Related papers: Attack--Defense Trees and Two-Player Binary Zero-S…

This paper extends Berge's maximum theorem for possibly noncompact action sets and unbounded cost functions to minimax problems and studies applications of these extensions to two-player zero-sum games with possibly noncompact action sets…

The game of the Towers of Hanoi is generalized to binary trees. First, a straightforward solution of the game is discussed. Second, a shorter solution is presented, which is then shown to be optimal.

We provide a formal definition of depth-limited games together with an accessible and rigorous explanation of the underlying concepts, both of which were previously missing in imperfect-information games. The definition works for an…

We show open games cover extensive form games with both perfect and imperfect information. Doing so forces us to address two current weaknesses in open games: the lack of a notion of player and their agency within open games, and the lack…

We study the two-player safe game of Competitive Diffusion, a game-theoretic model for the diffusion of technologies or influence through a social network. In game theory, safe strategies are mixed strategies with a minimal expected gain…

We study the problem of computing an Extensive-Form Perfect Equilibrium (EFPE) in 2-player games. This equilibrium concept refines the Nash equilibrium requiring resilience w.r.t. a specific vanishing perturbation (representing mistakes of…

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum…

We demonstrate that a ubiquitous feature of network games, bilateral strategic interactions, is equivalent to having player utilities that are additively separable across opponents. We distinguish two formal notions of bilateral strategic…

We prove the almost equivalence of the minimax theorem and the strong duality theorem for a large class of games and conic programs. The previous fundamental results on the equivalence of linear programming and two-player zero-sum games…

In this paper we show how the defense relation among abstract arguments can be used to encode the reasons for accepting arguments. After introducing a novel notion of defenses and defense graphs, we propose a defense semantics together with…

In this paper, we investigate under which conditions normal-form games are (guaranteed to be) strategically equivalent. First, we show for N-player games (N >= 3) that (A) it is NP-hard to decide whether a given strategy is a best response…

With the recent advances in solving large, zero-sum extensive form games, there is a growing interest in the inverse problem of inferring underlying game parameters given only access to agent actions. Although a recent work provides a…

Recently, in [K.R. Apt and S. Simon: Well-founded extensive games with perfect information, TARK21], we studied well-founded games, a natural extension of finite extensive games with perfect information in which all plays are finite. We…

Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…

This letter employs differential game theory to address the defense problem of a circular target area with perception constraints, involving a single defender and a single attacker. The defender is restricted to moving along the perimeter,…

Self-serving, rational agents sometimes cooperate to their mutual benefit. The two-player iterated prisoner's dilemma game is a model for including the emergence of cooperation. It is generally believed that there is no simple ultimatum…

Numerous analysis methods for quantitative attack tree analysis have been proposed. These algorithms compute relevant security metrics, i.e. performance indicators that quantify how good the security of a system is, such as the most likely…

Two player zero sum simultaneous action games are common in video games, financial markets, war, business competition, and many other settings. We first introduce the fundamental concepts of reinforcement learning in two player zero sum…

Attack trees are considered a useful tool for security modelling because they support qualitative as well as quantitative analysis. The quantitative approach is based on values associated to each node in the tree, expressing, for instance,…

Two-player zero-sum repeated games are well understood. Computing the value of such a game is straightforward. Additionally, if the payoffs are dependent on a random state of the game known to one, both, or neither of the players, the…