On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games

We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. secure equilibria) are guaranteed to exist in the multiplayer (resp. two-player) case. The existence of secure equilibria in the multiplayer case remained and is still an open problem. In this paper, we focus our study on the concept of subgame perfect equilibrium, a refinement of Nash equilibrium well-suited in the framework of games played on graphs. We also introduce the new concept of subgame perfect secure equilibrium. We prove the existence of subgame perfect equilibria (resp. subgame perfect secure equilibria) in multiplayer (resp. two-player) quantitative reachability games. Moreover, we provide an algorithm deciding the existence of secure equilibria in the multiplayer case.Comment: 32 pages. Full version of the FoSSaCS 2012 proceedings pape

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

Incentive Stackelberg Mean-payoff Games

We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that a strategy profile is a Nash equilibrium if no player can improve his payoff by changing his strategy unilaterally. In the setting of incentive and leader equilibria, there is a distinguished player called the leader who can assign strategies to all other players, referred to as her followers. A strategy profile is a leader strategy profile if no player, except for the leader, can improve his payoff by changing his strategy unilaterally, and a leader equilibrium is a leader strategy profile with a maximal return for the leader. In the proposed case of incentive equilibria, the leader can additionally influence the behaviour of her followers by transferring parts of her payoff to her followers. The ability to incentivise her followers provides the leader with more freedom in selecting strategy profiles, and we show that this can indeed improve the payoff for the leader in such games. The key fundamental result of the paper is the existence of incentive equilibria in mean-payoff games. We further show that the decision problem related to constructing incentive equilibria is NP-complete. On a positive note, we show that, when the number of players is fixed, the complexity of the problem falls in the same class as two-player mean-payoff games. We also present an implementation of the proposed algorithms, and discuss experimental results that demonstrate the feasibility of the analysis of medium sized games.Comment: 15 pages, references, appendix, 5 figure

Jamming Games in the MIMO Wiretap Channel With an Active Eavesdropper

This paper investigates reliable and covert transmission strategies in a multiple-input multiple-output (MIMO) wiretap channel with a transmitter, receiver and an adversarial wiretapper, each equipped with multiple antennas. In a departure from existing work, the wiretapper possesses a novel capability to act either as a passive eavesdropper or as an active jammer, under a half-duplex constraint. The transmitter therefore faces a choice between allocating all of its power for data, or broadcasting artificial interference along with the information signal in an attempt to jam the eavesdropper (assuming its instantaneous channel state is unknown). To examine the resulting trade-offs for the legitimate transmitter and the adversary, we model their interactions as a two-person zero-sum game with the ergodic MIMO secrecy rate as the payoff function. We first examine conditions for the existence of pure-strategy Nash equilibria (NE) and the structure of mixed-strategy NE for the strategic form of the game.We then derive equilibrium strategies for the extensive form of the game where players move sequentially under scenarios of perfect and imperfect information. Finally, numerical simulations are presented to examine the equilibrium outcomes of the various scenarios considered.Comment: 27 pages, 8 figures. To appear, IEEE Transactions on Signal Processin