Research

Sequential Games with Incomplete Information

Texas hold'em is a typical sequential game with incomplete information. In this game, all players have private information (hold cards), and share public information (community cards). Each player chooses an action (check, call, raise or fold) at every betting round until the game ends. Sequential game with incomplete information is a useful tool in many areas such as security problems, robust design of engineering systems, economy systems, and so on. We focus on providing not only a 'descriptive' solution but also a 'prescriptive' solution. On one hand, we study the philosophy and sufficient statistics to play the game in an optimal way. On the other hand, we also want an efficient computation method to compute the strategies.

Related work

1. Lichun Li, Olivier Massicot, and Cedric Langbort (2018), Sequential public signaling in routing games with feedback information, 2018 IEEE Conference on Decision and Control (CDC).
2. Lichun Li and Cedric Langbort (2018), Iterative Computation of Security Strategies of Matrix Games with Growing Action Set, special issue on Dynamic Games in Cyber Security in the journal of Dynamic Games and Applications.
3. Lichun Li, Cedric Langbort and Jeff Shamma (2018), An LP Approach for Solving Zero-Sum Repeated Bayesian Games, IEEE transaction on Automatic Control (accepted).
4. Lichun Li and Jeff Shamma (2018), Efficient Strategy Computation in Zero-Sum Asymmetric Repeated Games, IEEE transaction on Automatic Control (accepted).
5. Lichun Li and Cedric Langbort (2017), Iterative Computation of Security Strategies in Matrix Games with Growing Action Set, The 2017 conference on Decision and Conference.
6. Lichun Li, Cedric Langbort, and Jeff Shamma (2017), Computing Security Strategies in Finite Horizon Repeated Bayesian Games, 2017 American Control Conference. (invited)
7. Lichun Li, Eric Feron, and Jeff Shamma (2016), Finite Horizon Repeated Asymmetric Games: Both Players' Viewpoints, The 2016 conference on Decision and Control.
8. Lichun Li and Jeff Shamma (2015), Efficient Computation of Discounted Asymmetric Stochastic Games, The 2015 conference on Decision and Control.
9. Lichun Li and Jeff Shamma (2014), LP Formulation of Asymmetric Zero-Sum Stochastic Games, The 2014 conference on Decision and Control.

Fun papers to read

1. M. Bowling, N. Burch, M. Johanson, and O. Tammelin (2015), Heads-up Limit Hold'em Poker Is Solved, Science.

Games in Air Transportation System via CTOP

Aircraft flying through congested airspace usually experiences severe delays, especially during bad weather. The Federal Aviation Administration (FAA) rations capacity to reduce en route delay. This is accomplished using the recently developed Collaborative Trajectory Options Programs (CTOPs) which allow the flight operators to communicate their route preferences through Trajectory Option Set (TOS), and assign each flight the most preferred possible route with the lowest adjusted cost in its TOS. The route assigned to a flight and the associated adjusted cost depend not only its own TOS but also the other influenced flights' TOS's. FAA, therefore, can construct a non-zero sum matrix game to model the route assignment problem in CTOP. The non-zero sum matrix game is, however, not fully available to the airlines, since each airline only has his own adjusted costs. Assuming the other flights' interests are totally against his, one flight treats the original non-zero sum matrix game as an `artificial' zero-sum matrix game, and uses the Nash equilibrium of the `artificial' zero-sum matrix game as its strategy to submit its TOS. This `artificial' Nash equilibrium guarantees the flight its adjusted cost, but may differ a lot from the original Nash equilibrium, which results in huge overall delay in the air transportation system. Our objective is to help FAA to make use of his global information to guide flights towards the `real' Nash equilibrium of the CTOP game.

Related work

1. Lichun Li, JP. Clarke, Eric Feron and Jeff Shamma (2017), Robust Trajectory Option Set Planning in CTOP via Bayesian Game Model, 2017 American Control Conference.

Want to know more about CTOP?

1. Basic Concepts: http://tfmlearning.fly.faa.gov/CTOP%20Field%20Training/res/movie.swf.
2. Trajectory Assignment Algorithm: http://tfmlearning.fly.faa.gov/CTOP_Trajectory_Assignment/res/index.html.
3. CTOP substitution: http://tfmlearning.fly.faa.gov/CTOP_Substitution/res/index.html.

Game based defense against smart jamming in LTE networksLTE networks are vulnerable to control-channel jamming attacks from smart jammers who can “learn” network parameters and “synchronize” themselves with the network even when they are not attached to it. Such a smart jammer can launch very effective denial-of-service (DOS) and loss of service attacks without even hacking the network or its components. Hence, pursuing autonomous techniques to address this potentially devastating problem has become an active research topic. The smarter jammers can be distinguished into two types, cheater aiming at maximize its resources, and Saboteur with the intent of causing highest possible damage. We model the interactions between the network and the jammer as a repeated asymmetric game, and derive a suboptimal defense strategy with guaranteed performance for the network.

Related work

1. Farhan M. Aziz, Lichun Li, Jeff Shamma, and Gordon L. Stuber (2017), LTE Network and Smart Jammer Strategies in Infinite-Horizon Asymmetric Repeated Game, IEEE Transactions on Vehicular Technology (submitted).

Event Triggered State Estimation and Control

Event triggering is an information transmission strategy with which a transmission is triggered by an event. Compared with traditional periodic transmission strategy, event triggering, in simulations and experiments, showed great potential to reduce average communication frequency while still maintaining comparable system performances. My interests cover several aspects of event triggering, including whether event triggering is the optimal transmission rule in stochastic systems, whether there is separation principle in event triggered systems, a sufficient condition to guarantee that event triggered systems is efficiently attentive, and so on.

Related work