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Rationality and the ‘price is right’
Journal
of Economic
Behavior
Rationality Randall
and Organization
21 (1993) 99-105.
North-Holland
and the ‘price is right’
W. Bennett
and Kent A. Hickman*
Gonzaga University, Spokane, WA, USA Received
October
1991. final version
received June 1992
The television game show ‘The Price Is Right’ offers a unique laboratory for observing decision making behavior because rewards are much higher than those encountered in a typical economics experiment and because of the substantial opportunity which contestants have for formulating their strategies. Analysis of contestant behavior substantiates (1) the persistence of decision making errors despite the penalties associated with such errors, and despite the existence of simple strategy which outperforms contestants’ behavior and (2) that learning drives competitors toward more effective behavior.
The television game show, ‘The Price Is Right’, offers a unique laboratory for observing decision making behavior by individuals motivated by economic rewards. It is especially interesting when contrasted with typical experimental economics studies, because its rewards for successful performance, generally an appliance or other consumer good, are several magnitudes of order higher than the nominal rewards offered in typical laboratory experiments.’ It is also of considerable interest in comparison with laboratory settings because the opportunity for learning the rules and formulating strategy is substantial.’ This may be contrasted with experiments where rules and objectives are explained immediately prior to the experiment, and the study is conducted with little opportunity for subjects to develop their ‘game-plans’, perhaps only a practice round (or none at all). Correspondence to: Kent Hickman, School of Business, Gonzaga University, Spokane, Washington 99258, USA. *We have benefitted from the constructive comments of Stuart Thiel, Richard Day (the editor), and two anonymous referees. The remaining errors are our own. ‘Retail values of prizes in our sample ranged from $335 to $1,995, the mean value being $1,070. Additionally, a ‘win’ in the component of the program we studied entitled the successful contestant the opportunity to compete for more goods - typically vacations, a set of furniture, an automobile or other item with a relatively high value. 2The bidding component of the program has incorporated the same set of rules and format for a number of years, and the show is broadcast each weekday. Furthermore, in each one hour program six bidding contests are held with four bidders participating in each contest. The three non-winning contestants remain at the bidding podium and engage in each game until they either win or the program is over for the day. Thus, a minimum of one contestant participates in four games (in which case at least three other contestants participate in three contests each), and the average contestant participates in 2.67 games (24 bids divided by 9 players per show). 0167-2681/93/$06.00
0
1993-Elsevier
Science Publishers
B.V. All rights reserved
100
R.W. Bennett and K.A. Hickman, Rationality and ‘the price is right’
Our analysis of a considerable body of data obtained from this source substantiates (1) the persistence of decision making errors despite the penalties associated with such errors, and despite the existence of a simple strategy which outperforms contestants’ behavior and (2) that learning drives competitors toward more effective behavior. 1. The data ‘The Price Is Right’ participants are chosen from a field of candidates who must pursue their own selection by writing for tickets, making travel arrangements, etc. The program’s producer likely screens for extroversion and often includes a subject from tour groups attending the program. The sample, therefore, is clearly not random. The same, however, can be said about typical laboratory experiments that, for example use students enrolled in a macroeconomics class. Moreover, including individuals who seek participation is not unlike sampling market data when traders enter voluntarily (e.g., stock traders, options traders, futures traders, etc.). 2. The game ‘The Price Is Right’ program is televised one hour per day, live days per week. Four contestants are selected from the studio audience at the beginning of each show. Each player is called sequentially to take his/her place at the bidding podium, with the order of selection determining the bidding order for the initial game. Selections are based upon a very brief interview of individuals as they enter the studio, presumably to determine their extroversion, clarity of speech, etc. Contestants are not informed of their selection prior to their name being called by the show’s announcer. A prize is revealed to the bidders after they have taken their places at the bidding podium. The object of the game is to come closest to the suggested retail price, without exceeding it. If all bids are high, the game is replayed, in the same order with the same prize. If a bidder bids the exact price, a $100 bonus is awarded to the winner (this occurred 12 times in the 315 contests observed). Each of the four contestants is instructed to make a verbal bid in the order they were called from the audience. Verbal advice from the audience is allowed and each bidder is allowed about live seconds to make a bid. The winning bidder is rewarded by being given the prize which was the object of the contest (the value of which is revealed at the end of each game). The winner then leaves the bidding podium to compete in a second game individually. Rewards from the second game are generally of greater value than the bidding portion of the show. Second game contestants then have a one-third chance of being in the final ‘Showcase Showdown’ at the end of the program, in which the prizes are worth tens of thousands of dollars. The
R. W. Bennett and K.A. Pickman, rationality and ‘rhe price is right’
101
prize won in the bidding game is not at risk in the subsequent games. The winner of the bidding game no longer competes in later bidding contests. The three unsuccessful contestants remain at the podium awaiting the end of the individual game when a second bidding contest begins. To proceed with the next bidding contest, a new bidder is called from the audience who takes the place at the podium which was vacated by the previous game’s winner. This new person is the designated first bidder in the new contest. A new prize is revealed and bidding proceeds with the new contestant bidding first and carry-over contestants bidding clock-wise from the first bidder. This procedure is replicated until six bidding games are completed during the one hour show. It is possible, therefore, that one or more contestants will participate in all six games without ever winning. Forty-eight one hour shows were viewed during February, March, and April 1990. The bids, the identity of the bidder, the order of the bids, the retail value of the prize, and the sex and approximate age of each bidder were recorded. The ordering of games within each show was also preserved as were the bids from games for which re-bidding was required (when all bids were above the actual value). In all, the dataset indudes 315 bidding contests, six contests per show times forty-eight shows, plus re-bidding games (34) and less some games when the program was interrupted by news bulletins, news conferences, etc. (7). 3. The optimal strategy The fourth bidder has two obvious advantages in the game. First, he or she may observe the previous three bids and then adjust the estimated value based on this information. Second, the ex-ante probability of winning for one of the three prior bidders may be slashed to zero (‘cut-off’) by the fourth contestant bidding any of the prior bids plus one dollar. In fact, analysis of the game’s rules yield the following rule for rational3 bidding: The fourth bidder should always bid either $1, the lowest existing bid plus one dollar (LOW + $l), the middle existing bid plus one dollar (MID+%l), or the existing high bid plus one dollar (HI+$I), unless, of course, the fourth bidder knows within a narrow range the exact price. Berk (1990) has shown that the fourth bidder’s probability of winning should be at least l/3 with rational bidding.4 The results bear out the 3Rational bidding we define as that which maximizes the chance of winning the contest. 41n his analysis, Berk formulates propositions which address optimal strategies across a variety of contestant beliefs. Berk relies on the assumption that uninformed as well as informed contestants share the same distributional beliefs. His asymmetric information propositions are conditioned upon the probability that a contestant is informed. This approach allows Berk to hypothesize that when players follow rational strategies (a) the fourth bidder should win at least l/3 of the time. and (b) that contestants should bid in descending order at least l/8 of the time. Empirically, Berk is able to reject the rationality hypothesis and is unable to detect evidence consistent with learning.
102
R.W. Bennett and K.A. Hickman,
Rationality
and ‘the price is right’
advantage held by the fourth bidder. The first bidder won 20.3%, the second bidder won 18.5x, the third bidder won 19.6x, and the fourth bidder 41.6% of the contests that had winners. 4. Contestant
behavior
To overcome the limitations of the assumptions which must be made in order to test contestant rationality based on an equilibrium bidding strategy across all contestants [see Berk (1990)], this paper focuses on the fourth bidder’s behavior. If all fourth contestants are bidding optimally, they may be segregated into two types, depending on their priors5 A ‘U-type’ bidder has completely diffuse priors about the value of the prize and does not update on the basis of other contestant’s bids. A U-type bidder should bid either $1, LOW+$l, MED+$l, or HI+$l. The second type of bidder is an ‘R-type’ bidder, one who’s prior’s are not completely diffuse and/or updates during a particular round. It is unlikely that an R-type bidder will bid $1, LOW +$l. MED+$l, or HI + $1. Thus, these two types of bidders may be distinguished from one another. In our data there were 143 bids consistent with U-type priors and 172 bids consistent with R-type bidders. Of these, 64 U-type bids won (44.8%) and 53 R-type bids won (30.8%). Since U-type bidders did significantly better than R-type bidders (t = 2.56), it would be in their best interest, on average, for R-type contestants to ignore their priors and bid one of the four optimal bids. To explicitly explore this strategy, note that if a winning bid was that just below an R-type bid, then this R-type bidder would have won by making the appropriate optimal bid. The only cost associated with bidding the optimal bid analogue to the R-type bid would be the forfeiture of the chance to claim the $100 bonus for making an exact bid. Had all R-type bidders followed the optimal strategy, four would have lost the bonus for bidding the exact price (though retaining the win and the prize itself), while eighteen additional Rtype bidders would have won, bringing the total wins in the R-category to 71 or 41.3%, in line with the results for U-type bidders. This evidence substantiates the contention that R-type bidders should have ignored their priors to optimize their chances of winning. 4.1. Biased bidding The first three bidders may have simply bid their unbiased estimate of the actual retail value. In such a case, the average of the first three bids should be equally dispersed about the retail price. This was tested using a sign test: an observation was coded negative if the average of the first three bids was ‘We would like to thank
an anonymous
referee for suggesting
this approach
to the analysis.
R. W. Bennett and K.A. Hickman,
Rationality
103
and ‘the price is right’
below the retail value and coded positive if the average bid exceeded retail value. The results of the test documents the existence of a downward bias in bidding on the part of the first three contestants, 204 of the 315 bid averages (64.8%) were below the retail value. The t-value of 5.24 is significant at 0.01. This result suggests that the fourth bidder could take advantage of the downward bias in bidding by bidding HI+$l when uninformed. This strategy was tested by tallying the number of times a strategy of always bidding HI+$l would have resulted in a win for the fourth bidder. (Of the 315 fourth bids observed, 238 did not bid HI+$l, while 77 did). Had all fourth bidders made the highest bid by one dollar, then 47% (148) would have won. This compares favorably with the 37% (117) who actually won. The two proportions are significantly different (t=2.53), indicating that the HI+$l outperforms the empirical action of the fourth bidders. The strategy of bidding HI +$l also outperformed bidding $1 (which would have resulted in wins 18.7% of the time), bidding LOW +$l (15.6% wins), or bidding MED+$l (18.7% wins). 4.2. A second-best
outcome
The sequential nature of the game and the advantage held by the fourth bidder suggest a second-best outcome for the fourth bidder: when the first bidder wins, the fourth bidder will repeat as the fourth bidder in the next contest. Thus, the fourth bidder should be reluctant to cut-off the first bidder. However, as demonstrated in the preceding section, it is optimal for uninformed fourth bidders to bid HI+$l. Therefore, one would expect first bidders to be cut-off less frequently than either the second or third bidders unless the first bidder has made the highest bid among these three contestants and should be cut-off in order to capture the highest probability of winning.6 First bidders were cut-off nine times in which the fourth contestant was not following the HI+$l strategy. In similar circumstances, second and third bidders were cut-off nine and six times, respectively. Contrary to the secondbest strategy, fourth bidders were as likely to cut-off the first bidder as either of the other two opponents. Two of the nine first bidder cut-offs resulted in wins, whereas six of the nine cut-offs of the second bidder won, as did two of the six third bidder cut-offs. Clearly, cutting-off the first bidder was a suboptimal decision in spite of its relative frequency. 4.3. Learning Although
ample
opportunity
is available
6Foregoing the opportunity to cut-off the high bidder the fourth bidder in the next contest is a sub-optimal winning with the HI + $1 bid.
for forming
bidding
strategies
by
in order to preserve the chance of being strategy given the 47% probability of
104
R.W. Bennett and K.A. Hickman,
Rationality
and ‘the price is right’
viewing the program before seeking participation in the game, it may be that ‘armchair’ viewing is no substitute for actual participation. The behavior rules one formulates in the comfort of the living room may break down in the glare of the studio lights, the noise of the studio audience, and the realization that millions of viewers are observing one’s actions. In short, rationality under ‘pressure’ may require training. To test whether there is evidence of learning as each day’s games proceed we use a logit regression relating ‘correct’ bids (bidding $1, LOW+$l, MED + $1, or HI + $1) to game number and some control variables. A positive relationship between ‘correct’ bids and game number is consistent with players learning. We define RATIONAL as a dummy variable equal to one if the fourth bid was either $1, LOW+$l, MED+$l, or HI+$l, and equal to zero otherwise. GAMENO is defined as the game number of the respective contest that day (varying in our sample from 1 to 6 on days where there were no rebid rounds due to overbidding, up to 1 to 8 on days with two rebid rounds). Our control variables are SEX4, which is the sex of the fourth bidder (1 for male and 0 for female), and AGE4 which is the estimated age of the fourth bidder. The control variables account for the possibilities that players may systematically vary in their aggressive behavior depending upon their age and sex. Our sample is made up of the 46 complete shows from the 48 shows discussed above. The two shows that had a portion preempted were discarded, since we were unable to determine correct game numbers. There are 310 observations in this sample. The estimated equation is RATIONAL = 0.08 + 0.13GAMENO + 0.24SEX4 - 0.03AGE4 (t= 1.02) (t= -2.57) (t=0.19) (t=2.23) likelihood ratio = 11.42, significant at 0.01 level. The results are consistent with learning. The coefficient on GAMENO is positive and significant at the 0.05 level. 7 There are more ‘correct’ bids in the later rounds. The coefficient on AGE4 is negative and statistically significant at the 0.01 level. We interpret this to mean that older players are less likely to cut off previous bidders in order to maximize their chance of winning (are less aggressive). The sign on SEX4’s coefficient is positive, indicating that males are more likely to cut off previous bidders, but the coefficient is not statistically significant. The regression results are also consistent with certain players deferring ‘The regression was also estimated using PREVGAME, the number of games previously played by the contestant, in lieu of GAMENO. The PREVGAME coefficient was positively signed with an associated t-value of 1.57 (significant at the 0.13 level). Spearman correlations between RATIONAL and GAMENO, and between RATIONAL and PREVGAME were 0.115 and 0.092, respectively, significantly different from zero at 0.05 and 0.11 levels.
R.W. Bennett and K.A. Hickman,
Rationality
105
and ‘the price is right’
utilization of an aggressive strategy until later rounds of the contest. Such players may have been socialized to dislike playing games in an ‘aggressive’ or ruthlessly rational manner. If these players are selected for the first round, they may avoid aggressive play while retaining a high probability of eventually winning. In later rounds the chances of eventually winning are smaller, and the trade-off is accordingly more favorable to optimizing play. Casual sociology would suggest that women may be more likely than men and older people than younger people to deprecate ruthless play, also consistent with the regression’s implications.’ One of the ‘correct’ bids, that of bidding $1, does not involve aggressive or ruthless behavior on the part of the fourth bidder. We tallied the frequency of $1 bids according to game number in order to segregate behavior consistent with learning from that which is also consistent with avoiding aggressiveness. Bids of $1 were made 4, 4, 6, 6, 11, and 10 times in games 1, 2, 3, 4, 5, and 6, respectively. Thus, in the first three games fourteen $1 bids were observed, while in the last three games $1 was bid twenty-seven times. The probability of observing such frequencies is 0.016 under the assumption that a $1 bid is equally likely to occur early or late in the program. This result is consistent with learning, yet is not consistent with contestants deferring aggressive play. 5. Conclusions Many economists assume forces exist in markets which eliminate errors in judgement. Sub-optimal behavior by market participants lowers their expected rewards eventually eliminating their participation, while feedback causes corrective action through learning. Evidence from ‘The Price Is Right’ game show documents persistent decision-making errors despite the penalties associated with the sub-optimal behavior and the ample opportunity for contestants to formulate strategy before-hand. Learning is evident in the data, driving competitors toward more effective behavior. These results suggest that optimal decision-making is best learned in the actual environment in which the decisions are made, that is, there’s no substitute for ‘on-the-job training’. The implications are clear for unique environments where the rewards and penalties are great, for example, for commodities traders or military personnel. *We are indebted
to an anonymous
referee for this interpretation
of the regression
results.
Reference Berk, Jonathan B., 1990, The price is right, but are the bids? An empirical investigation rational decision making, Working paper (University of California at Los Angeles).
of
of Economic
Behavior
Rationality Randall
and Organization
21 (1993) 99-105.
North-Holland
and the ‘price is right’
W. Bennett
and Kent A. Hickman*
Gonzaga University, Spokane, WA, USA Received
October
1991. final version
received June 1992
The television game show ‘The Price Is Right’ offers a unique laboratory for observing decision making behavior because rewards are much higher than those encountered in a typical economics experiment and because of the substantial opportunity which contestants have for formulating their strategies. Analysis of contestant behavior substantiates (1) the persistence of decision making errors despite the penalties associated with such errors, and despite the existence of simple strategy which outperforms contestants’ behavior and (2) that learning drives competitors toward more effective behavior.
The television game show, ‘The Price Is Right’, offers a unique laboratory for observing decision making behavior by individuals motivated by economic rewards. It is especially interesting when contrasted with typical experimental economics studies, because its rewards for successful performance, generally an appliance or other consumer good, are several magnitudes of order higher than the nominal rewards offered in typical laboratory experiments.’ It is also of considerable interest in comparison with laboratory settings because the opportunity for learning the rules and formulating strategy is substantial.’ This may be contrasted with experiments where rules and objectives are explained immediately prior to the experiment, and the study is conducted with little opportunity for subjects to develop their ‘game-plans’, perhaps only a practice round (or none at all). Correspondence to: Kent Hickman, School of Business, Gonzaga University, Spokane, Washington 99258, USA. *We have benefitted from the constructive comments of Stuart Thiel, Richard Day (the editor), and two anonymous referees. The remaining errors are our own. ‘Retail values of prizes in our sample ranged from $335 to $1,995, the mean value being $1,070. Additionally, a ‘win’ in the component of the program we studied entitled the successful contestant the opportunity to compete for more goods - typically vacations, a set of furniture, an automobile or other item with a relatively high value. 2The bidding component of the program has incorporated the same set of rules and format for a number of years, and the show is broadcast each weekday. Furthermore, in each one hour program six bidding contests are held with four bidders participating in each contest. The three non-winning contestants remain at the bidding podium and engage in each game until they either win or the program is over for the day. Thus, a minimum of one contestant participates in four games (in which case at least three other contestants participate in three contests each), and the average contestant participates in 2.67 games (24 bids divided by 9 players per show). 0167-2681/93/$06.00
0
1993-Elsevier
Science Publishers
B.V. All rights reserved
100
R.W. Bennett and K.A. Hickman, Rationality and ‘the price is right’
Our analysis of a considerable body of data obtained from this source substantiates (1) the persistence of decision making errors despite the penalties associated with such errors, and despite the existence of a simple strategy which outperforms contestants’ behavior and (2) that learning drives competitors toward more effective behavior. 1. The data ‘The Price Is Right’ participants are chosen from a field of candidates who must pursue their own selection by writing for tickets, making travel arrangements, etc. The program’s producer likely screens for extroversion and often includes a subject from tour groups attending the program. The sample, therefore, is clearly not random. The same, however, can be said about typical laboratory experiments that, for example use students enrolled in a macroeconomics class. Moreover, including individuals who seek participation is not unlike sampling market data when traders enter voluntarily (e.g., stock traders, options traders, futures traders, etc.). 2. The game ‘The Price Is Right’ program is televised one hour per day, live days per week. Four contestants are selected from the studio audience at the beginning of each show. Each player is called sequentially to take his/her place at the bidding podium, with the order of selection determining the bidding order for the initial game. Selections are based upon a very brief interview of individuals as they enter the studio, presumably to determine their extroversion, clarity of speech, etc. Contestants are not informed of their selection prior to their name being called by the show’s announcer. A prize is revealed to the bidders after they have taken their places at the bidding podium. The object of the game is to come closest to the suggested retail price, without exceeding it. If all bids are high, the game is replayed, in the same order with the same prize. If a bidder bids the exact price, a $100 bonus is awarded to the winner (this occurred 12 times in the 315 contests observed). Each of the four contestants is instructed to make a verbal bid in the order they were called from the audience. Verbal advice from the audience is allowed and each bidder is allowed about live seconds to make a bid. The winning bidder is rewarded by being given the prize which was the object of the contest (the value of which is revealed at the end of each game). The winner then leaves the bidding podium to compete in a second game individually. Rewards from the second game are generally of greater value than the bidding portion of the show. Second game contestants then have a one-third chance of being in the final ‘Showcase Showdown’ at the end of the program, in which the prizes are worth tens of thousands of dollars. The
R. W. Bennett and K.A. Pickman, rationality and ‘rhe price is right’
101
prize won in the bidding game is not at risk in the subsequent games. The winner of the bidding game no longer competes in later bidding contests. The three unsuccessful contestants remain at the podium awaiting the end of the individual game when a second bidding contest begins. To proceed with the next bidding contest, a new bidder is called from the audience who takes the place at the podium which was vacated by the previous game’s winner. This new person is the designated first bidder in the new contest. A new prize is revealed and bidding proceeds with the new contestant bidding first and carry-over contestants bidding clock-wise from the first bidder. This procedure is replicated until six bidding games are completed during the one hour show. It is possible, therefore, that one or more contestants will participate in all six games without ever winning. Forty-eight one hour shows were viewed during February, March, and April 1990. The bids, the identity of the bidder, the order of the bids, the retail value of the prize, and the sex and approximate age of each bidder were recorded. The ordering of games within each show was also preserved as were the bids from games for which re-bidding was required (when all bids were above the actual value). In all, the dataset indudes 315 bidding contests, six contests per show times forty-eight shows, plus re-bidding games (34) and less some games when the program was interrupted by news bulletins, news conferences, etc. (7). 3. The optimal strategy The fourth bidder has two obvious advantages in the game. First, he or she may observe the previous three bids and then adjust the estimated value based on this information. Second, the ex-ante probability of winning for one of the three prior bidders may be slashed to zero (‘cut-off’) by the fourth contestant bidding any of the prior bids plus one dollar. In fact, analysis of the game’s rules yield the following rule for rational3 bidding: The fourth bidder should always bid either $1, the lowest existing bid plus one dollar (LOW + $l), the middle existing bid plus one dollar (MID+%l), or the existing high bid plus one dollar (HI+$I), unless, of course, the fourth bidder knows within a narrow range the exact price. Berk (1990) has shown that the fourth bidder’s probability of winning should be at least l/3 with rational bidding.4 The results bear out the 3Rational bidding we define as that which maximizes the chance of winning the contest. 41n his analysis, Berk formulates propositions which address optimal strategies across a variety of contestant beliefs. Berk relies on the assumption that uninformed as well as informed contestants share the same distributional beliefs. His asymmetric information propositions are conditioned upon the probability that a contestant is informed. This approach allows Berk to hypothesize that when players follow rational strategies (a) the fourth bidder should win at least l/3 of the time. and (b) that contestants should bid in descending order at least l/8 of the time. Empirically, Berk is able to reject the rationality hypothesis and is unable to detect evidence consistent with learning.
102
R.W. Bennett and K.A. Hickman,
Rationality
and ‘the price is right’
advantage held by the fourth bidder. The first bidder won 20.3%, the second bidder won 18.5x, the third bidder won 19.6x, and the fourth bidder 41.6% of the contests that had winners. 4. Contestant
behavior
To overcome the limitations of the assumptions which must be made in order to test contestant rationality based on an equilibrium bidding strategy across all contestants [see Berk (1990)], this paper focuses on the fourth bidder’s behavior. If all fourth contestants are bidding optimally, they may be segregated into two types, depending on their priors5 A ‘U-type’ bidder has completely diffuse priors about the value of the prize and does not update on the basis of other contestant’s bids. A U-type bidder should bid either $1, LOW+$l, MED+$l, or HI+$l. The second type of bidder is an ‘R-type’ bidder, one who’s prior’s are not completely diffuse and/or updates during a particular round. It is unlikely that an R-type bidder will bid $1, LOW +$l. MED+$l, or HI + $1. Thus, these two types of bidders may be distinguished from one another. In our data there were 143 bids consistent with U-type priors and 172 bids consistent with R-type bidders. Of these, 64 U-type bids won (44.8%) and 53 R-type bids won (30.8%). Since U-type bidders did significantly better than R-type bidders (t = 2.56), it would be in their best interest, on average, for R-type contestants to ignore their priors and bid one of the four optimal bids. To explicitly explore this strategy, note that if a winning bid was that just below an R-type bid, then this R-type bidder would have won by making the appropriate optimal bid. The only cost associated with bidding the optimal bid analogue to the R-type bid would be the forfeiture of the chance to claim the $100 bonus for making an exact bid. Had all R-type bidders followed the optimal strategy, four would have lost the bonus for bidding the exact price (though retaining the win and the prize itself), while eighteen additional Rtype bidders would have won, bringing the total wins in the R-category to 71 or 41.3%, in line with the results for U-type bidders. This evidence substantiates the contention that R-type bidders should have ignored their priors to optimize their chances of winning. 4.1. Biased bidding The first three bidders may have simply bid their unbiased estimate of the actual retail value. In such a case, the average of the first three bids should be equally dispersed about the retail price. This was tested using a sign test: an observation was coded negative if the average of the first three bids was ‘We would like to thank
an anonymous
referee for suggesting
this approach
to the analysis.
R. W. Bennett and K.A. Hickman,
Rationality
103
and ‘the price is right’
below the retail value and coded positive if the average bid exceeded retail value. The results of the test documents the existence of a downward bias in bidding on the part of the first three contestants, 204 of the 315 bid averages (64.8%) were below the retail value. The t-value of 5.24 is significant at 0.01. This result suggests that the fourth bidder could take advantage of the downward bias in bidding by bidding HI+$l when uninformed. This strategy was tested by tallying the number of times a strategy of always bidding HI+$l would have resulted in a win for the fourth bidder. (Of the 315 fourth bids observed, 238 did not bid HI+$l, while 77 did). Had all fourth bidders made the highest bid by one dollar, then 47% (148) would have won. This compares favorably with the 37% (117) who actually won. The two proportions are significantly different (t=2.53), indicating that the HI+$l outperforms the empirical action of the fourth bidders. The strategy of bidding HI +$l also outperformed bidding $1 (which would have resulted in wins 18.7% of the time), bidding LOW +$l (15.6% wins), or bidding MED+$l (18.7% wins). 4.2. A second-best
outcome
The sequential nature of the game and the advantage held by the fourth bidder suggest a second-best outcome for the fourth bidder: when the first bidder wins, the fourth bidder will repeat as the fourth bidder in the next contest. Thus, the fourth bidder should be reluctant to cut-off the first bidder. However, as demonstrated in the preceding section, it is optimal for uninformed fourth bidders to bid HI+$l. Therefore, one would expect first bidders to be cut-off less frequently than either the second or third bidders unless the first bidder has made the highest bid among these three contestants and should be cut-off in order to capture the highest probability of winning.6 First bidders were cut-off nine times in which the fourth contestant was not following the HI+$l strategy. In similar circumstances, second and third bidders were cut-off nine and six times, respectively. Contrary to the secondbest strategy, fourth bidders were as likely to cut-off the first bidder as either of the other two opponents. Two of the nine first bidder cut-offs resulted in wins, whereas six of the nine cut-offs of the second bidder won, as did two of the six third bidder cut-offs. Clearly, cutting-off the first bidder was a suboptimal decision in spite of its relative frequency. 4.3. Learning Although
ample
opportunity
is available
6Foregoing the opportunity to cut-off the high bidder the fourth bidder in the next contest is a sub-optimal winning with the HI + $1 bid.
for forming
bidding
strategies
by
in order to preserve the chance of being strategy given the 47% probability of
104
R.W. Bennett and K.A. Hickman,
Rationality
and ‘the price is right’
viewing the program before seeking participation in the game, it may be that ‘armchair’ viewing is no substitute for actual participation. The behavior rules one formulates in the comfort of the living room may break down in the glare of the studio lights, the noise of the studio audience, and the realization that millions of viewers are observing one’s actions. In short, rationality under ‘pressure’ may require training. To test whether there is evidence of learning as each day’s games proceed we use a logit regression relating ‘correct’ bids (bidding $1, LOW+$l, MED + $1, or HI + $1) to game number and some control variables. A positive relationship between ‘correct’ bids and game number is consistent with players learning. We define RATIONAL as a dummy variable equal to one if the fourth bid was either $1, LOW+$l, MED+$l, or HI+$l, and equal to zero otherwise. GAMENO is defined as the game number of the respective contest that day (varying in our sample from 1 to 6 on days where there were no rebid rounds due to overbidding, up to 1 to 8 on days with two rebid rounds). Our control variables are SEX4, which is the sex of the fourth bidder (1 for male and 0 for female), and AGE4 which is the estimated age of the fourth bidder. The control variables account for the possibilities that players may systematically vary in their aggressive behavior depending upon their age and sex. Our sample is made up of the 46 complete shows from the 48 shows discussed above. The two shows that had a portion preempted were discarded, since we were unable to determine correct game numbers. There are 310 observations in this sample. The estimated equation is RATIONAL = 0.08 + 0.13GAMENO + 0.24SEX4 - 0.03AGE4 (t= 1.02) (t= -2.57) (t=0.19) (t=2.23) likelihood ratio = 11.42, significant at 0.01 level. The results are consistent with learning. The coefficient on GAMENO is positive and significant at the 0.05 level. 7 There are more ‘correct’ bids in the later rounds. The coefficient on AGE4 is negative and statistically significant at the 0.01 level. We interpret this to mean that older players are less likely to cut off previous bidders in order to maximize their chance of winning (are less aggressive). The sign on SEX4’s coefficient is positive, indicating that males are more likely to cut off previous bidders, but the coefficient is not statistically significant. The regression results are also consistent with certain players deferring ‘The regression was also estimated using PREVGAME, the number of games previously played by the contestant, in lieu of GAMENO. The PREVGAME coefficient was positively signed with an associated t-value of 1.57 (significant at the 0.13 level). Spearman correlations between RATIONAL and GAMENO, and between RATIONAL and PREVGAME were 0.115 and 0.092, respectively, significantly different from zero at 0.05 and 0.11 levels.
R.W. Bennett and K.A. Hickman,
Rationality
105
and ‘the price is right’
utilization of an aggressive strategy until later rounds of the contest. Such players may have been socialized to dislike playing games in an ‘aggressive’ or ruthlessly rational manner. If these players are selected for the first round, they may avoid aggressive play while retaining a high probability of eventually winning. In later rounds the chances of eventually winning are smaller, and the trade-off is accordingly more favorable to optimizing play. Casual sociology would suggest that women may be more likely than men and older people than younger people to deprecate ruthless play, also consistent with the regression’s implications.’ One of the ‘correct’ bids, that of bidding $1, does not involve aggressive or ruthless behavior on the part of the fourth bidder. We tallied the frequency of $1 bids according to game number in order to segregate behavior consistent with learning from that which is also consistent with avoiding aggressiveness. Bids of $1 were made 4, 4, 6, 6, 11, and 10 times in games 1, 2, 3, 4, 5, and 6, respectively. Thus, in the first three games fourteen $1 bids were observed, while in the last three games $1 was bid twenty-seven times. The probability of observing such frequencies is 0.016 under the assumption that a $1 bid is equally likely to occur early or late in the program. This result is consistent with learning, yet is not consistent with contestants deferring aggressive play. 5. Conclusions Many economists assume forces exist in markets which eliminate errors in judgement. Sub-optimal behavior by market participants lowers their expected rewards eventually eliminating their participation, while feedback causes corrective action through learning. Evidence from ‘The Price Is Right’ game show documents persistent decision-making errors despite the penalties associated with the sub-optimal behavior and the ample opportunity for contestants to formulate strategy before-hand. Learning is evident in the data, driving competitors toward more effective behavior. These results suggest that optimal decision-making is best learned in the actual environment in which the decisions are made, that is, there’s no substitute for ‘on-the-job training’. The implications are clear for unique environments where the rewards and penalties are great, for example, for commodities traders or military personnel. *We are indebted
to an anonymous
referee for this interpretation
of the regression
results.
Reference Berk, Jonathan B., 1990, The price is right, but are the bids? An empirical investigation rational decision making, Working paper (University of California at Los Angeles).
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