Robust Stackelberg Equilibria in Extensive-Form Games and Extension to Limited Lookahead

Stackelberg equilibria have become increasingly important as a solution concept in computational game theory, largely inspired by practical problems such as security settings. In practice, however, there is typically uncertainty regarding the model about the opponent. This paper is, to our knowledge, the first to investigate Stackelberg equilibria under uncertainty in extensive-form games, one of the broadest classes of game. We introduce robust Stackelberg equilibria, where the uncertainty is about the opponent's payoffs, as well as ones where the opponent has limited lookahead and the uncertainty is about the opponent's node evaluation function. We develop a new mixed-integer program for the deterministic limited-lookahead setting. We then extend the program to the robust setting for Stackelberg equilibrium under unlimited and under limited lookahead by the opponent. We show that for the specific case of interval uncertainty about the opponent's payoffs (or about the opponent's node evaluations in the case of limited lookahead), robust Stackelberg equilibria can be computed with a mixed-integer program that is of the same asymptotic size as that for the deterministic setting.Comment: Published at AAAI1

The curse of ties in congestion games with limited lookahead

We introduce a novel framework to model limited lookahead in congestion games. Intuitively, the players enter the game sequentially and choose an optimal action under the assumption that the k - 1 subsequent players play subgame-perfectly. Our model naturally interpolates between outcomes of greedy best-response (k = 1) and subgame-perfect outcomes (k = n, the number of players). We study the impact of limited lookahead (parameterized by k) on the stability and inefficiency of the resulting outcomes. As our results reveal, increased lookahead does not necessarily lead to better outcomes; in fact, its effect crucially depends on the existence of ties and the type of game under consideration

Analysis and Optimization of Deep Counterfactual Value Networks

Recently a strong poker-playing algorithm called DeepStack was published, which is able to find an approximate Nash equilibrium during gameplay by using heuristic values of future states predicted by deep neural networks. This paper analyzes new ways of encoding the inputs and outputs of DeepStack's deep counterfactual value networks based on traditional abstraction techniques, as well as an unabstracted encoding, which was able to increase the network's accuracy.Comment: Long version of publication appearing at KI 2018: The 41st German Conference on Artificial Intelligence (http://dx.doi.org/10.1007/978-3-030-00111-7_26). Corrected typo in titl

A Decision-Making Framework for Control Strategies in Probabilistic Search

This paper presents the search problem formulated as a decision problem, where the searcher decides whether the target is present in the search region, and if so, where it is located. Such decision-based search tasks are relevant to many research areas, including mobile robot missions, visual search and attention, and event detection in sensor networks. The effect of control strategies in search problems on decision-making quantities, namely time-to-decision, is investigated in this work. We present a Bayesian framework in which the objective is to improve the decision, rather than the sensing, using different control policies. Furthermore, derivations of closed-form expressions governing the evolution of the belief function are also presented. As this framework enables the study and comparison of the role of control for decision-making applications, the derived theoretical results provide greater insight into the sequential processing of decisions. Numerical studies are presented to verify and demonstrate these results