Abstract. In this paper we use defense trees, an extension of attack trees with countermeasures, to represent attack scenarios and game theory to detect the most promising actions attacker and defender. On one side the attacker wants to break the system (with as little efforts as possible), on the opposite side the defender want to protect it (sustaining the minimum cost). As utility function for the attacker and for the defender we consider economic indexes (like the Return on Investment (ROI) and the Return on Attack (ROA)). We show how our approach can be used to evaluate effectiveness and economic profitability of countermeasures as well as their deterrent effect on attackers, thus providing decision makers with a useful tool for performing better evaluation of IT security investments during the risk management process.

In this paper we consider the classical problem of dividing a land among many agents so that everybody is satisfied with the parcel she receives. In the literature, it is usually assumed that all the agents are endowed with cardinally comparable, additive, and monotone utility functions. In many economic and political situations violations of these assumptions may arise. We show how a family of cardinally comparable utility functions can be obtained starting directly from the agents' preferences, and how a fair division of the land is feasible, without additivity or monotonicity requirements. Moreover, if the land to be divided can be modeled as a finite dimensional simplex, it is possible to obtain envy free (and a fortiori fair) divisions of it into subsimplexes.The main tool is an extension of a representation theorem of Gilboa and Schmeidler [Gilboa, I., Schmeidler, D., 1989, Maxmin expected utility with non-unique prior. J. Math. Econ. 18,[141][142][143][144][145][146][147][148][149][150][151][152][153].

This paper defines models of cooperation among players partitioning a completely divisible good (such as a cake or a piece of land). The novelty of our approach lies in the players' ability to form coalitions before the actual division of the good with the aim to maximize the average utility of the coalition. A social welfare function which takes into account coalitions drives the division. In addition, we derive a cooperative game which measures the performance of each coalition. This game is compared with the game in which players start cooperating only after the good has been portioned and has been allocated among the players. We show that a modified version of the game played before the division outperforms the game played after the division.

For fair-division or cake-cutting problems with value functions which are normalized positive measures (i.e., the values are probability measures) maximin-share and minimax-envy inequalities are derived for both continuous and discrete measures. The tools used include classical and recent basic convexity results, as well as ad hoc constructions. Examples are given to show that the envyminimizing criterion is not Pareto optimal, even if the values are mutually absolutely continuous. In the discrete measure case, sufficient conditions are obtained to guarantee the existence of envy-free partitions.

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