Computational Results for Extensive-Form Adversarial Team Games

We provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary. We define three different scenarios according to the communication capabilities of the team. In the first, the teammates can communicate and correlate their actions both before and during the play. In the second, they can only communicate before the play. In the third, no communication is possible at all. We define the most suitable solution concepts, and we study the inefficiency caused by partial or null communication, showing that the inefficiency can be arbitrarily large in the size of the game tree. Furthermore, we study the computational complexity of the equilibrium-finding problem in the three scenarios mentioned above, and we provide, for each of the three scenarios, an exact algorithm. Finally, we empirically evaluate the scalability of the algorithms in random games and the inefficiency caused by partial or null communication

Ad auctions and cascade model: GSP inefficiency and algorithms

The design of the best economic mechanism for Sponsored Search Auctions (SSAs) is a central task in computational mechanism design/game theory. Two open questions concern the adoption of user models more accurate than that one currently used and the choice between Generalized Second Price auction (GSP) and Vickrey-Clark-Groves mechanism (VCG). In this paper, we provide some contributions to answer these questions. We study Price of Anarchy (PoA) and Price of Stability (PoS) over social welfare and auctioneer's revenue of GSP w.r.t. the VCG when the users follow the famous cascade model. Furthermore, we provide exact, randomized, and approximate algorithms, showing that in real-world settings (Yahoo! Webscope A3 dataset, 10 available slots) optimal allocations can be found in less than 1s with up to 1000 ads, and can be approximated in less than 20ms even with more than 1000 ads with an average accuracy greater than 99%.Comment: AAAI16, to appea

Extensive-Form Perfect Equilibrium Computation in Two-Player Games

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 the players at each decision node). The scientific challenge is intrinsic to the EFPE definition: it requires a perturbation over the agent form, but the agent form is computationally inefficient, due to the presence of highly nonlinear constraints. We show that the sequence form can be exploited in a non-trivial way and that, for general-sum games, finding an EFPE is equivalent to solving a suitably perturbed linear complementarity problem. We prove that Lemke's algorithm can be applied, showing that computing an EFPE is $\textsf{PPAD}$-complete. In the notable case of zero-sum games, the problem is in $\textsf{FP}$ and can be solved by linear programming. Our algorithms also allow one to find a Nash equilibrium when players cannot perfectly control their moves, being subject to a given execution uncertainty, as is the case in most realistic physical settings.Comment: To appear in AAAI 1

A Game Theoretical Analysis of Localization Security in Wireless Sensor Networks with Adversaries

Wireless Sensor Networks (WSN) support data collection and distributed data processing by means of very small sensing devices that are easy to tamper and cloning: therefore classical security solutions based on access control and strong authentication are difficult to deploy. In this paper we look at the problem of assessing security of node localization. In particular, we analyze the scenario in which Verifiable Multilateration (VM) is used to localize nodes and a malicious node (i.e., the adversary) try to masquerade as non-malicious. We resort to non-cooperative game theory and we model this scenario as a two-player game. We analyze the optimal players' strategy and we show that the VM is indeed a proper mechanism to reduce fake positions.Comment: International Congress on Ultra Modern Telecommunications and Control Systems 2010. (ICUMT'10