Abstract
The present paper analyzes possible bridges between two types of graphical models: on the one hand, Bayesian Networks, and on the other hand, Graphs of Deterrence associated with a particular category of qualitative games called matrix Games of Deterrence, in which players do not look for optimal outcomes but for acceptable ones. Three related-types of relations are scrutinized: implications and rebuttals; priors and hidden parts of the graph; probability and playability.
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Notes
- 1.
which does not mean of course that such outcome can always be reached.
- 2.
In such a case, playability, as introduced here, meets Rufus Isaacs’ playability concept according to which in a qualitative differential game, a player’s strategy is playable if it enables the player to reach his/her target, in which case the player under consideration will get an outcome equal to 1, against a 0 if the target is not reached [3].
- 3.
This third condition is a direct implication of the proverb according to which “you have everything to fear from the one who has nothing to lose.”
- 4.
Since a player’s strategy is playable by default if the player under consideration has no positively playable strategy, there is no need to define a playability by default index of a strategy. It is enough to have such index at the player’s level.
- 5.
For instance, a game of type E is a game in which the corresponding graph contains only E-paths, while a game of type R/C is a game which graph contains R paths and C-graphs.
- 6.
In other words, an evidence is considered true if it is rebutted by no other evidence.
- 7.
We shall see that things are different in the case of fuzzy games.
- 8.
and independent from the existing set of propositions.
- 9.
- 10.
This will be the case in general for games of type E, since in these games all strategies of odd rank, except roots, are not playable.
- 11.
This is exactly what playability is about (absence of deterrence).
- 12.
This means that issues pertaining to social climate are not taken into consideration: this simplified case considers only one possible cause of a criminal act.
- 13.
Let us recall that T means the existence of some underground terrorist group.
- 14.
This approach does not contradict the one developed in the example here above.
- 15.
This section focuses on E-type games, but of course similar results and conclusions would hold for R-type games.
- 16.
The same conclusion can be obtained by comparing the positive playabilities of strategies of even rank, taking in account this time the fact that such positive playabilities are increasing with the rank [10].
- 17.
The justification of such assumption will be discussed in the next section.
- 18.
In other words if p = 1, then v = J(T).
- 19.
This of course might not be the case with another type of graph.
- 20.
No social climate being taken into account.
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Acknowledgements
The present paper is based on the work developed within the European FP7 research project Law Enforcement and Intelligence Learning Applications (LEILA). LEILA aims at developing serious games enabling to improve the skills and competencies of intelligence analysts, in particular through getting the ability to generate and interpret inference schemes associated with Graphs of Deterrence.
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Rudnianski, M., Sadana, U., Bestougeff, H. (2016). Bayesian Networks and Games of Deterrence. In: Petrosyan, L., Mazalov, V. (eds) Recent Advances in Game Theory and Applications. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-43838-2_11
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