What do you do when after three days of sleepless coding, your bug count goes from a good 14 to zero? You find a void in life that can only be filled with formulating meaningless game-theoretic constructs and presenting them to your readers.
So I find myself in this situation last night, and began thinking of a particular category of games that are quite common in life but we rarely ever get to beat them because we can’t formulate them in time. Regular readers will know how important I consider identifying a game in order to win it. The game is actually about a cooperative multiplayer strategy, but when discussing with a couple of people, I quickly realized the “undeclared couple” in your group is a scenario common enough for it to be used as an example. These principles apply in practically every walk of life when you are in a situation where you do not know the objective functions of other players, and especially if two players are cooperating against your interests. Note that we won’t discuss winning strategies here, since they are discussed in depth in classical game theory. We are just trying to make an effort to identify such games when they are played, so that we become better equipped to react when it does happen.
A lot of times, losing such games can lead to frustration, resentment and anger. You feel treated “unfairly” because people sided with other people. It just gets messy because you try to humanize people when you lose so you can blame them, whereas if you were on the winning side, you would just say, “Hey, I looked after my interests. What’re you so worked up about?” Goes without saying, the workplace is the most high-stakes game with hidden cooperative players – although I have to admit, personally I’ve not come across any work-related cases yet (it may have something to do with the fact that I work in a company where it’s acceptable to flame a VP if you have something to say). In personal relationships, families, newly weds, etc., it’s much too common for comfort.
Let’s start with a simpler example of Poker. If you had a cooperative player sitting diametrically opposite from you on a poker table (i.e. you have half the players on the table between your turn and their turn), you gain a distinct edge. Aside from the statistically trivial possibility of your chances being doubled because you get two hands in the game, you also gain a distinct edge in manipulating players who believe that every single player has an objective of making money only for themselves. Simply relaxing this constraint, and where one player is helping another player make money, can make the game so much more advantegous to the cooperative players. In a game of poker, however, the only way to convey information to other players is through your moves. There are games where we have more information at our disposal, should we choose to use it.
This second example applies to practically EVERY situation where a group is involved – be it clubs, activity groups, friend groups, colleagues, a bunch of aunts and uncles, whatever – you name it. We shall look to the example of two of your friends who might be secretly attracted to each other but are too embarrassed to admit it, and require the entire group you hang out with for various reasons (the reasons are faily obvious, but this isn’t an article on pop-psychology, so we’ll leave the reasons to themselves). Really really think back onto those times when two people constantly hang out together, and will seeminly have their objective functions at variance with each other (they will go a long way to say this out loud a million times). I’ve been personally irritated at least twice by such behaviour, so I know the feeling.
So here’s the situation. Two people want to do something “different” from what everyone else wants to do (damn, I guess I’ll write a blog on pop-psychology yet). In a simple one-vote strategy, they lose out. Every player, express their opinion, and assuming a simple model, the group decides to do what got voted the most. If there is a declared couple in the group, they may resolve contention among themselves and present two votes on the game – not all that powerful really. It’s the undeclared couple that gains immense power, especially if other players are not cautious. Now that I think of it, you could look at the voting strategy as a simple betting round of Poker. Each player votes once, but the last player has an advantage since they know every other vote and they can make a move that is more ameable to the group. Then if there are players who haven’t folded or haven’t gone all-in with all that they had to stake, we have a “flop” where players present their “cards” which are statements made in order to sway votes, and another round of betting takes place.
However, one player, gets two votes, and one of those votes is not put on the table until every other vote has been cast. One player can first cast a vote, and if the suggestion is shot down by the time the voting reaches their partner, the partner can present a vote based on better information about what the group wants, while still maintaining an amicable position for both players.
It’s very important to identify such behaviour patterns not only to win that specific round of betting, but to ensure your credibility in the group is not threatened. Over time, this “undeclared couple” will try to weed out those who present a threat to themselves or those who may call their bluff (one of the winning strategies for such games).
This is where we deviate from mathematical game theory into a social phenomenon called “labelling” which too, I comment about a lot. Labelling is the assignment of a label to a certain population to “differentiate” it from the non-labelled population. We see it all around us on a large scale – religion, names, skin color, whatever. I want you to do a simple experiment tomorrow morning. From the start of the day till evening, simply gague your emotional response every time someone uses the inclusive word “us” that includes you. I know it may sound very trivial, but you’ll be surprised at the results.
The untrained mind has an instinctive urge to be “part of” a social group, and it makes us happy. Nothing wrong with that. Now, when you have cooperative players in a game, their differing opinions are defended by the second player who can label the first player as “us”, maintaining their social standing within the group. Any lone player, however, does not have resort to this defense. Over time, both players, for all public appearences, individually start labelling a threatening player as “not us”. They will do rounds within a group and start subtle suggestive reinforcement techniques to indicate how you are not a team player (ever notice how this phrase is parodied heavily in so many TV Shows?) Common statements include, “See how he doesn’t like what we all like to do?” (the minute other players hear “we all” their endorphin system kicks in).
Over time, you may find your opinions become completely irrelevant regardless of what intrinsic value they hold towards the “declared objective” of the group, since the group no longer lets you in on their real objective function.
So now you know why game theory is so important in real life. Ever find yourself in a scenario where your team at work suddenly ignores everything you have to say? Ever notice how a group of two or three people are favoured by the boss regardless of whether they are really optimal for the team? Ever notice how one morning you wake up and find yourself being called “not a team player”, and you have no clue where it’s coming from? Then go read cooperative gaming strategies, cause you’ve just been duped!
