Games on graphs with a public signal monitoring

We study pure Nash equilibria in games on graphs with an imperfect monitoring based on a public signal. In such games, deviations and players responsible for those deviations can be hard to detect and track. We propose a generic epistemic game abstraction, which conveniently allows to represent the knowledge of the players about these deviations, and give a characterization of Nash equilibria in terms of winning strategies in the abstraction. We then use the abstraction to develop algorithms for some payoff functions.Comment: 28 page

On Relevant Equilibria in Reachability Games

We study multiplayer reachability games played on a finite directed graph equipped with target sets, one for each player. In those reachability games, it is known that there always exists a Nash equilibrium (NE) and a subgame perfect equilibrium (SPE). But sometimes several equilibria may coexist such that in one equilibrium no player reaches his target set whereas in another one several players reach it. It is thus very natural to identify "relevant" equilibria. In this paper, we consider different notions of relevant equilibria including Pareto optimal equilibria and equilibria with high social welfare. We provide complexity results for various related decision problems

The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games

We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game G, does there exist a pure-strategy Nash equilibrium of G where player 0 wins with probability 1. Moreover, this problem remains undecidable if it is restricted to strategies with (unbounded) finite memory. However, if mixed strategies are allowed, decidability remains an open problem. One way to obtain a provably decidable variant of the problem is restricting the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively.Comment: 23 pages; revised versio

Computer aided synthesis: a game theoretic approach

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 games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

Parametric LTL on Markov Chains

This paper is concerned with the verification of finite Markov chains against parametrized LTL (pLTL) formulas. In pLTL, the until-modality is equipped with a bound that contains variables; e.g., $\Diamond_{\le x}\ \varphi$ asserts that $\varphi$ holds within $x$ time steps, where $x$ is a variable on natural numbers. The central problem studied in this paper is to determine the set of parameter valuations $V_{\prec p} (\varphi)$ for which the probability to satisfy pLTL-formula $\varphi$ in a Markov chain meets a given threshold $\prec p$, where $\prec$ is a comparison on reals and $p$ a probability. As for pLTL determining the emptiness of $V_{> 0}(\varphi)$ is undecidable, we consider several logic fragments. We consider parametric reachability properties, a sub-logic of pLTL restricted to next and $\Diamond_{\le x}$, parametric B\"uchi properties and finally, a maximal subclass of pLTL for which emptiness of $V_{> 0}(\varphi)$ is decidable.Comment: TCS Track B 201

Day-ahead allocation of operation reserve in composite power systems with large-scale centralized wind farms

This paper focuses on the day-ahead allocation of operation reserve considering wind power prediction error and network transmission constraints in a composite power system. A two-level model that solves the allocation problem is presented. The upper model allocates operation reserve among subsystems from the economic point of view. In the upper model, transmission constraints of tielines are formulated to represent limited reserve support from the neighboring system due to wind power fluctuation. The lower model evaluates the system on the reserve schedule from the reliability point of view. In the lower model, the reliability evaluation of composite power system is performed by using Monte Carlo simulation in a multi-area system. Wind power prediction errors and tieline constraints are incorporated. The reserve requirements in the upper model are iteratively adjusted by the resulting reliability indices from the lower model. Thus, the reserve allocation is gradually optimized until the system achieves the balance between reliability and economy. A modified two-area reliability test system (RTS) is analyzed to demonstrate the validity of the method.This work was supported by National Natural Science Foundation of China (No. 51277141) and National High Technology Research and Development Program of China (863 Program) (No. 2011AA05A103)

Percentile Queries in Multi-Dimensional Markov Decision Processes

Markov decision processes (MDPs) with multi-dimensional weights are useful to analyze systems with multiple objectives that may be conflicting and require the analysis of trade-offs. We study the complexity of percentile queries in such MDPs and give algorithms to synthesize strategies that enforce such constraints. Given a multi-dimensional weighted MDP and a quantitative payoff function $f$, thresholds $v_i$ (one per dimension), and probability thresholds $\alpha_i$, we show how to compute a single strategy to enforce that for all dimensions $i$, the probability of outcomes $\rho$ satisfying $f_i(\rho) \geq v_i$ is at least $\alpha_i$. We consider classical quantitative payoffs from the literature (sup, inf, lim sup, lim inf, mean-payoff, truncated sum, discounted sum). Our work extends to the quantitative case the multi-objective model checking problem studied by Etessami et al. in unweighted MDPs.Comment: Extended version of CAV 2015 pape

Wind-pv-thermal power aggregator in electricity market

This paper addresses the aggregation of wind, photovoltaic and thermal units with the aim to improve bidding in an electricity market. Market prices, wind and photovoltaic powers are assumed as data given by a set of scenarios. Thermal unit modeling includes start-up costs, variables costs and bounds due to constraints of technical operation, such as: ramp up/down limits and minimum up/down time limits. The modeling is carried out in order to develop a mathematical programming problem based in a stochastic programming approach formulated as a mixed integer linear programming problem. A case study comparison between disaggregated and aggregated bids for the electricity market of the Iberian Peninsula is presented to reveal the advantage of the aggregation

The Complexity of Nash Equilibria in Stochastic Multiplayer Games

We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game G, does there exist a Nash equilibrium of G where Player 0 wins with probability 1? Moreover, this problem remains undecidable when restricted to pure strategies or (pure) strategies with finite memory. One way to obtain a decidable variant of the problem is to restrict the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively. Finally, we single out a special case of the general problem that, in many cases, admits an efficient solution. In particular, we prove that deciding the existence of an equilibrium in which each player either wins or loses with probability 1 can be done in polynomial time for games where the objective of each player is given by a parity condition with a bounded number of priorities