Last day, Ms. Merkel said "At least, this is the second best outcome" in the treaty concerning the EU fiscal unification. She wished if all EU nations had agreed to participate the fiscal unification plan as the best outcome. However, there are some nations, such as the U.K., who objected to the participation in the rescuing the European economy by the fiscal unification. Although there are substantial numbers of the EU countries agreed to participate in rescuing the European economy by their unified fiscal stimulus plan, the best outcome (all the EU nations participate) was not accomplished.
The matrix shown above is the Prisoners' Dilemma matrix modified to explain the Prisoners' Dilemma in the EU parliament concerning this treaty on the fiscal unification. At this time, this Prisoners' Dilemma matrix is based on the mixed strategy which considers all agents do not act like the prisoner in the Prisoners' Dilemma theory. In the pure strategy of the Prisoners' Dilemma theory, all agents decide to take their action 100% rationally, do not trust each other to cooperate together, and cannot exchange the information between them. By contrast, the mixed strategy takes the possibility of agents not acting 100% rationally, cooperating together, and exchanging information between agents. Therefore, we never know how these agents select their choice.
In this matrix, there are two groups of EU nations, Pro-Europeanists, such as Germany, France, and Benelux nations, and Euro-Sceptics, such as the U.K., Sweden, and Czech. This model generalised to suppose all EU nations belong to either groups, and both groups' decision has a 50% influence over European economy.
The bottom left cells of this matrix are deleted because it is less likely that the Euro-Sceptics sign the treaty whereas the Pro-Europeanists do not.
If this game is based on the pure strategy, the Eurosceptic group would definitely not sign the treaty. The benefit to the Euro-Sceptic group will gain the tremendously high benefit by not signing the treaty when the Pro-Europeanist group sign the treaty. Furthermore, in the pure strategy, the Pro-Europeanist group would have given up signing the treaty as follow:
Because, in the pure strategy, both groups are afraid of the situation that the other group gains the free riding benefit by not signing the treary. The pure strategy does not take account of any action motivated by an intuition, a superstitious belief, altruism, an expectation that the opponent may cooperate, and an anticipation without logics. All groups select their choice completely based on the benefit coming from the rational and logical but selfish interest if it were the pure strategy. Therefore, in the pure strategy, both groups take the possibility that the Pro-Europeanists would not sign the treaty while the Euro-Sceptics would sign the treary (This is a very odd case which would not happen in the real world) into their consideration. So, that is why the Ms. Merkel's wanting outcomes are the least likely in the pure strategy. This is the reason why it would be the case, even in the real world situation, that both would not sign up the treaty even though both groups could maximise the utility if both sign up the treaty if it were based on the pure strategy.
By contrast, the last resolution on the treaty was based on the mixed strategy. Even some Euro-Sceptic leaning nations took account of the possible benefit for themselves coming from signing the treaty by knowing almost 100% of the Pro-Europeanist leaning nations would sign the treaty. In the real world, especially in such a big scale rather than two prisoners in a separated shuttered cell, there are always cheap talks, a flexible flow of information exchange, and irrationality caused by human-emotion and belief in something superstitious, and/or anticipated outcomes rather than the outcomes derived from logical analyses. Thus, everyone knew that all the Pro-European leaning nations were more likely to sign the treaty, and the Euro-Sceptics leaning nations would not make the loss by any choice they could select. This is why Ms. Merkel really wanted all the EU nations signed the treaty.
The matrix of the outcomes in the mixed strategy is as follows:
The outcome of the last resolution could avoid the worst case scenario, in which all the Euro-Sceptic leaning nations did not signed the treaty, and either 100% or 25% of the Pro-European leaning nations signed the treaty. If the worst case scenario took place, all the nations who signed the treaty had to suffer, and the rest of the nations who did not sign the treaty could gain the free-riding benefit. This is what Ms. Merkel was afraid of, and Mr. Cameron would have induced if not only the U.K. but also substantial numbers of nations did not sign the treaty.
The outcome was the second best according to what Ms. Merkel said. Majority of the EU member nations (more than 50%) agreed with the treaty so that the outcome became the middle right cell. Although it could not be in the bottom right cell, it did cause neither the decline of the power of the EU economy (The center cell) nor the collapse of the Eurozone (The top left cell: The collapse would be 100% possible in the pure strategy), nor the free riding by the Eurosceptic leaning nations (The top middle cell and the top right cell).
Nonetheless, it was almost falling into the worst case scenario (either the free riding by the Euro-Sceptic leaning nations or the collapse of the European Integration) unless the Pro-Europeanists had given up signing the treaty by knowing all the other nations would not sign the treaty. This is why Mr. Cameron's reaction caused to significantly lose the trust in the U.K. from the EU. At least, Mr. Cameron should have acted not explicitly like what he has done. He should have been wise enough not let any one to know the U.K. has wanted to keep the distance from the fiscal unification. The way Mr. Cameron acted was to make the Pro-Europeanist nations to think the U.K. is quite happy to sacrifice the EU for her own sake. I did not disagree with the Euro-Scepticism at all. But, I just wanted him to know this Game Theory! All political leaders, diplomats, and any those who have to face a big complicated decision making have got to study this Game Theory!!