Battle of Sexes

Battle of Sexes

The battle of sexes was the chosen game in this case. The game is a two-player coordinated game, with a column player and a row player. For a better understanding of the game, one could use a couple named Jack and Jill. Jack plays basketball while Jill loves opera. While deciding on data, they can either choose to go to opera or the basketball event. Both players prefer to go to the same place. Assuming that the players would not communicate, where would they go? The dilemma presents the basics of the game, in which the two players want the same results. The following payoff matrix represents the battle of sexes.

The game makes the assumption that the couple does not have any form of communication with each other. They know that there are two options that they are meant to decide on, but they cannot directly talk to each other. In that regard, it is a challenge for either of them to decisively make their way to a certain destination since they face the risk of making the wrong decision and eventually regretting it. It is a situation of dilemma, which in itself makes the project even more interesting.

Another twist in the game is the fact that the couple has each partner preferring to attend a different event. There is the presumable male figure in the couple who would enjoy it most if he attended a football match on the evening in question. On the contrary, there is a female figure in the couple who would instead have the highest degree of fun in the event that they attended a ballet concert. It would be boring for either of the couples to attend an event that does not fall under their personal preference mantra.

An even higher element of challenge is posed on the project, in that the two married partners would prefer to end up in the same event on the evening in question. In that respect, the male figure, for instance, would have some element of comfort sitting with his partner even if they are in a ballet concert, which is not his preferred event. Similarly, the female figure would have some element of comfort sitting with her partner even in an instance where the two are watching football rather than watching ballet.

To have a perfect quantitative representation of the situation, the various events and partners, and utilities were denoted in the form of numbers. The first instance is that which had the male figure attending the ballet alone. It is a scenario where he does not enjoy the event, besides the fact that he does not also have the luxury of enjoying the wife’s company. In that regard, his score is 0. Secondly is a scenario where the male figure attends the football match, but he is alone. In that case, he is in an event where he prefers attending. That grants him a score of 1. However, he is alone and does not get to enjoy his partner’s company. It makes him have an overall utility of just 1. Similarly, for the female figure, in an instance where she attends the ballet alone, she is in an event where she prefers, and that grants her a utility score of 1. Nonetheless, the fact that she is sited all alone makes it impossible for her to enjoy her husband’s company, which has a score of 0. Collectively, the combination has a total utility score of just 1.

In another instance where the female figure attends a football match all alone, she faces double tragedy. For one, she is in an event where she does not prefer. Consequently, she has a score of 0 in that sense. Furthermore, she is in an event where she does not enjoy her husband’s company. Based on that, she also receives a score of 0. In total, the combination grants the female figure a utility score of 0. A scenario where the female figure attends ballet along with her husband, she is poised to have a double win. She is in an event where she actually enjoys attending. That gives her a score of 1. Moreover, she is situated with her husband, and that gives her the freedom to enjoy his company, which bears a score of 1 as well. As a result, the collective utility which is drawn by the woman with respect to attending a ballet with her husband is 2.

The figure below captures the sentiments of the project perfectly. It has various events, players, and utilities in the form of quantitative numbers.

Theoretical concept

Theoretically, the game has two Nash equilibria. One where the two partners choose to go to the opera and another where they choose to go to the football event. The game also has mixed strategies, where the players choose to go to the event that they mostly prefer. That is, Jack goes to the football match while Jill goes to the opera. As such, the Nash equilibria, in this case, is deficient in some ways. That is, one player does better than the other does consistently, which makes the Nash equilibria unfair. Again, when there is a mixed strategy, Nash equilibria, it becomes ineffective because it would give the players fewer returns that they would get by going to their favourite side.

Game theories present one possible solution to the game as the use of correlated equilibrium. That is, if the players can access a common randomizing device, they can then correlate their strategies depending on the device’s outcomes. For example, Jack and Jill could choose to flip a coin and decide where they will go. If it is tails, they go to the opera, and if it is headed, they go to the football. As such, when the results of the coin-flipping come out, none of them has an incentive to change the decision. This is because discoordination has a lower payoff than coordination.

Comparing the Theoretical and Practical Performance

The results of the experiments show minimum earnings for most of the players. That is, in the first round, most of the players earned $ 0.25. Thus, the player’s behaviours are similar to the theoretical Nash equilibria, where both players choose what they do not like. One possible explanation is that the players thought that their partners would choose their preferred options. Thus, they gambled with the choice of raising earnings. The results, however, differ from the theoretical concepts in some way. While choosing a person’s favourite option is the dominating strategy, the players in the lab experiment choose the dominated strategy. Thus 90 % of the subjects did not behave like real research subjects.  The possible explanation is that most of the subjects, in this case, were students with game theory knowledge. As such, they understood the probabilities and tried to gamble with the chances rather than following the steps that a nonprofessional would take. The table below shows the result of the first part of the experiment:

Model Uses

The experiment or its modification would help in real-life situations in various ways. One, when two inter-dependent companies are adopting the same technology, the best option may be to choose the same technology. Take, for example; when Sony and Toshiba are adopting Blu-ray or HD technology, it will benefit them both if they choose the same technology. This is because the customers and suppliers would shift towards the chosen technology, raising demand and reducing costs at the same time. Choosing different technology would increase conflicting views from the customers and increase the cost of supplies. The problem comes in when the two companies cannot communicate about their choices because they are hiding their corporate strategies. The conditions make it a perfect example of a battle of sexes. In this regard, the knowledge of the game, its rules and its outcomes would be essential while dealing with such a situation.