOCO oNO IN00 CMNOHH4- IrHIrH H rH H4- IH rH4 IHrH4* Iodecided not to gamble, the top card in the unknown payoffdeck was turned anyway, showing what he wov.ld have won orlost; had he gambled. For each fcubeeqv.er.t- .-ensicn, theywere told QtB&jj that the unknown payoff deck was new.Two hundred poker chips were stacked in fro.it of £ 9ROd those with a monetary incentive were told that eachchip was worth 5 cents; their initial stake was worthRatings . At the end of each ettalon, Se were given an11-point scale from -5 to *5» along which they rated theiaeans of the known payoff dec-, and of the unknown payoffdeck of that session. They were also asked to describe,their gambling strategies and changes in strategy. Afterthe third session, j>s were also asked what they would havedone diffe ently in the first tv/o sessions..Subjects . Each of 36 men undergraduates enrolled inthe University Summer Session was paid $3.00 to participate.They were randomly divided into two groups of IS £8 each.ResultsChoices. The scores were proportions? of choices togamble on both +1 and -1 trials during each of four 25-trial blocks. For example, if an 3 gambled on 3 »f the 12or lj 4-1 trial.3 of a particular block, his proportion forthat block was .250 or .231. Table 1 presents means and6SDs of these proportions for each combination and range;the means are plotted in Figure 1. Analysis of variancewas performed on arc-sine transforms of the proportions.The results of this analysis (Table 2), in conjunctionwith the relationships shown In Table 1 and Figure 1,suggest the following conclusions: (a) under all combina-tions of range and incentive , more risk-taking occurred on-1 trials than on +1 trials (P .001); (b) incentive hadlittle effect on the total number of risks taken; (c)more gambling occurred with deck M than with deck N on ««1trials and the reverse on -1 trials (P .01); and (d)gambling with deck V/ is affected by both value and incen-tive; there was more gambling with the 5 cent incentivethan with no incentive on «•! trials* and the converse on-1 trials (P<.001).In addition, there were a number of significant inter-actions Involving blocks of trials. As of now, however,no rational explanations can be offered. Therefore, de-tailed description of the interactions involved would beof little use.Ratings . Table 3 shows the means of Sb* ratings ofthe means of the known an:' unknown payoff decks for eachcombination of range and incentive. The means for theknown payoff deoks were from -.22 to f»«tfr| those for theunknown payoff decks were from -.66 to 1.05. Thus, theS3SN0dS3d 9NI"I8V\IV9 dO NOIlUOdOUdTable 29*mmrj of Analysis of VarianceSource Of as -Incentive (I) 1 710.00 710.00Ss/I 34 7lf6/o.oo 2,047.71Value (V) 1 103*825.00 103.825.00 33.72***(Known Payoff)Range (It) 2 2,722.80 1,361.40 2.22Blocks (B) 3 4,364.80 I.454.93 4.90**V 1 B 3 2. 961. 70 987.23 3.28*V x R 2 3,671.20 1,835.60 8.73**R x B 6 1,122.10 187-01 8.87**R x B x V 6 2,206.50 367.75 2.25*V x I 1 2,910.50 2,910.50 1.07B x I 3 170.40 56.80 0.19R x I 2 585.40 292.70 0.47V x I x R 2 3,212.20 1,606.10 13.66***R x I x B 6 37O.OO 61.66 2.82*V x I x B 3 714.50 238.16 1.39ft x B x V x I 6 5.399.70 154.27 1.57B| x V/I 3^ 94,647.86 2,701.36Ea x B/I 102 30,946.24 296.53Ss x R/I 68 42,77^.16 611. 0jSm x V x B/I 102 30,619.01 300. 16Ss x V x R/I 68 21,441.39 210.203s x R x B/I 204 4,463*30 21.80Ss x V x B x R/I 204 33*233.87 162.91* P c.05** P c.01*** P<.0019Table 3Mear.s of Rating of Deck MeansRange —qi WOT—„ JJnknown» .33 .16 ,** -o.66* .33 .16 .oo 1.03W -.22.83 0.66means for the known payoff deck were closer to the truemean of zero and were less variable than the means for theunknown payoff decks. Neither set of means varied system-atically with incentive or range of unknown payoff. Norwere there any systematic relationships between these deckmeans and either overall proportions of risks or propor-tions of risks for the last 25 trials. Most Ss reportedfollowing a gambler's fallacy strategy and none reportedan awareness of gambling differentially with differentdecks of unknown payoffs. Incentive had no differentialeffect.DiscussionThe decision to gamble or not to gamble followingknown outcomes of loss or gain of a poker chip was investi-gated as a function of three ranges of unknown payoff in-volving the loss or gain of chips worth nothing or worthfive cents. Previous findings (Myers & Sadler, 1961;Myers & Katz, I96I) of more gambling when the alternativeto gambling was the loss of a chip than when the alterna-tive was the gain of a chip were confirmed. Monetary in-centive reduced this difference: trials when the alterna-tive was -1 were followed by fewer choices to gamble forchips worth 5 cents than for those worth nothing, while11trials where the alternative was 4-1 were followed by morechoices to gamble for chips worth 5 cents than for thoseworth nothing. Thus, contrary to the Implication of find-ings for two-choice situations and in accordance with thenotion that monetary payoff and range are functionallyequivalent, for all three ranges monetary incentive yieldedan increase in gambling on 4-1 trials and a decrease on -1trials.With monetary incentive, increasing the range resultedin more gambling after the +1 alternative and less gamblingafter the -1 alternative. With no monetary incentive, in-creasing the range reduced gambling after the -1 alternativebut after the 4*1 alternative gambling increased from thenarrow to medium range and then decreased to the lowestvalue with the wide range.Other experiments have shown the form of value andrange interaction obtained for the 5 oent incentive group.With three ranges vr to and including the medium range ofthe present study, Myers and Sadler found more gamblingconsistently with wider ranges when the alternative wasthe gain of a chip, but less gambling with wider rangeswhen the alternative was the loss of a chip. With rangesN and M, Myers and Katz obtained similar results, endSuydam (l?6l), using a very different procedure, also found12this convergence of curves for positive and negativevalue I over several ranges.Figure 2 presents a possible explanation of the con-vergence effect. Response strength is plotted as a func-tion of increasing ran;;e, the various curves representinggradients of approach and avoidance (tendency to gamble andnot gamble) against positive and nogative alternatives togambling. The position of the curves is derived from thefollowing assumptions: (a) both approach and avoidancetendencies Increase as range increases, (b) the slope ofthe avoidance gradient is steener than that of the approachgradient when the alternative is the loss of one chip, and(c) the slope of the approach gradient is steeper than thatof the avoidance gradient when the alternative is the gainof one chip. If amount of gambling is considered to bedirectly related to net response strength (the differencebetween approach and avoidance), Figure 2 describes the ex-perimental effects summarized above. The above pointslead to the prediction that the curves will continue toconverge as range increases. Assumption (c) appears tocontradict a pri-nary assumption of Miller (1959) • However,Miller's gradients are invariably plotted as a function ofeither distance or time to a goal. Little data exist onrate of change of the gradient as a function of change inH19N3U1S 3SN0dS3Hmotivating conditions and there are no a priori groundsfor rejecting assumptions (b) or (c). Since it If doubt-ful that 3s would ever gamble more on +1 trials than on-1 trials, no range can exist where the +1 gradients arefurther apart than the -1, which would occur if the approach-avoidance curves were linear over all ranges, linear gradi-ents have been used as a first approximation merely for thesake of simplicity. If amount of gambling is considered tobe directly related to nec response s-crengtn (the differencebetween approach and avoidance), Figure 2 describes the ex-perimental effects summarized above. The above pointslead to the prediction that the curves will continue toconverge as range increases.If the monetary worth of the alternative remains con-stant as incentive changes, incentive can be substitutedfor range. However, data for the 5 cent incentive repre-sent not only the effect of increasing the monetary worthof each payoff for gambling but also the effect of increas-ing the monetary worth of each alternative to gambling.If number of ohips ami monetary worth of chips functionsimilarly, (a) increasing the monetary worth of the payofffor gambling increases the tendency to gamble on the 4-1trial 8 an d not to gamble on -1 trials and (b) increasingthe monetary worth of the alternative to gambling decreases15the tendency to gamble on +1 trials and not to gamble on-1 trials. The data of the present study suggest that theeffect of increased monetary worth of the payoff for gamb-ling was the greater since Ss gambled more on *1 trialsand less on -1 trials with the 5 cent incentive than withno incentive. The wide range showed this effect mostclearly. However, a study is required which will separatethe effects of increased incentive for gambling and in-creased incentive for not gambling. Such a study is represented by the following design which varies the raonetaryworth of both alternative and payoff for gambling.Payoff for GamblingIt1*Alternative5/5*The effect upon gambling behavior due to monetary•forth of the payoff for gambling will be inferred fromdifferences in the column means and the effect due tomonetary worth, of the alternative will be inferred from16differences in the row means. In addition, interactiondata will be available which is lacking in the presentstudy.With no incentive, in both the present study and Myersand Rats' f study, instead of continued convergence from Mto W, the curves diverged. At present, this result cannotbe explained. Further research is required with mere levelsof range, incentive and values of the alternative than havethus far been employed.SummaryThe decision to gamble was investigated as a functionof monetary incentive, range of payoff a for gambling, andvalue of payoff in lieu of gambling. One group of 18 menundergraduates gambled for chips only and another group of18 gambled for chips worth 5 cents each. Three ranges ofunknown payoffs were used, one at each of three sessions.The alternative to gambling was a constant hnown payoff.Neither incentive nor range influenced the total num-ber of risks taken. More gambling occurred when the alter-native to gambling wa3 a loss than when It was a gain. Aseither range or monetary incentive Increased, more gamblingoccurred when the alternative was a gain ana ltfl when itwas a loss.17ReferencesCoomb, C. H. i * Pruitt, D. G. Components of risk in deci-sion-making: probability and variance preferences.I* MB • Psychol . » i960, 60, 265-27?.Edwards, V. The theory of decision making, fg* chol .Bull., 195'! 1 £1, 380-^17.Edward?, W. Reward probability, amount, and informationas determines of sequential two-alternative decisions.J. ^xd. Psychol . , 1956, £2, 177-188.Oocdnow, J. Determinants of choice In two-choice situa-tions. Amer . Psychol . , 1955, 6q» 106-116,Miller, W. E. Extensions of liberalized S-R theory. InKoch, S. (Ed.), fe.yoholOk v : A Study of A Science.New York: McGraw-Hill, 1959.Hosteller, F. & Nogee, P. An experimental measurement ofutility. J. Pol. vcon . , 1951» j}jMyers, J. L. &. Fort, J . G. A sequential aneljeis of gamb-ling behavior. Parer presented at meeting of Fsycho-ror.lc Society, Columbia University, 1961.Myers, J. L. , & Katn, L. Ran ;e of payoffs and feedbackin riik-taking. Mimeographed report, University ofMatMUft uf.etts , 1961.Myers, J. L. > & Sadler, S. Effects of ranp-e of payoffs asa variable in risk-taking. J. exr . Ps,ycl cl . , 1961, 60,:-'C6-30Q.Myers, J. L. i Taub, H. A., ft Reilly, R. Dif rerentlal cost,gain, and relativo frequency of reward in a sequentialohoice situation. J. I's.voho^. , In Press.Hoyden, L. H. , Suppes, P., & Walsh, K. a model for theexperimental, measurement of the utility of gambling.Sehav. 3ci.» 1939* i# il-lti.Bttydam, u. M. Two parameters of risk-taking behavior. Un-published Master's problem, University of Massachu-setts, 1961.Taub, H. A., & Myers, J. L. Differential monetary aalnsin a two-choice situation. J. exp . Psychol. , 19bl,61, 1.57-162.AcknowledgmentsI would like to express my approbation to Dr. JoroiueL. Myers, who directed thin stucy, for his ruany construc-tive Bulges tionu in the design anu execution of the experl-raont.I would also like to express my appreciation to urB.Albert E. Oons and Helen F. Cullon for their valunMecomments made vhii.^ serving member u of BJ thenia com-mit tee.APPROVED IJ

Monetary incentive and range of payoffs as determiners of risk taking.

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Monetary incentive and range of payoffs as determiners of risk taking.

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