# The Brazilian Games

Ya. Here are some video extracts of the documented experiments I carried out in São Paulo, during Spring 2015.

Now, the two games that you can watch here are what I ended up calling:

The Terrorist:

It is a Bayesian game, and here is an extract of one of my draft chapters, where I explain it:

“A Bayesian game that can help to clarify the above could be the following: imagine a busy airport. There has been a tip-off that a terrorist attack is going to take place and a police officer spots an armed suspect that matches the description given by the police’s intelligence. The suspect is a terrorist with probability p or not with probability 1 –p.

They must decide simultaneously whether to shoot or not. The police officer would want to shoot if the suspect does, that is if the suspect is the actual terrorist. But he would rather not shoot in the contrary case. On the other hand, the suspect would rather shoot even if the officer does not, as he would be caught and convicted. However, if the suspect was not the terrorist, he would rather not shoot as he would be convicted just for illegal detention of a gun. Admittedly, this is a simplistic scenario, but I think it can nevertheless help us understand the dynamics of a Bayesian game.

Two possible normal forms are possible, depending on the type of the suspect, which is what we call the prior.

The police officer is the column player and the first cell of each normal form is the prior, in other word the belief that the officer holds in respect to the suspect’s type (Good, Bad). For the suspect under a Good scenario we have a strictly dominant strategy of not shooting. Conversely, if the suspect is the actual terrorist, he has a strictly dominant strategy of shooting.

According to the above, we can cross out and remove the first and second column of the first and second normal forms, respectively. This leaves us with fever choices and, following the calculation of the payoffs of the mixed strategies, we see that the officer’s payoff are (-1)(1-p) and (-2)(p). In order for him to be indifferent, the two equations must be equal, which leads to p = 1/3. What this means is that the officer should shoot with such probability and not shoot with probability of 2/3.”

Ok, the writing carries on so I will spare you…

And, the other one:

The Coordination Game (how imaginative! what a cracking title!)

It unfolds as follows: two players are selected to perform a duo. They are given a list of three different musical scenarios, labelled here (for simplicity) a,b and c, out of which they are asked to select one, without being able to exchange this private information of theirs with the other player. The task is implicitly to select the same scenario, which appeals to their ability to establish secondary, if not Schelling, salience.

The three scenarios are chosen so that there is always one out of them that ‘should’ stick out, in that it exhibits features that are in discordance with the other two, be it texture, pitch, rhythm, density, dynamics or any other musical parameter. This should hypothetically help further isolating this particular scenario as one of particular salience.

From my draft chapter again:

“In this case, there is no maxmin strategy, which in game theory, and as the term implies, is the strategy that will ensure the best worse possible scenario.

Players have to coordinate absolutely, in order to be rewarded.

The reason why this scenario is introduced is to allow the presentation of two important concepts, those of focal points and salience.

Focal points, according to Thomas Schelling (Nobel 2005, Economic Science), are features that might be relevant to some or all agents, thus influencing their response and decision-making: “focal point[s] for each person’s expectation of what the other expects him to expect to be expected to do”. (Schelling, 1960, p.57)

“This interdependence of expectations is precisely what distinguishes a game of strategy from a game of chance or a game of skill.” (Schelling, 1960, p.86)

Salience is akin to the degree of relevance that one event has with respect to an agent. In this sense, one could say that a focal point has a high level of salience.”

Here, instead, the participants talk about the motivations behind their choices:

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