The Battle of the Sexes: Consider the Battle of the Sexes Game

Introduction

The battle of the sexes (BoS) game is synonymous with conflicts between male and female. While they may agree on some issues, for example, going for dinner, there may be no agreement on which restaurant. One may want to go to Red Lobster while the other may want to go to KFC. The BoS game is a static two player game where the players generally agree but disagree specifically on how to coordinate their actions. It is the perfect example of a non-cooperative game. Thus, Huck and Miller indicates that it is very challenging since it is difficult to predict how each player will proceed. This game has multiple Nash equilibria. In fact, the game is characterized by three Nash equilibria – one in mixed strategies and two in pure strategies.

Analyzing problems using the BoS game

The BoS game can be used as a framework for analyzing various kinds of conflicts related to coordination. In this game, coordination is attempted by the players in either of two ways, in order to solve a problem. It is always better when both of them cooperate as they will reap rewards. However, they will not agree on the preferred method of solving the problem. Morrow sees this game as being representative of the essence of a distributional problem.

Variations of the game

A number of variations have been made to the basic game in order to allow for unique solutions. Two of these approaches are:

• Allowing participants to communicate without making any binding agreement before starting the game. In this scenario, players make simultaneous announcements in relation to how they will play. This allows for symmetric equilibrium which facilitates more frequent coordination between players than in the mixed equilibrium version of the most basic BoS game.
• Allowing one of the players – for example, the column player, an outside option. This scenario makes provision for a specified payoff in the event that the column player decides not to play the game. If this player decides to play nonetheless, then it conveys information since no one would want to play if the payoff is less than the outside option that has been communicated. This variation is described as the forward induction approach.

These two approaches facilitate easier player coordination.

Conclusion

The BoS game is one of the classic games in game theory. Several studies including experiments have been done with reference to and suggesting variants to the basic game. Some of these have been successful in improving coordination.