# Category Archives: game theory

## Shaking the Tree

Life often results in situations such that no strategy suggests any further moves. We just don’t know what to do next. In a game of perfect information, where each player knows all the previous moves, this can signal stalemate. Take chess: given both sides know everything that has transpired and have no reason to believe that the opponent will make a mistake, there can come a time when both sides will realize that there are no winning strategies for either player. A draw is then agreed upon.

The situation is not as simple in games of incomplete information. Let’s assume some information is private, that some moves in the game are only known to a limited number of players. For instance, imagine you take over a game of chess in the middle of a match. The previous moves would be known to your opponent and the absent player, but not to you. Hence you do not know the strategies used to arrive at that point in the game, and **your opponent knows that you do not know**.

Assume we are in a some such situation where we do not know all the previous moves and have no further strategic moves to make. This is to say we are waiting, idling, or otherwise biding our time until something of significance happens. Formally we are at an equilibrium.

A strategy to get out of this equilibrium is to “shake the tree” to see what “falls out”. This involves making information public that was thought to be private. For instance, say you knew a damaging secret to someone in power and that person thought they had successfully hidden said secret. By making that person believe that the secret was public knowledge, this could cause them to act in a way they would not otherwise, breaking the equilibrium.

How, though, to represent this formally? The move made in shaking the tree is to make information public that was believed to be private. To represent this in logic we need a mechanism that represents public and private information. I will use the forward slash notation of Independence Friendly Logic, /, to mean ‘depends upon’ and the back slash, , to mean ‘independent of.’

To represent private strategy Q, based on secret S, and not public to party Z we can say:

Secret Strategy) If, and only if, no one other than Y depends upon the Secret, then use Strategy Q
(∀YS) (∃z/S) ~(Y = z) ⇔ Q

To initial ‘shaking the tree’ would be to introduce a new dependency:

Tree Shaking) there is someone other than Y that depends on S
(∃zS) ~(Y = z)

Tree Shaking causes party Y’s to change away from Strategy Q since Strategy Q was predicated upon no one other than Y knowing the secret, S. The change in strategy means that the players are no longer idling in equilibrium, which is the goal of shaking the tree.

Posted in game theory, independence friendly logic, logic, philosophy. Tagged with , , .

## More on Philosophy Publishing: Cartels and Rhetoric

Here is a selection three reviewers’ comments from two well-ranked journals about a paper of mine:

1. “Be that as it may, there really isn’t a recognizable philosophical project here that would merit consideration by [Misspelled Journal Name].”
2. “I do not see how the author can improve the paper, since its motivation is ungrounded.”
3. “This paper makes interesting, important claims and it should with improvements appeal to a broad and diverse audience.”

It would be one thing if all reviews were like 1 and 2. I’d be some mix of crazy, mistaken and uninformed. The issue is review 3. That reviewer saw my work completely differently than the others, basically exactly as I was hoping it would be understood.

How can the disparity in views be explained?

One way could be to blame ‘cartels’ of academics. The idea behind academic cartels is that reviewers belong to some school of thought, a cartel. They, consciously or not, favor work that supports their cartel by referencing them or providing more arguments in their support. By supporting ‘their’ work and rejecting others’, they increase the relative importance of themselves and their friends in academic standing.

Under the the cartel theory, reviewers 1 and 2 rejected my paper more because my ‘philosophical project’ did not support them and their projects, than me not having a project or some actual problem. This view is backed by the fact that reviews 1 and 2 had almost no engagement with any specific claims or arguments in my paper, but instead made critical generalizations about what was said or how it was said. For instance, reviewer 1 said I relied too heavily on Prominent Philosopher X and reviewer 2 said I had not read enough of same Prominent Philosopher X. The criticisms are basically meaningless since they could mean any number of things — no details of what I had wrong were given — and I could take them to just be a smokescreen for their bias.

I’m sure some of this is going on, but I don’t think cartel bias is the main issue. More likely is overwork. It is just easier to make up a BS criticism than an actual criticism. Again, consider the criticism having to do with Prominent Philosopher X: the underlying issue is that they both criticised without ever mentioning what exactly I had said wrong. Moreover, a journal editor would have a tough time arguing with this sort of accusation. I think the reviewers were more concerned with having something defensible to say than saying anything substantive.

Said differently, journal referees are highly risk averse. There is no incentive for them to get themselves into a position that requires more work. They already put in extra time to be the referee, so making difficult arguments is overmatched by making defensible, if nonsensical, arguments.

There are two approaches to this problem: top down from the journals and bottom up for the paper writers. Journals can institute policies that incentivize better reviews. A review of reviews, if you will. A new journal that only accepts reviews of other papers could be formed. This meta-journal would highlight the best and the worst, showing what good reviews and (anonymous) poor reviews are. This would help value service to the community as a reviewer, have pedagogical use in showing best practices and wouldn’t make people avoid being reviewers.

As a writer I advocate figuring out the best rhetoric such that the poor overworked reviewer will think they are getting what they want. Then, if they really don’t like the paper, they will have to come up with a more substantive criticism. Rhetoric, rhetoric, rhetoric: the arguments and conculsions will be the same, but how they are dressed up will be different. I think some philosophers believe themselves to be above ‘mere’ rhetoric, but from everything I’ve seen, this belief just serves to cover up how much we are affected by it. We drink our own Cool-Aid all too often, and a smart writer should use this to their advantage.

Posted in argumentation, game theory, philosophy.

## So Prisoners Don’t Follow the Dilemma

We report insights into the behavior of prisoners in dilemma situations that so famously carry their name. We compare female inmates and students in a simultaneous and a sequential Prisoner’s Dilemma. In the simultaneous Prisoner’s Dilemma, the cooperation rate among inmates exceeds the rate of cooperating students. Relative to the simultaneous dilemma, cooperation among first-movers in the sequential Prisoner’s Dilemma increases for students, but not for inmates. Students and inmates behave identically as second movers. Hence, we find a similar and significant fraction of inmates and students to hold social preferences.

Posted in economics, game theory.

## On Philosophy Publishing

There has been some discussion in the philosophy blogosphere on citation rates in academic philosophy journals. Since I recently decided that I was going to try to get my work published, I have spent a bit of time thinking about this. When John Protevi at NewAPPS asked about citation patters,  I left a comment, but the topic really warrants a longer treatment. Here are some thoughts:

Let me postulate, for this discussion, that doing philosophy and publishing are very different enterprises. That is, the content of the philosophy is separate from the distribution of it, and while you hope that your philosophy has some merit, we are currently concerned with getting it published regardless.

Consider the top philosophy journals, not as philosophy journals, but just as publications. Do these journals compete with each other? Yes, but they also cooperate more. If anything, the top journals are in coopetition. While the journals do compete for the best new content, consider how they make their money. They make their money by being purchased, in this case by academic libraries with limited resources. They will only get purchased if the libraries (and philosophy departments) feel that there is active research going on that they need to access. So it is much more important for journals to have an active discussion amongst themselves to give the appearance of active research being done (again regardless of merit).

It is not so much that they compete with each other, than they are in competition with everyone outside their area.

Now, how do these journals show that they have an active discussion? They reference each other, back and forth. This mutual referencing fosters the importance of the discussion, and hence the journals too. Once the discussion has begun, all other journals that wish to publish on the topic will have to reference back to the original journals, again fostering the original journal’s importance.  Hence a journal, or group thereof, that fosters a discussion—a niche if you will—will effectively block out other journals. All other or new journals will always be playing catch-up since they will inherently have fewer references and hence be less important.

This suggests that citations and referencing is a highly strategic business practice. Journals need to get themselves into the discussion somehow to make themselves relevant. If possible, they want to be the nexus of the discussion.

One interesting consequence is that it is less the individual researchers or papers that are cited, but that the journal is cited at all. The journal wants to be in on the discussion, and it doesn’t matter how it gets there. This suggests a bias towards references that include the journal or involve the journal in discussions, whether those references are relevant or not.

This leads to the treatment of ‘stars’ within the profession. If the journals publish the writing of a ‘star’ they will immediately get themselves into a position where people need to have that person’s work. So it is a good strategy for a journal to play into ‘star’ writers and to burnish their reputation (e.g. dedicated journal issues, invited papers) since this will make their research seem important and require people who do research to reference the work of the star in that journal.

Consider, then, why we cite. Is it to give credit to those who did great work? Sure, but there is too much at stake in terms of reputation (reputation yields job offers and money) for that to be the sole reason.

Is it to show we know what we are talking about? Unlikely but possible: journal publishing is not done to show that you have the done the reading, and if you are talking about something important then it doesn’t matter who is referenced.

Is it to make our lives easier, so we don’t have to argue every point? Likely at times, this is again too simplistic in terms of other issues.

Is it because it plays into the business model of the journals? Probably more than we want to admit.

Conclusions?

As mentioned above, journals will be biased towards self referencing their publication. Hence, if your work can be framed in a way that allows for journal self references, all the better. Same goes for citing stars. This also means that the bias could allow for references to go unchallenged: e.g. reference Hume for everything (or David Lewis), and always have some references to big journals. Conversely, less prominent work can be slipped in unnoticed if it is sandwiched between stars and big journals.

Perhaps there is an optimal ratio of prominent authors and different top journal references to less prominent references to give the appearance of new-ness and importance to the discussion.

At any rate, journal publishing exists at the intersection of business and philosophy, and it does no good to treat the double blind review as the only factor in getting published.

Posted in game theory, news, philosophy.

## An Introduction to the Game Theoretic Semantics view of Scientific Theory

What is a scientific theory?  In an abstract sense, a scientific theory is a group of statements about the world.  For instance the Special Theory of Relativity has, “The speed of light in a vacuum is invariant,” as a core statement, among others, about the world.  This statement is scientific because, in part, it is meant to hold in a ‘law-like’ fashion: it holds across time, space and observer.

The Popperian view is that we have scientific theories and we test those theories with experiments.  This means that given a scientific theory, a set of scientific statements about phenomena, we can deductively generate predictions.  These predictions are further statements about the world.  If our experiments yield results that run counter to what the theory predicts — the experiments generate statements that contradict the predictions, the theory did not hold across time, space or observer — then the theory eventually becomes falsified.  Else the theory may be considered ‘true’ (or at least not falsified) and it lives to fight another day.

The game theoretic semantics (GTS) view is that truth is the existence of a winning strategy in a game.  In terms of the philosophy of science, this means that our theories are strategic games (of imperfect information) played between ourselves and Nature.  Each statement of a theory is a description of a certain way the world is, or could be.  An experiment is a certain set of moves — a strategy for setting up the world in a certain way — that yields predicted situations according to the statements of the theory.  If our theory is true and an experiment is run, then this means that there is no way for Nature to do anything other than yield the predicted situation.  Said slightly differently: truth of a scientific theory is knowing a guaranteed strategy for obtaining a predicted Natural outcome by performing experiments.  If the strategy is executed and the predicted situations do not obtain, then this means that Nature has found a way around our theory, our strategy.  Hence there is no guaranteed strategy for obtaining those predictions and the theory is not true.

An example:

Take Galileo’s famous experiment of dropping masses off the Tower of Pisa.  Galileo’s theory was that objects of different mass fall at equal rates, opposing the older Aristotelian view that objects of greater mass fall faster.

According to the Popperian view Galileo inferred from his theory that if he dropped the two balls of different mass off the tower at the same time, they would hit the ground at the same time.  When he executed the experiment, the balls did hit the ground at the same time, falsifying the Aristotelian theory and lending support to his theory.

The GTS view is that dropping balls of unequal mass off a tower is a strategic game setup.  This experimental game setup is an instance of a strategy to force Nature to act in a certain way, namely to have the masses hit at the same time or not.  According to Galilean theory, when we are playing this game with Nature, Nature has no choice other than to force the two masses to hit the ground at the same time.  According to Aristotelian theory, when playing this game, Nature will force the more massive ball to hit the ground first.  History has shown that every time this game is played, the two masses hit the ground at the same time.  This means that there is a strategy to force Nature to act in the same way every time, that there is a ‘winning strategy’ for obtaining this outcome in this game with Nature.  Hence the Galilean theory is true: it got a win over the Aristotelian theory.

Why you might want to consider doing things the GTS way:

GTS handles scientific practice in a relatively straightforward way.  Theories compete against Nature for results and against each other for explanatory power.  Everything is handled by the same underlying logic-game structure.

GTS is a powerful system.  It has application to  game theory, computer science, decision theory, communication and more.

If you are sympathetic to a Wittgensteinian language game view of the world, GTS is in the language game tradition.

More on GTS:

Posted in game theory, logic, philosophy, science. Tagged with , , , , .

## Risky Kakanomics

Gloria Origgi writes:

This is an application of the theory of kakonomics, that is, the study of the rational preferences for lower-quality or mediocre outcomes, to the apparently weird results of Italian elections. The apparent irrationality of 30% of the electorate who decided to vote for Berlusconi again is explained as a perfectly rational strategy of maintaining a system of mediocre exchanges in which politicians don’t do what they have promised to do and citizens don’t pay the taxes and everybody is satisfied by the exchange. A mediocre government makes easier for mediocre citizens to do less than what they should do without feeling any breach of trust.

She argues that if you elect a crappy politician, then there is little chance of progress, which seems like a bad thing. People do this, though, because maintaining low political standards allows people to have low civic standards: if the politicians are corrupt, there is no reason to pay taxes. Likewise, the politicians who have been elected on the basis of being bad leaders have no incentive to go after tax cheats, the people who put them in office. Hence there is often a self-serving and self-maintaining aspect to making less than optimal decisions: by mutually selecting for low expectations, then everyone cooperates in forgiving bad behavior.

This account assumes that bad behavior of some sort is to be expected. If someone all of a sudden starts doing the ‘right thing’ it will be a breach of trust and violating the social norm. There would be a disincentive to repeat such a transaction again, because it challenges the stability of the assumed low quality interaction and implied forgiveness associated with it.

I like Origgi’s account of kakonomics, but I think there is something missing. The claim that localized ‘good interactions’ could threaten the status quo of bad behavior seems excessive. Criticizing someone who makes everyone else look bad does happen, but this only goes to show that the ‘right’ way of doing things is highly successful. It is the exception that proves the rule: only the people in power — those that can afford to misbehave — really benefit from maintaining the low status quo. Hence the public in general should not be as accepting of a low status quo as a social norm, though I am sure some do for exactly the reasons she stated.

This got me thinking that maybe there was another force at work here that would support a low status quo. When changing from one regime to another, it is not a simple switch from one set of outcomes to the other. There can be transitional instability, especially when dealing with governments, politics, economics, military, etc. If the transition between regimes is highly unstable (more so if things weren’t that stable to begin with) then there would be a disincentive to change: people won’t want to lose what they have, even if it is not optimal. Therefore risk associated with change can cause hyperbolic discounting of future returns, and make people prefer the status quo.

Adding high risk with the benefits of low standards could make a formidable combination. If there is a robust black market that pervades most of the society and an almost certain civil unrest given political change (throw in a heavy-handed police force, just for good measure), this could be strong incentive to not challenge an incumbent government.

Posted in economics, game theory, mind, philosophy. Tagged with , , , .

## EIFL (Domainless Logic)

I saw this post by Mark Lance over at New APPS and he brought up one of the issues that I have recently been concerned with: What is a logical domain?  He said:

So our ignorance of our domain has implications for which sentences are true.  And if a sentence is true under one interpretation and false under another, it has different meanings under them.  And if we don’t know which of these interpretations we intend, then we don’t know what we mean.

I am inclined to think that this is a really serious issue…

When we don’t know what we, ourselves, mean, I regard this as THE_PHILOSOPHICAL_BAD, the place you never want to be in, the position where you can’t even speak.  Any issue that generates this sort of problem I regard as a Major Problem of Philosophy — philosophy in general, not just of its particular subject.

A little over a year ago I was trying to integrate probability and logic in a new way.  I developed indexed domains in order that different quantifications ranged over different values.  But then I said:

(aside:
I prefer to use an artifact of Independence Friendly logic, the dependence indicator: a forward slash, /. The dependence indicator means that the quantifier only depends on those objects, variables, quantifiers or formulas specified. Hence

means that the variable x is randomly instantiated to Heads or Tails, since the only things that Яx is logically aware of are Heads and Tails. Therefore this too represents a coin flip, without having multiple domains.)

I used the dependence slash to indicate the exact domain that a specific quantification ranged over.  This localized the domain to the quantifier.  About a week after publishing this I realized that the structure of this pseudo-domain ought to be logically structured: (Heads, Tails) became (Heads OR Tails).  The logical or mathematical domain, as an independent structure, can therefore be completely done away with.  Instead a pseudo-domain must be specified by a set of logical or mathematical statements given by a dependence (or independence) relation attached to every quantifier.

For example:

∀x/((a or b or c) & (p → q))…

This means that instantiating x depends upon the individuals a, b or c, that is, x can only be a, b or c, and it also can only be instantiated if (p → q) already has a truth value.  If  ((p → q) → d) was in the pseudo-domain, then x could be instantiated to d if (p → q) was true; if ¬d was implied, then it would be impossible to instantiate x to d, even if d was implied in some other part of the pseudo-domain.  Hence the pseudo-domain is the result of a logical process.

The benefit of this approach is that it better represents the changing state of epistemic access that a logical game player has at different times.  You can have a general domain for things that exist across all game players and times that would be added to all the quantifier dependencies (Platonism, if you will), but localized pseudo-domains for how the situation changes relative to each individual quantification.

Moreover, the domain has become part of the logical argument structure and does not have an independent existence, meaning fewer ontological denizens.  And, to answer the main question of this post, every domain is completely specified, both in content and structure.

I’m inclined to call this logic Domainless Independence Friendly logic, or DIF logic, but I really also like EIFL, like the French Tower: Epistemic Independence Friendly Logic.  Calling this logic epistemic emphasizes the relative epistemic access each player has during the logical game that comes with the elimination of the logical domain.

## Metta World Peace, James Harden and Furbizia

Everyone is saying that Metta World Peace (the basketball player formerly known as Ron Artest) is crazy for elbowing James Harden in the face. I can’t say that I disagree, but I think there is more to the story.

Did no one else notice that James Harden walked right into World Peace while he was celebrating? Watch the video. Harden walks directly into MWP. He doesn’t do anything that would cause a foul, but if he were going to actually try to receive an inbound pass, he would have walked away from opposing players, not at them.

Instead he gets real close to an ecstatic opponent known for outbursts. I’m sure he didn’t want to get elbowed in the head, but he did put himself in a position to get fouled, to take the charge as it were. If he had only been fouled, not elbowed, by a jumping MWP then people might be talking about how Harden had cleverly gotten another foul on one of the Laker’s best players through strategic gamesmanship alone.

When asked if he would shake Harden’s hand, Metta World Peace said he wouldn’t. Everyone condemned him for this too, but I’m with MWP this time. If MWP sees Harden as having taken advantage of his celebration as a cheap way to get him in trouble, then it is understandable that he wouldn’t want to shake the man’s hand. This doesn’t excuse the elbow, but it does explain the attitude.

Posted in economics, game theory. Tagged with , .

## 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.

## Consequences

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.

### Reputation

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.

## Trembling Hands

At least since Selten (1975) game theorists have considered that given a series of decisions there is some small probability that the person making the decisions will make a mistake and do something irrational, even if she knows the right thing to do.  This is called the trembling hand approach: although a person rationally knows the right (rational) thing to do, sometimes her hand trembles and she chooses incorrectly.

Therefore, given a game defined by a finite set of iterated decisions and payoffs in which all the rational moves are known by both players (think Tic Tac Toe), there is a ‘perturbed’ game in which the rational choices are not made.  So consider playing a game of Tic Tac Toe:  Either player can always force a draw in Tic Tac Toe and hence prevent loss.  However, it is easy enough to make a mistake (through inattentiveness, eg) and allow your opponent to win.

 Tic Tac Toe Game Tree showing possible decisions for the first two moves

I believe this approach is a good start but does not go nearly far enough to incorporate probability into game theory.  The issue stems from the trembling hand approach assuming that irrational behavior occurs because of ‘some unspecified psychological mechanism.’  This is fine, but then every trembling hand probability, every chance of making an irrational decision, is defined as a separate, independent probability.  This means that making an irrational decision is based on chance, as if we roll a die every decision we make.

Perhaps some people have this problem, that they act irrationally at probabilistic rates, but this doesn’t seem either realistic, or fit with the idea that a psychological mechanism was at work.  If some psychological mechanism was at work, then we would expect

1. The probabilities of making mistakes would not be independent of each other, since they have a common source.
2. There would be a much higher chance of irrationality at times when the psychological issue manifests itself.

One example of what I have in mind is the effectiveness of gamesmanship in sport.  Gamesmanship is the art of getting into your opponents head and causing them to make mistakes.  Consider this description of “furbizia” in Italian soccer by Andrea Tallarita:

Perhaps nothing has been more influential in determining the popular perception of the Italian game than furbizia, the art of guile… The word ‘furbizia’ itself means guile, cunning or astuteness. It refers to a method which is often (and admittedly) rather sly, a not particularly by-the-book approach to the performative, tactical and psychological part of the game. Core to furbizia is that it is executed by means of stratagems which are available to all players on the pitch, not only to one team. What are these stratagems? Here are a few: tactical fouls, taking free kicks before the goalkeeper has finished positioning himself, time-wasting, physical or verbal provocation and all related psychological games, arguably even diving… Anyone can provoke an adversary, but it takes real guile (real furbizia) to find the weakest links in the other team’s psychology, then wear them out and bite them until something or someone gives in – all without ever breaking a single rule in the book of football. (via)

If we try to explain the an instance of someone making an irrational play in a game due to gamesmanship/furbizia according to the trembling hand model, we run into difficulty.  The decision tree according to the ‘trembling hand’ theory would have a series of decisions each with a low probability of making an irrational mistake:

.01 — .01 — .01 — .01 — .01

Hence it cannot explain why someone would crack later in the game as opposed to earlier, since all the probabilities are equal.  Nor can it explain why people make irrational decisions at higher rates when playing against a crafty opponent than they would make otherwise. Therefore the trembling hand model cannot explain the effectiveness of gamesmanship.

But the decision tree given linked, non-independent probabilities might have the chance of an irrational decision given by:

.01 — .05 — .1 — .17 — .25

This model has an increasing chance of irrational action.  As time progresses, it becomes increasingly likely that an irrational choice will occur due to the gamesmanship of the opponent.

I’ll refer to this model generally as induced irrationality.  Induced irrationality occurs when the chance of making a rational decision decreases due to some factor, or when the chances of making irrational decisions over time change in concert, or both.

Other phenomena follow this pattern.  Bullying comes to mind: it is similar to gamesmanship in its breaking or bending of ‘rules’ over time to get in someone’s head and thence get them to do things they would rather not do.  The bullied will act irrationally in the presence of the bully and potentially more so as the bullying continues, perhaps even leading to “snapping”— doing something seriously irrational.

Phobias are also similar: for whatever reason a person has a phobia, and given the presence of that object or situation, the otherwise rational person will make different decisions.

Moreover this may have something to do with the Gambler’s Fallacy:   By making a gambler associate a pattern to some random act, such as by showing the gambler all the recent values of a roulette wheel in order to convince the gambler to believe that the wheel likely will land on red (or losing a few bets to a shill in 3 card monte, or seeing a pattern in the stock market, etc.), the casino has planted a belief in the gambler.  Hence, as time goes on and red is not landed upon, the gambler increasingly thinks it is ever more likely that red will hit (even though it has the same low chance as it always did). Hence the gambler will likely bet more later — more irrationally —  as he expects red to be increasingly likely to hit.

Hence, though trembling hands may be a factor in irrational decision making, it does not seem like it is the only possibility or even the most significant in a number of interesting cases.

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Selten, R. (1975). ‘Re-examination of the Perfectness Concept for Equilibrium Points in Extensive Games.’ International Journal of Game Theory, 4: 22–55.

My brother beat the Tic Tac Toe playing chicken when the Chinatown Fair Arcade (NYC) still operated.  I assume that there was a computer choosing the game moves and it happened to glitch when my brother was playing: though the machine claimed it won, if you looked at the Xs and Os, my brother had won.  We asked the manager for our promised bag of fortune cookies.  He said he didn’t actually have a bag since the chicken wasn’t ever supposed to lose.

Posted in economics, game theory. Tagged with , .