This paper focuses on the optimal allocation of multi-stage attacks with uncertainty in attacker’s intention. We model attack planning problem using a Markov decision process and characterize intention finite set reward functions–each represents type attacker. Based this modeling, we employ paradigm worst-case absolute regret minimization from robust game theory develop mixed-integer linear pro...

We study continuity properties of stochastic game problems with respect to various topologies on information structures, defined as probability measures characterizing a game. will establish the value function under total variation, setwise, and weak convergence structures. Our analysis reveals that for bounded is continuous variation structures in both zero-sum games team problems. Continuity ...

We introduce generous, even-matched, and greedy strategies as concepts for analyzing games. A two person prisoner's dilemma game is described by the four outcomes (C,D), (C,C), (D,C), and (D,D). In a generous strategy the proportion of (C,D) is larger than that of (D,C), i.e. the probability of facing a defecting agent is larger than the probability of defecting. An even-matched strategy has th...

An inspection game is here a non-cooperative two-person-game between an inspector and an inspectee. It models a situation where the inspector controls the inspectee who has an incentive to violate certain legal obligations. A recent survey of inspection games applied to data verification, for example in nuclear material safeguards, is given in [1]. Dresher [2] described a sequential inspection ...

In 1967 Aumann and Maschler presented their celebrated model for games with incomplete information, see [1] and references therein. The game they consider consists in a set of, say I, standard discrete time two person zero-sum games. At the beginning one of these zero-sum games is picked at random according to a probability p. The information which game was picked is transmitted to Player 1 onl...

Formalization of a 2 Person Zero-Sum Game 1. There are two players, P1 and P2. 2. P1 has a set A = {a1, a2, . . . , am} of m pure strategies (or actions). 3. P2 has a set B = {b1, b2, . . . , bn} of n pure strategies (or actions). 4. Each player has a utility for each (ai, bj) pair of actions. The utility for P1 is denoted U1(ai, bj) and the utility for P2 is denoted U2(ai, bj). Since this is a...

We study a robust optimal stopping problem with respect to a set P of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from P . We show that the upper Snell envelope Z of the reward process Y is a supermarti...

1 Summary We discuss strategies in non-zero sum games of perfect information on graphs. The study of non-zero sum games on graphs is motivated by the advent of computational tasks on the worldwide web and related security requirements which have thrown up many interesting areas of interaction between game theory and computer science. For example, signing contracts on the web requires interactio...