Infographic about statistical studies related to schizophrenia

Here you have an infographic created by me in order to make you aware of some of the most interesting statistical studies on topics related to schizophrenia. I am sure that this statistics will make you reflect on aspects about schizophrenia that you never thought of before. I hope you find it interesting.

Information sourced from Wikipedia | www.wikipedia.org de Adrián Villalba Maillo

Game theory: the occupation of the city of Kent

Lately I've been learning the basics of game theory and I've been interested in finding a special situation in real life that could be solved using game theory. Since I have not found any situation related to the topic of this blog, I have decided to apply what I have learned about game theory in another field, the military field. I hope you find this topic as interesting as I do.

Game theory: the occupation 

of the city of Kent

In the ninth century, the territory of England was divided into the Anglo-Saxon heptarchy, the name given during Late Antiquity and the High Middle Ages to the set of Anglo-Saxon petty kingdoms placed in the center, south and east of the island of Great Britain that generally are identified with Essex, Estanglia, Kent, Mercia, Northumbria, Sussex and Wessex, that eventually were united in the Kingdom of England. At this time, the invasion and looting of different cities of the seven kingdoms carried out by the Viking Grand Army was very frequent. The Great Viking Army, known by the Anglo-Saxons as the Great Pagan Army, was a coalition of Nordic warriors, mainly from Denmark, Sweden and Norway.

In this historical context, we imagine the invasion and occupation perpetrated by the Vikings of a certain English city of the time, for example Canterbury (called at that time Cantwareburh), the capital of the medieval kingdom of Kent. During the occupation of the city, the King of Kent manages to escape from Canterbury and flees to the neighboring kingdom of Sussex, one of his allies. Once in Sussex, the King of Kent asks the King of Sussex to help him recover the city of Canterbury by sending his army to defeat the Vikings. As an incentive, the King of Kent promises the King of Sussex that if he recovers the capital of his kingdom, he will give him half the wealth of the kingdom of Kent valued at 50,000 gold coins.

Despite this, the King of Sussex is aware of the large number of soldiers of the Viking army, as well as its ferocity and mastery in combat. Bearing this in mind, the King of Sussex asks for help from another of his allied kingdoms, the kingdom of Essex, another of the neighboring kingdoms of the kingdom of Kent. The King of Sussex asks the King of Essex to combine the strength of their respective armies to conquer Canterbury, since they will only achieve this objective if the two armies attack together. As an incentive, the King of Sussex agrees to pay the King of Essex half of the reward offered by the King of Kent, 25,000 gold coins, provided the King of Essex helps him. The king of Essex agrees to help the king of Sussex and the two kings agree that their respective armies will meet at the gates of Canterbury within a week in order to fight against the Vikings. In this case, for strategical reasons, their armies will have to give a surprise attack from different positions and this will require that the two armies head to Canterbury separately.

Once the two kings come back to their respective kingdoms with the excuse of preparing their armies for battle, the two kings reflect on the obvious alternative that they both have. The two kings know that if one of them sends his army within a week to Canterbury, the other king has the option of not sending his army, which would imply the sure annihilation of the army that went to Canterbury. The reason why one of the kings may decide not to send his army is obvious: if the King of Essex sent his army to Canterbury and the King of Sussex decided not to, the Essex army would be destroyed and the King of Sussex would have free run for the military occupation of the kingdom of Essex, which would bring him benefits of 50,000 gold coins, the total wealth of the kingdom of Essex. Likewise, the king of Essex may decide to do the same and take possession of the kingdom of Sussex, whose wealth is equal to the wealth of the kingdom of Essex, that is to say, 50,000 gold coins. The two  kings know for sure three things:

- If only one of the two armies approaches to Canterbury, this army will be annihilated by the Vikings and the king who has not sent his soldiers will be able to occupy the defeated kingdom.

- If the two armies go to Canterbury, they will defeat the Vikings and each victorious king will be granted half the reward of the King of Kent.

- If no army goes to Canterbury, neither of the two kings will get benefits.

Payoff matrix

In this payoff matrix, the results are not expressed in earnings, but in the opportunity cost of each alternative, that is to say, the loss of potential gain from other alternatives when one alternative is chosen.

	To respect the alliance	To break the alliance
To respect the alliance	- 25,000 / - 25,000	- 100,000 / 0
To break the alliance	0 / - 100,000	-50,000 / -50,000

Nash equilibrium

In this case, the Nash equilibrium or best response for both of them would be to break their alliance, since no player has anything to gain by changing only their own strategy. Bearing this in mind, the two kings seem to have two viable options:

- To violate their agreement, since they cannot trust in each other (as often happens in real world politics), or refuse to collaborate from the beginning, it depends on how long it takes them to realize all the alternatives they have and their costs.

- To modify the terms and conditions of the agreement. For instance, they could arrange for their respective armies to meet at an agreed location away from Canterbury from where they could head together to Canterbury. In this way none of them would run the risk of being annihilated by the Vikings, but they would have to develop another military strategy that would allow them to win the battle.