Analysis of “Battle of the Sexes: Experimental Evidence and Individual Evolutionary Learning”

Abstract

Analysis of “Battle of the Sexes: Experimental Evidence and Individual Evolutionary Learning” describes a multifaceted study of human behavior by Arifovic, Ledyard, and Shi (2011) applying game theory –– that is, how does one group in pursuit of a goal respond to a challenge by another group pursuing a similar goal when a certain level of risk-taking is at issue? To illustrate this concept outside the realm of the topic in question, imagine yourself as a member of a society where deception in the form of theft might gain your something in the short term (if you’re not caught) but cost you in the long term (if you are discovered by other members of your society to be fraudulent). Do you risk your standing and perhaps your freedom by taking $10,000 when being honest like the others means merely earning an okay living? How about your life?

Analysis of “Battle of the Sexes: Experimental Evidence and Individual Evolutionary Learning”

In “Battle of the Sexes,” Arifovic, Ledyard, and Shi (2011) examined how women and men behave toward one another under four conditions: 1) each sex is aware of the reward the opposite sex receives for behaving a certain way, and rewards are symmetrical; 2) each sex is aware of the reward the opposite sex receives for behaving a certain way, and rewards are asymmetrical; 3) neither sex is fully aware of the reward the opposite sex receives for behaving a certain way, and rewards are symmetrical; and 4) neither sex is fully aware of the reward the opposite sex receives for behaving a certain way, and rewards are asymmetrical.

The aim was to place the observed results in the context of human evolutionary psychology –– an ever-expanding and controversial field within the broader discipline of evolutionary biology ––and explain them on the basis of individual gain versus population gain. What we do for individual rewards does not necessarily translate into a species reward, since excessive risk-taking by a group lowers the chances of a given individual surviving to pass on its genes –– even if it is impossible to identify in advance which individuals will pay the price. Specifically, do people playing this game converge on specific, predictable behavioral patterns that differ on the basis of the variables described above? If Player A knows how Player B will react and exactly what she stands to gain by so doing, does Player A lean toward a different strategy than he would if he is unaware of whether Player B’s reward is greater or less than his own?

Hypotheses and Methods

In terms of statistics, the researchers theorized that when a player knew the full extent of the other’s rewards for playing a certain way, he or she would trend toward the Nash equilibrium –– the pattern observed when a player stands to gain nothing by altering his or her strategy when he or she knows the other player is in precisely the same situation (Arifovic et al., 2001). Any risk-taking is quickly counterbalanced by risk minimization. The researchers hypothesized that when players were not supplied with full information about their opponents’ payoffs or preferred strategies or both, they would alternate between high-risk and low-risk behaviors rather than toe the Nash-equilibrium line.

The researchers drew on experiments by others going back at least 60 years, but with slightly different designs and, importantly, typically not involving human subjects. In the “Battle of the Sexes” study, all 40 players –– 20 pairs of people playing in one-on-one games –– competed in a match consisting of 40 rounds of play. Results were collected and analyzed using a zTree software package.

Conclusions

The researchers’ predictions were largely in line with what they expected to see, with predictability rising in concert with players’ “knowing each other” better. This hews with what evolution and natural selection tend to follow. It is instructive to note that regardless of the strategy a given player chose or evolved, the presence of a consistent strategy was more predictive of a positive outcome than the lack or apparent lack of a strategy; a seemingly scattershot approach resulted in a lower yield in terms of the percentage of maximum possible payoff than did either a Nash-oriented strategy or an alternating high-risk, low-risk strategy (Arifovic et al., 2011).

In the end, the authors conclude that the experiment invites as many questions as it answers. In particular, in order to modify what they call an Individual Evolutionary Learning (IEL) model, more information about matches played over longer periods than 20 rounds are needed. Hence other designs based on the “Battle of the Sexes” study should be approached with this important criterion in mind.

Reference

Arifovic, J. , Ledyard, J. & Shi, L. (2011). Repeated battle of sexes: Experimental evidence and individual evolutionary learning. Manuscript. Retrieved from http://www.ewi-ssl.pitt.edu/econ/files/seminars/110412_sem809_Jasmina%20Arifovic.pdf