Paul J. Healy 'P.J.'
MAIN RESEARCH TEACHING OTHER C.V.
In the Price is Right game show, players compete in "Contestants' Row" to win a prize and the right to play additional games on the show. In Contestants' Row, four bidders sequentially announce guesses ("bids") of the prize. The logic of game theory (due in large part to the work of Nobel laureates John Nash - subject of the movie "A Beautiful Mind" - and Reinhard Selten) makes certain clear predictions about how people should behave in this game. For example, if the fourth bidder wants to maximize her chances of winning, she should either "cut off" one of the previous three bidders (outbidding them by exactly one dollar) or bid one dollar. In a previous study (Berk et al. (1996)) it was shown that fourth bidders on the TV show employ one of these strategies only 57 percent of the time.
Why don't fourth bidders always play optimally? Do they fear that cutting off another player will induce that player to reciprocate in a later rounds of Contestants' Row? Are they worried about how their behavior will be perceived by the studio and television audiences? Or, are they simply unable to calculate the optimal strategy in this situation? We also observe sub-optimal play by earlier bidders; is this because they have the difficult task of predicting future bidders' behavior when choosing their own optimal choices? By playing the game in the laboratory with careful manipulations of the details of the game, we can explore the exact causes of sub-optimal play.
First, our laboratory subjects play the game 50 times. If subjects have difficulty calculating the optimal strategy in early periods, we should see better performance in later periods as subjects learn better strategies. Second, we compare a setting where subjects play face-to-face and know the identities of their competitors to a setting of anonymity where subjects play by computer and cannot track competitors' identities. If subjects worry about the perceptions of others or are concerned about reciprocation in later periods, the veil of anonymity should allow them to behave more strategically. Finally we compare the original game to modified versions of the game with two simplifications: using only three bidders, and not allowing for the period to repeat if all subjects overbid in a given period. These simplifications make the game easier for the bidders to analyze.
Our first result is that subjects in the laboratory play the game very similarly to contestants on television. This confirms that our laboratory environment is a reasonable proxy for real-world, high-stakes competitive environments. (This is a common finding - laboratory studies using student subjects often generate behavior very similar to the behavior of professionals in high-stakes environments, including stock traders and professional auction bidders.) Second, we find that subjects perform slightly better as the game progresses, indicating some degree of learning. Third, subjects are more strategic in anonymous treatments. For example, fourth bidders will cutoff earlier bidders much more frequently under anonymity, but when decisions are publicly observable they tend to leave a gap between their bid and the next-lowest bid. This indicates that subjects are fair-minded or worried about future reciprocation. By having subjects rotate roles - alternating which gets to be the fourth bidder - we can test whether reciprocation is an issue. We do not find any evidence that subjects target each other for reciprocation; however, we do find that some groups use cutoff strategies frequently while other groups almost never use them. Thus, some groups develop a "norm" of cut-throat behavior while other groups develop a norm of cooperation. Finally, we find that when the game is simplified (by having fewer bidders or no resale rounds), players play much closer to the game-theoretic predictions. Thus, the original Price Is Right is too complex for players to solve, so they apparently use simple heuristics to guide their play. When the game is simplified, the optimal strategies become apparent.
Ultimately, by understanding the basic science behind people's behavior in simple games such as these, we can begin to describe how competitors should behave in other, more important real-world settings, such as R&D battles, labor negotiations, firm location decisions, repeated auctions, or long-term competition between two rival firms.