16 research outputs found
Multi-Layer Cyber-Physical Security and Resilience for Smart Grid
The smart grid is a large-scale complex system that integrates communication
technologies with the physical layer operation of the energy systems. Security
and resilience mechanisms by design are important to provide guarantee
operations for the system. This chapter provides a layered perspective of the
smart grid security and discusses game and decision theory as a tool to model
the interactions among system components and the interaction between attackers
and the system. We discuss game-theoretic applications and challenges in the
design of cross-layer robust and resilient controller, secure network routing
protocol at the data communication and networking layers, and the challenges of
the information security at the management layer of the grid. The chapter will
discuss the future directions of using game-theoretic tools in addressing
multi-layer security issues in the smart grid.Comment: 16 page
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
Determinacy in Discrete-Bidding Infinite-Duration Games
In two-player games on graphs, the players move a token through a graph to
produce an infinite path, which determines the winner of the game. Such games
are central in formal methods since they model the interaction between a
non-terminating system and its environment. In bidding games the players bid
for the right to move the token: in each round, the players simultaneously
submit bids, and the higher bidder moves the token and pays the other player.
Bidding games are known to have a clean and elegant mathematical structure that
relies on the ability of the players to submit arbitrarily small bids. Many
applications, however, require a fixed granularity for the bids, which can
represent, for example, the monetary value expressed in cents. We study, for
the first time, the combination of discrete-bidding and infinite-duration
games. Our most important result proves that these games form a large
determined subclass of concurrent games, where determinacy is the strong
property that there always exists exactly one player who can guarantee winning
the game. In particular, we show that, in contrast to non-discrete bidding
games, the mechanism with which tied bids are resolved plays an important role
in discrete-bidding games. We study several natural tie-breaking mechanisms and
show that, while some do not admit determinacy, most natural mechanisms imply
determinacy for every pair of initial budgets
Infinite-Duration Bidding Games
Two-player games on graphs are widely studied in formal methods as they model
the interaction between a system and its environment. The game is played by
moving a token throughout a graph to produce an infinite path. There are
several common modes to determine how the players move the token through the
graph; e.g., in turn-based games the players alternate turns in moving the
token. We study the {\em bidding} mode of moving the token, which, to the best
of our knowledge, has never been studied in infinite-duration games. The
following bidding rule was previously defined and called Richman bidding. Both
players have separate {\em budgets}, which sum up to . In each turn, a
bidding takes place: Both players submit bids simultaneously, where a bid is
legal if it does not exceed the available budget, and the higher bidder pays
his bid to the other player and moves the token. The central question studied
in bidding games is a necessary and sufficient initial budget for winning the
game: a {\em threshold} budget in a vertex is a value such that
if Player 's budget exceeds , he can win the game, and if Player 's
budget exceeds , he can win the game. Threshold budgets were previously
shown to exist in every vertex of a reachability game, which have an
interesting connection with {\em random-turn} games -- a sub-class of simple
stochastic games in which the player who moves is chosen randomly. We show the
existence of threshold budgets for a qualitative class of infinite-duration
games, namely parity games, and a quantitative class, namely mean-payoff games.
The key component of the proof is a quantitative solution to strongly-connected
mean-payoff bidding games in which we extend the connection with random-turn
games to these games, and construct explicit optimal strategies for both
players.Comment: A short version appeared in CONCUR 2017. The paper is accepted to
JAC
Determinacy in Discrete-Bidding Infinite-Duration Games
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a non-terminating system and its environment. In bidding games the players bid for the right to move the token: in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. Bidding games are known to have a clean and elegant mathematical structure that relies on the ability of the players to submit arbitrarily small bids. Many applications, however, require a fixed granularity for the bids, which can represent, for example, the monetary value expressed in cents. We study, for the first time, the combination of discrete-bidding and infinite-duration games. Our most important result proves that these games form a large determined subclass of concurrent games, where determinacy is the strong property that there always exists exactly one player who can guarantee winning the game. In particular, we show that, in contrast to non-discrete bidding games, the mechanism with which tied bids are resolved plays an important role in discrete-bidding games. We study several natural tie-breaking mechanisms and show that, while some do not admit determinacy, most natural mechanisms imply determinacy for every pair of initial budgets
LIPIcs
Network games are widely used as a model for selfish resource-allocation problems. In the classicalmodel, each player selects a path connecting her source and target vertices. The cost of traversingan edge depends on theload; namely, number of players that traverse it. Thus, it abstracts the factthat different users may use a resource at different times and for different durations, which playsan important role in determining the costs of the users in reality. For example, when transmittingpackets in a communication network, routing traffic in a road network, or processing a task in aproduction system, actual sharing and congestion of resources crucially depends on time.In [13], we introducedtimed network games, which add a time component to network games.Each vertexvin the network is associated with a cost function, mapping the load onvto theprice that a player pays for staying invfor one time unit with this load. Each edge in thenetwork is guarded by the time intervals in which it can be traversed, which forces the players tospend time in the vertices. In this work we significantly extend the way time can be referred toin timed network games. In the model we study, the network is equipped withclocks, and, as intimed automata, edges are guarded by constraints on the values of the clocks, and their traversalmay involve a reset of some clocks. We argue that the stronger model captures many realisticnetworks. The addition of clocks breaks the techniques we developed in [13] and we developnew techniques in order to show that positive results on classic network games carry over to thestronger timed setting
LIPIcs
Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common modes to determine how the players move the token through the graph; e.g., in turn-based games the players alternate turns in moving the token. We study the bidding mode of moving the token, which, to the best of our knowledge, has never been studied in infinite-duration games. Both players have separate budgets, which sum up to . In each turn, a bidding takes place. Both players submit bids simultaneously, and a bid is legal if it does not exceed the available budget. The winner of the bidding pays his bid to the other player and moves the token. For reachability objectives, repeated bidding games have been studied and are called Richman games. There, a central question is the existence and computation of threshold budgets; namely, a value t\in [0,1] such that if\PO's budget exceeds , he can win the game, and if\PT's budget exceeds 1-t, he can win the game. We focus on parity games and mean-payoff games. We show the existence of threshold budgets in these games, and reduce the problem of finding them to Richman games. We also determine the strategy-complexity of an optimal strategy. Our most interesting result shows that memoryless strategies suffice for mean-payoff bidding games
LIPIcs
Network games are widely used as a model for selfish resource-allocation problems. In the classicalmodel, each player selects a path connecting her source and target vertices. The cost of traversingan edge depends on theload; namely, number of players that traverse it. Thus, it abstracts the factthat different users may use a resource at different times and for different durations, which playsan important role in determining the costs of the users in reality. For example, when transmittingpackets in a communication network, routing traffic in a road network, or processing a task in aproduction system, actual sharing and congestion of resources crucially depends on time.In [13], we introducedtimed network games, which add a time component to network games.Each vertexvin the network is associated with a cost function, mapping the load onvto theprice that a player pays for staying invfor one time unit with this load. Each edge in thenetwork is guarded by the time intervals in which it can be traversed, which forces the players tospend time in the vertices. In this work we significantly extend the way time can be referred toin timed network games. In the model we study, the network is equipped withclocks, and, as intimed automata, edges are guarded by constraints on the values of the clocks, and their traversalmay involve a reset of some clocks. We argue that the stronger model captures many realisticnetworks. The addition of clocks breaks the techniques we developed in [13] and we developnew techniques in order to show that positive results on classic network games carry over to thestronger timed setting
A Network Formation Game for the Emergence of Hierarchies
We propose a novel network formation game that explains the emergence of
various hierarchical structures in groups where self-interested or
utility-maximizing individuals decide to establish or severe relationships of
authority or collaboration among themselves. We consider two settings: we first
consider individuals who do not seek the other party's consent when
establishing a relationship and then individuals who do. For both settings, we
formally relate the emerged hierarchical structures with the novel inclusion of
well-motivated hierarchy promoting terms in the individuals' utility functions.
We first analyze the game via a static analysis and characterize all the
hierarchical structures that can be formed as its solutions. We then consider
the game played dynamically under stochastic interactions among individuals
implementing better-response dynamics and analyze the nature of the converged
networks