4 research outputs found
Coverage and Vacuity in Network Formation Games
The frameworks of coverage and vacuity in formal verification analyze the effect of mutations applied to systems or their specifications. We adopt these notions to network formation games, analyzing the effect of a change in the cost of a resource. We consider two measures to be affected: the cost of the Social Optimum and extremums of costs of Nash Equilibria. Our results offer a formal framework to the effect of mutations in network formation games and include a complexity analysis of related decision problems. They also tighten the relation between algorithmic game theory and formal verification, suggesting refined definitions of coverage and vacuity for the latter
A Game of Pawns
We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its next location. This leads to a path in the graph, which determines the winner. Traditionally, the control of vertices is predetermined and fixed. The novelty of pawn games is that control of vertices changes dynamically throughout the game as follows. Each vertex of a pawn game is owned by a pawn. In each turn, the pawns are partitioned between the two players, and the player who controls the pawn that owns the vertex on which the token is located, chooses the next location of the token. Control of pawns changes dynamically throughout the game according to a fixed mechanism. Specifically, we define several grabbing-based mechanisms in which control of at most one pawn transfers at the end of each turn. We study the complexity of solving pawn games, where we focus on reachability objectives and parameterize the problem by the mechanism that is being used and by restrictions on pawn ownership of vertices. On the positive side, even though pawn games are exponentially-succinct turn-based games, we identify several natural classes that can be solved in PTIME. On the negative side, we identify several EXPTIME-complete classes, where our hardness proofs are based on a new class of games called Lock & Key games, which may be of independent interest
A Game of Pawns
We introduce and study pawn games, a class of two-player zero-sum turn-based
graph games. A turn-based graph game proceeds by placing a token on an initial
vertex, and whoever controls the vertex on which the token is located, chooses
its next location. This leads to a path in the graph, which determines the
winner. Traditionally, the control of vertices is predetermined and fixed. The
novelty of pawn games is that control of vertices changes dynamically
throughout the game as follows. Each vertex of a pawn game is owned by a pawn.
In each turn, the pawns are partitioned between the two players, and the player
who controls the pawn that owns the vertex on which the token is located,
chooses the next location of the token. Control of pawns changes dynamically
throughout the game according to a fixed mechanism. Specifically, we define
several grabbing-based mechanisms in which control of at most one pawn
transfers at the end of each turn. We study the complexity of solving pawn
games, where we focus on reachability objectives and parameterize the problem
by the mechanism that is being used and by restrictions on pawn ownership of
vertices. On the positive side, even though pawn games are
exponentially-succinct turn-based games, we identify several natural classes
that can be solved in PTIME. On the negative side, we identify several
EXPTIME-complete classes, where our hardness proofs are based on a new class of
games called Lock & Key games, which may be of independent interest.Comment: Full version of CONCUR 2023 pape
Responsibility and verification: Importance value in temporal logics
We aim at measuring the influence of the nondeterministic choices of a part
of a system on its ability to satisfy a specification. For this purpose, we
apply the concept of Shapley values to verification as a means to evaluate how
important a part of a system is. The importance of a component is measured by
giving its control to an adversary, alone or along with other components, and
testing whether the system can still fulfill the specification. We study this
idea in the framework of model-checking with various classical types of
linear-time specification, and propose several ways to transpose it to
branching ones. We also provide tight complexity bounds in almost every case.Comment: 22 pages, 12 figure