Tips on A Game Theory Strategy: Battle of the Sexes
Tips for effective strategies and predictions
I have a real passion for applied game theory. Applied game theory is a branch of economics, and of daily life, wherein individuals (called players) anticipate each others moves, and actions. This is done in order to “win”, i.e., maximize a player’s benefit at the lowest possible cost, in a potentially competitive situation.
In my life, I treat almost everything other than art, love, spirituality, and the appreciation of beauty, as if it is a game with rules, strategies, keeping score, and knowing when I have won.
With this in mind, please consider that there are a number of game theories applicable to different scenarios, and fields including business, personal growth, predictive analytics, and A.I.
A person who uses applied game theory as I do, needs to access the decisions made by themselves, as well as the other players in a game.
The choices of these players make as they interact will ultimately determine the final outcome of any game.
Applied game theory is also used in real world situations, such as financial analysis, business, relationship strategies, and more. Originally, game theory was restricted to parlor games such as Poker, Bridge, and in recent times, video games.
With social media, and A.I. becoming more influential than ever, applied game theory now is more frequently used to determine how groups of people interact, or are likely to do so.
Applied game theory can be used to determine outcomes, even in a scenario as simple as a cocktail party. Anytime we have two or more players interacting and also have a quantifiable outcome, applied game theory can be extremely valuable.
Here is an introduction to this concept and the series of stories connected to it…
In the past few years I have combined the concepts of predictive analytics, futurism, business, A.I., and applied game theory, to make out certain scenarios and problems and how they might be most effectively addressed. Here I have named specific scenarios, describing each, and possible solutions, from a game theory model.
Consider, that if you explore these ideas slowly and with patience, they will make perfect sense. If you are impatient, and rush through them, you are likely to become confused, and overwhelmed.
The game and strategy I am addressing here is called the “Win/Win Game that Lacks Key Information” Strategy (WWGLKIS)
Name of game: The “Win/Win Game that Lacks Key Information” Strategy (WWGLKIS)
Common name for This Strategy: Battle of the Sexes:
Type of game: Win/Win (Coordination game)
Number of competitors or players: 2
The Challenge: This problem and the solution come directly out of classical game theory. Both players (Jeff and Jean) seek the same end-game (everyone wins) but all lack the essential information needed to achieve that end result.
Scenario: Jeff and Jean (or any couple) agreed to meet this evening, but cannot recall if they will be attending the opera or a football game (and the fact that they forgot is common knowledge). The husband would prefer to go to the football game. The wife would rather go to the opera. Both would prefer to go to the same place rather than different ones. If they cannot communicate, where should they go?
No matter how statistics and probabilities are calculated, there is no possible way for both players to come out ahead. In fact using mathematical calculation to come to a best choice here is inadequate, because this approach does not account for the additional harm (dissatisfaction) that might come from not only going to different locations but going to the wrong one as well (e.g. he goes to the opera while she goes to the football game, satisfying neither).
This presents an interesting case for the game-based thinker since each choice (known as the Nash equilibria in game theory) is deficient in some way.
Ultimately the results will be unfair; with one player consistently doing better than the other.
No matter how much the players use rational thinking to explore different strategies to solve this dilemma (called “mixed strategy Nash equilibrium”) it is inefficient. The players will mis-coordinate with probability, leaving each player with an expected return of less than the return one would receive from constantly going to one’s less favored event.
Solution or a Potentially Successful Strategy: One possible resolution of the difficulty involves the use of a concept called “correlated equilibrium*”. In this scenario, each player possesses subjective beliefs about what actions their partner might take (possibly including correlation between the actions of different partners or even other players), and each player’s strategy is the best response to those beliefs. So the justification is that correlated equilibrium is exactly the set of things that might happen if everyone forms subjective beliefs about what another player might do, according to any possible procedure (not just correct anticipation of what their opponents will actually do), and then chooses an optimal response. There’s a big hidden assumption here because the players’ belief systems have to satisfy a common prior assumption, which imposes a strong consistency condition on belief systems across players. Roughly, everyone has to agree on the course of actions that will result by each player’s belief and how they will change, or how their beliefs might change.
Clearly, the problem is that there are a number of random choices available, and though all of the players want all of the other players to win, they do not have access to enough information to achieve that result. What are they to do? The best, and simplest solution in its simplest form, if the players of the game have access to a commonly observed series of facts, is for all the players to decide on one, agreed to approach to determine what choice is to be made. This needs to be a choice that no matter what it may be, will in the end, be agreeable to all of the players. For example, if the couple could flip a coin before choosing their strategies, they might agree to correlate their strategies based on the coin flip by, say, choosing football in the event of heads and opera in the event of tails.
Notice that once the results of the coin flip are revealed, neither the husband nor wife have any incentives to alter their proposed actions. To alter their proposed actions, would result in mis-coordination and a lower benefit (payoff) than by simply adhering to the agreed upon strategies. The result here is that everyone wins (perfect coordination) and, prior to the coin flip, all of the players have already agreed that whatever happens, “heads” or “tails” they will happily accept the result.
The Takeaway Concerning This Strategy
There are certain changes that might arise in a game space which changes how this strategy will unfold, and how a prediction can be made.
For instance, one player may allow another player the option of “burning money” — that is, allowing that player to give up some of the benefits they might receive (utility.) Thus one player might, for some reason decide to allow the other player to have a greater benefit at the end game, though all players, including the one receiving less, still believing they are a winner.
In some situations involving WWGLKIS a player in the game may seem intent on feeling like they have lost even if they have won. There are many reasons for this, that I will not go into here.
The key point is that this person can only feel like a winner if they are forced or influenced by the other player (s) to recognize that, in spite of how they feel they are in fact winning. If this cannot be done successfully than all the players lose because in a win/win scenario all players need to believe they have won. Of course, in the game of life, if all players get what they want, they will likely be happier than they would be in a win/lose scenario.
WWGLKIS applies well to diplomatic relations and to coopetition in the marketplace.
The key is for all the players is to define and remember what psychological element the game is trying to capture for them, and the emotional needs of the other players. In HAGT (Harrison’s Applied Game Theory), certain aspects of human psychology are accepted as given:
1. All human agendas are about maintaining or expanding territory.
2. Anyone can gather all the accurate facts and connect them to come to an absurd conclusion.
3. Intuition aside, deductive, and inductive reasoning (please wiki these terms) with solid fact-checking and verifiable statistics mixed with Bayes probabilities will give you solid ground to come to a probable or at least defensible strategy, and an accurate prediction.
Here is a great Story @rishabhnsharma
Here is one from the archives @LewisCoaches
Learn more about my philosophy and extensive teachings here
To learn more about studying directly with me, just email me at [email protected]. I will respond personally.
Author: Lewis Harrison is a Manifestation Coach, and a blog and copywriter for hire.
He is the creator of the Ask Lewis Mentoring Method as well as HAGT — Harrison’s Applied Game Theory. He is the Executive Director of the International Association of Healing Professionals an educational organization that offers programs around the world in Intentional Living. He is also Independent Scholar, with a passion for knowledge, personal development, self-improvement, creativity, innovation, and problem-solving. You can read all of his Medium stories at [email protected].
For a decade, Lewis was the host of a humor-based Q & A talk show on NPR (National Public Radio) affiliated WIOX FM in NY.
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