Trembling Hands 2: Inducing Irrationality

Given an intelligent rational opponent, one who has complete information of the decision tree in a game, it may be very difficult to implement an optimal strategy. All possible moves may be accounted for and hence a stalemate may exist from the outset.

One way to proceed is to act as if your opponent may make a mistake — her hand may tremble — allowing your optimal strategy to obtain. Previously I argued that there is more too the story than merely hoping that your opponent will err at some probabilistic rate. I gave examples where errors were induced, such that they were more likely at certain times or under certain conditions.

The cannonical example given was that of furbizia (gamesmanship or guile), which causes a football opponent to make a mistake. By acting in certain ways — eg “time-wasting, physical or verbal provocation and all related psychological games, arguably even diving” — it can cause an opponent to wear out and crack. Since furbizia, by definition, occurs outside the rules and regular strategies of the game of football (and without breaking any rules), how are we to account for it?

Just Walk Away

First let’s define the Walk Away principle. The Walk Away principle states that any subgame can be walked away from, just dropped, at any point in a game. For example, during football match a player may just walk off the field and go home. Not only are all the payoffs of the game lost when a person walks away, even further payoffs, such as loss of fans and teammate’s respect, can be lost. Still, this is an option for any player at any point of a match. Imagine that news of a family member being gravely injured reached the player mid-game. Then it might make sense to just walk off the field. Another example is that of a stock portfolio. Given a certain stock portfolio, grave penalties may be incurred if money is taken out of it too soon. However, if a disaster strikes, large sums of money are needed quickly and it makes sense to liquidate the stock portfolio during those times. In this case, the economic subgame represented by the portfolio is being walked away from.

The Walk Away principle highlights that no sub-game is played in a vacuum, that there are always global variables — emergency or other unusual situations — that could radically change a person’s decision making.

Consider this scene from the movie Out of Sight: George Clooney is a fugitive and Jennifer Lopez is a marshal pursuing him. The FBI has George Clooney trapped in a hotel and Jennifer Lopez is watching one of the exits. As George Clooney goes by Jennifer Lopez, he waves at her in a friendly way – they had already been aquainted. Instead of reporting seeing him to the other officers, she freezes and does nothing, allowing Clooney to escape. Instead of playing the subgame that would have gotten her a reward by bringing in a fugitive, she, in essence, (mentally) walked away from it. From the perspective of her job and other officers, she acted irrationally. However, she decided to play a different game. That game included extending the relationship with Clooney, which would have ended had he been arrested. From that perspective, she acted rationally.

I mention this example because it shows two games that had mutually exclusive payoffs, arresting the fugitive vs. continuing the relationship, and that even though she was playing the former game, Clooney’s action — waving at her — induced her to play the latter game. Also important is that if she had not already had some relationship with Clooney, his actions would not have had such an effect on her.

Trembling hands, in these cases, may then be seen not so much as an opponent acting irrationally, but as having been induced to play a subgame with mutually exclusive payoffs from the current game (like boxing during football). However, as mentioned, it is a necessary condition that there is something prior which allows a person to be induced to play a different game. How to know who is susceptible to being so induced, and what will induce them?

Counter Intelligence and Psychological Hacking

Knowing who is susceptible and how to induce irrationality them is a counterintelligence problem. If you knew ahead of time that a company had backdated stock options, you might suspect that they would be very worried about anyone looking into their procedures. If you were then able to find a way to publicize these nefarious dealings, you could blackmail them into acting in what would otherwise be considered irrational. But the opportunity only comes with the right intelligence.

In general, unless we are personally very wealthy or in charge of a wealthy organization, we will not have an intelligence service. But this doesn’t mean we can’t gather intelligence, even over the course of a sports game. Trash talking can be seen as a psychological search strategy: by liberally insulting every competitor and saying how great you are, anyone who rises, who argues –who doesn’t walk away– may be potentially unfocussed on the game at hand. Trash talking costs very little, just some breath, but getting angry and distracted can be very costly. The more clever the trash talk, the strategic fouls, and gamesmanship in general, the wider and more sophisticated the search, the psychological hacking, becomes.

Given the results of the search, eg player 15 is most affected by being called $%!#, the gamesmanship can then be focused on the candidates most likely to react badly and at the worst possible times. This is an exploitation of the Walk Away principle. Instead of walking away from the insults, the opponent walks away from the game, if only for a few seconds: the candidate is induced into playing a subgame with mutually exclusive payoffs.

Often stakes are very high in competition and hence gathering intelligence is important. Yes the intelligence gathering and implementation/ furbizia requires effort, but as Sun Tzu notes, “Hostile armies may face each other for years, striving for the victory which is decided in a single day. This being so, to remain in ignorance of the enemy’s condition simply because one grudges the outlay of a hundred ounces of silver in honors and emoluments, is the height of inhumanity.” (The Art of War  XIII.2) What is some trash talk in the face of winning a championship, or paying off a spy when thousands of lives are on the line? Intelligence gathering and strategic implementation generally dominates simply playing by the rules.

This interpretation of furbizia/ gamesmanship as an intelligence search explains its utility and provides a way to understand furbizia in a wider setting. The high return and low relative cost explains its prevalence.

Wave-Decision Duality

Different situations and search procedures need to be combined with traditional trembling hands dynamics to better evaluate decision strategies. For example, if an intelligence search yields results according to some function of time and factors x, then the chances of an opponent making a mistake will vary according to (f(x, t), σ), where σ is the chance of a non-induced trembling hands error. If f(x, t) finds results quickly compared to the game length, then the chance of the opponent making a mistake becomes high, and a radically different strategy should be employed to maximize upon these errors. If f(x, t) predicts when a mistakes will occur, then too a strategy tailored to these circumstances will be needed.

How are we to understand the function f(x, t)? Since it represents a kind of search, we can expect that at least some instances will fall under existing research: search theory, human & machine learning, and associated disciplines have been the subject of much interest and study. However, though we do not know which search will be used to gather the intelligence, the idea that we are doing a search lets us assume that it will return a result at some varying probability.

Combining this probability with a game theory strategy yields a both decision-like and statistical (or wave) -like property for every move in a game. Considering a game tree, each node has value for irrational behavior given by the search function, and a rational decision determined by a Nash (or other) equilibrium solution.


Backwards Induction Paradox

Equilibrium solutions to a game can be calculated with equal justification starting from the top of the game tree and working towards the payoffs or from the bottom of the game tree and working backwards from the payoffs to the initial choices. This leads to the paradox of backwards induction, which occurs when the strategy that is suggested by backwards induction is based upon parts of the game that could never be reached by using that strategy, making that strategy based upon irrational results. The traditional trembling hands solution to this paradox states that one simply assumes the rational opponent could make a mistake, have their hand tremble, justifying the reliance on the otherwise unreachable parts of the decision tree.

Now, given an associated search function in the game tree, hoping for irrationality is replaced by a search that induces it. Since this search induces irrationality, it makes sense to allow for, if not expect, irrationality. This justifies using backwards induction as a strategy even if it relies upon parts of the game that should not ever be rationally reached, especially for iterated games.


Since the search finds information about the opponent to be used during the game — but doesn’t have to be found during the game — braggadocio and cultivating a personality off the field is a can reveal information about an opponent prior to the game, saving valuable time. Having a reputation may help prime opponents* to being induced before ever personally interacting with them. Though it may also warn opponents to be prepared, everyone should already know to be prepared due to furbizia’s high prevalence anyway, and hence little is lost by practicing gamesmanship. If anything, not playing with some degree of gamesmanship is the exception to the rule, witnessed by the comment that someone ‘plays the game the right way’ is said as a compliment: that person is so good that it is completely unnecessary to use gamesmanship.

You may not want to have a reputation for playing dirty in general, but this is outside the scope of the competitive struggle, especially if you are successful. And some people like anti-heroes and ‘bad-boys,’ so a less than straight-edge reputation is not strictly detrimental. Perhaps this interpretation of furbizia also helps explain the appeal of such types. Since furbizia is an effective strategy, there is value in being ‘bad.’ An ‘all options on the table’ strategy and reputation may also be worthwhile, too. Theoretically, then, although certain reputations can have ill effects, these consequences are not significant enough to rule out using effective strategies that lead to such reputations.

Moreover, having personality and reputation is not limited to the actual players, but may include the fans. Fans insulting or harassing opponent players, and cheering/ chanting loudly at key moments may help break an opponent’s concentration. All of these practices can help lead to a critical mistake by an opponent.

Defense and Counterintelligence

Is there a way to defend against furbizia? Though there are many types of games that allow for gamesmanship, I’ll make a few suggestions on defending against it.

One of the major differences between football/soccer and other sport is that the clock never stops in soccer. One half-time break and that is all. This is very different from, say, basketball, where time outs may be called. The time out allows players to take a break, catch their breath and reorganize.

Reorganization can break up a counter intelligence search: when the situation changes, prior searches may no longer be applicable, forcing the search to begin anew. For instance, a basketball the coach may recognize the symptoms of psychological stress and call a time out before any mistakes are made. Coaches and teammates who are able to diagnose warning signs, who understand furbizia themselves, will be able to take action such as calling time outs or separating teammates from dangerous situations before a problem occurs. Without any (or much fewer) breaks, such as in soccer, a chance to take a break and reorganize is harder to come by. Perhaps this is why furbizia in soccer is so well developed: it has the greatest opportunity to work in a game with fewer breaks.

Any and all other methods for disrupting the search, if only cracking a joke that makes the opponent laugh, calling the referee’s attention to the gamesmanship or being so friendly that your opponent feels bad insulting you, should be employed as applicable.

Alternatively, one can run counter-intelligence. If an opponent is committed to using furbizia, then the trick is to get them to over-commit to it. Either push them too far, so their gamesmanship does break an official rule of the game, or make them waste time and effort on it to the detriment of the rest of their play.  In the end, make furbizia work for you.

Posted in economics, game theory.