Qualitative Analysis of Milks and WheatsAnthony Curnes - [email protected] Advisor: Michael KearnsAbstractAs we saw in the conclusion of my first paper, “Quantitative Analysis of Milks andWheats,” the deficiency in social welfare often could be attributed to advantagedplayers not taking full advantage of their positions in the network. Thus, the questionarises, why was this the case? Were the advantaged players exhibiting inequalityaversion, where they deemed higher prices unfair to their neighbors and thus refusedto charge such prices? Or was it a case of risk aversion, with players wanting toensure themselves a minimum level of wealth? In order to answer this, I examinedthe qualitative data that was gathered from the experiment.IntroductionThe qualitative data from the Milks and Wheats experiment consisted of the 36 play-ers’ written responses to six questions which were posed to them after the experimentwas completed. The questions were as follows:1. What was your strategy during the experiment?2. What did you believe the strategy of the other players was?3. What was your opinion of the design of the game?4. What was your opinion of the interface?5. What did you enjoy most and least about the game?6. Do you have any further comments?For the purposes of this paper, I will focus mostly on the responses to the firstquestion, as well as any responses to the other questions that may have affected thestrategy of the players.AnalysisGrouping the Players’ StrategiesMy first step was to look at the responses to Q1 concerning the player’s own strategy.After examining the responses, I was able to divide them into five groups. The groupswere as follows:1• Degree-based• Fair• Risk-averse, passive• Risk-averse, aggressive• DeceptiveFigure 1: This chart demonstrates the distribution of the 36 players among the groups described below.A description and examples of each group is below (all examples sic):Degree-based: A player with a degree-based strategy set his prices based almostpurely on his degree and the degree of his neighbors. If he had a higher degree than hisneighbors, he would charge higher prices; a lower degree would mean lower prices. Ofcourse, the vast majority of participants modulated their strategies based on degree,but the distinguishing factor of players who fell into this group was the apparent lackof risk aversion or any time-dependent strategy.Examples: “When I had many low-degree neighbors, I would post higher prices .When I had few neighbors, especially when of high degree, I would post lower prices.”“Whenever I was highly connected, I tried to keep my price high, because I knewat least one of my neighbors would go for that price. Whenever I was not highlyconnected, I kept my price at 1 or at few times less than that when necessary.”Fair: A fair player would offer a “fair,” 1-to-1 trade no matter what the circumstance,and additionally he would reject trades at prices he deemed to be greedy. The pattern2of behavior exhibited was similar to a risk-averse player in that risk-averse playerswould also offer 1-to-1 trades, but the difference is that the fair player stated that heoffered these trades out of a sense of fairness rather than to try to ensure a minimumlevel of wealth at the end of the round.Examples: “tried to be fair and have a 1 to 1 ratio but some people wouldn’tcoop erate”“I wouldn’t gouge them extremely hard early on because then at the end of thegame even if I trade 5 for 10, the market would be illiquid for my other 5 goods thatI wanted to sell. Therefore, I gave them a fair price to rid them of their inventory soI could trade elsewhere.”Risk-averse, passive: A passive risk-averse player would try to unload all of hisendowment as quickly as possible, at a 1-to-1 price if possible or at a lower price asnecessary. This type of player had an extremely convex utility function and did notwant to risk charging a premium for his goods if it meant he would be left out ofthe market. This group is distinguished from the aggressive risk averse group in thatit did not try to reserve any of its endowment for risky ventures but simply wouldunload it as quickly as possible.Examples: “A lot of people, including me :(, would attempt to get rid of theirendowment quickly, so that they don’t get stuck with it at the end (because peoplerun out of theirs).”“I was most concerned with not ending up with useless goods.”Risk-averse, aggressive: An aggressive risk averse player would generally adopt atwo-pronged strategy based on his degree. If he had a low degree, he would act thesame as a passive risk-averse player, attempting to unload his endowment as quicklyas possible at something close to a 1-to-1 price. However, if he had a higher degreethan his neighbors, he would sell a portion of his endowment at a 1-to-1 price toensure a minimum level of wealth (the risk averse part) and reserve a small portionto sell late in the game when prices were higher (the aggressive part). This groupis distinguished from the degree based group in that a degree-based player with anadvantage would offer high prices from the start, whereas an advantaged player inthis group would unload a portion of his endowment before starting to increase prices.Examples: “I would try to sell 8 or 9 of my goods at $1 and then try to extractextra value from my last couple goods depending on whether I thought there wasanyone in my neighborhood with extra goods but no one else to sell it to”“I would usually trade 8 units for 1-1 and leave the rest 2 so i can bargain forsome marginal better prices. i feel that there isn’t much difference if you make 2 or2.5 because I value more the fact that I should earn 2 dollars for sure rather thangamble for a little more.”Deceptive: A deceptive player would try to exploit the setup of the game and thepsychology of their neighbors to gain wealth. A de ceptive player might attempt to3make his neighbor think he has less endowment remaining than he actually does,or think that he is executing deals at prices which he is not. These players wouldincorporate elements of the strategies of other groups as well, but I classify them inthis category if their dominant strategy appeared to be one of deception.Examples: “I found that if I put in 0 and 0 and it would get people to think therewas little endowment left on the table and sometimes they would lower their prices”“once i put a order i, I’d retract is