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Register a new userComputational Results for Extensive-Form Adversarial Team Games
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Andrea Celli
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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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.
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Securing networked infrastructures is important in the real world. The problem of deploying security resources to protect against an attacker in networked domains can be modeled as Network Security Games (NSGs). Unfortunately, existing approaches, including the deep learning-based approaches, are inefficient to solve large-scale extensive-form NSGs. In this paper, we propose a novel learning paradigm, NSG-NFSP, to solve large-scale extensive-form NSGs based on Neural Fictitious Self-Play (NFSP). Our main contributions include: i) reforming the best response (BR) policy network in NFSP to be a mapping from action-state pair to action-value, to make the calculation of BR possible in NSGs; ii) converting the average policy network of an NFSP agent into a metric-based classifier, helping the agent to assign distributions only on legal actions rather than all actions; iii) enabling NFSP with high-level actions, which can benefit training efficiency and stability in NSGs; and iv) leveraging information contained in graphs of NSGs by learning efficient graph node embeddings. Our algorithm significantly outperforms state-of-the-art algorithms in both scalability and solution quality.
Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding in extensive-form team games remains a significant challenge. While NP-hard in the worst case, there are provably efficient algorithms for certain families of team game. In particular, if the game has common external information, also known as A-loss recall -- informally, actions played by non-team members (i.e., the opposing team or nature) are either unknown to the entire team, or common knowledge within the team -- then polynomial-time algorithms exist (Kaneko and Kline, 1995). In this paper, we devise a completely new algorithm for solving team games. It uses a tree decomposition of the constraint system representing each teams strategy to reduce the number and degree of constraints required for correctness (tightness of the mathematical program). Our algorithm reduces the problem of solving team games to a linear program with at most $NW^{w+O(1)}$ nonzero entries in the constraint matrix, where $N$ is the size of the game tree, $w$ is a parameter that depends on the amount of uncommon external information, and $W$ is the treewidth of the tree decomposition. In public-action games, our program size is bounded by the tighter $tilde O(3^t 2^{t(n-1)}NW)$ for teams of $n$ players with $t$ types each. Since our algorithm describes the polytope of correlated strategies directly, we get equilibrium finding in correlated strategies for free -- instead of, say, having to run a double oracle algorithm. We show via experiments on a standard suite of games that our algorithm achieves state-of-the-art performance on all benchmark game classes except one. We also present, to our knowledge, the first experiments for this setting where more than one team has more than one member.
In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove that when following this optimization, the exploitability of a players strategy converges asymptotically to zero, and hence when both players employ this optimization, the joint policies converge to a Nash equilibrium. Unlike fictitious play (XFP) and counterfactual regret minimization (CFR), our convergence result pertains to the policies being optimized rather than the average policies. Our experiments demonstrate convergence rates comparable to XFP and CFR in four benchmark games in the tabular case. Using function approximation, we find that our algorithm outperforms the tabular version in two of the games, which, to the best of our knowledge, is the first such result in imperfect information games among this class of algorithms.
We focus on adversarial patrolling games on arbitrary graphs, where the Defender can control a mobile resource, the targets are alarmed by an alarm system, and the Attacker can observe the actions of the mobile resource of the Defender and perform different attacks exploiting multiple resources. This scenario can be modeled as a zero-sum extensive-form game in which each player can play multiple times. The game tree is exponentially large both in the size of the graph and in the number of attacking resources. We show that when the number of the Attackers resources is free, the problem of computing the equilibrium path is NP-hard, while when the number of resources is fixed, the equilibrium path can be computed in poly-time. We provide a dynamic-programming algorithm that, given the number of the Attackers resources, computes the equilibrium path requiring poly-time in the size of the graph and exponential time in the number of the resources. Furthermore, since in real-world scenarios it is implausible that the Defender knows the number of attacking resources, we study the robustness of the Defenders strategy when she makes a wrong guess about that number. We show that even the error of just a single resource can lead to an arbitrary inefficiency, when the inefficiency is defined as the ratio of the Defenders utilities obtained with a wrong guess and a correct guess. However, a more suitable definition of inefficiency is given by the difference of the Defenders utilities: this way, we observe that the higher the error in the estimation, the higher the loss for the Defender. Then, we investigate the performance of online algorithms when no information about the Attackers resources is available. Finally, we resort to randomized online algorithms showing that we can obtain a competitive factor that is twice better than the one that can be achieved by any deterministic online algorithm.
Many real-world applications involve teams of agents that have to coordinate their actions to reach a common goal against potential adversaries. This paper focuses on zero-sum games where a team of players faces an opponent, as is the case, for example, in Bridge, collusion in poker, and collusion in bidding. The possibility for the team members to communicate before gameplay---that is, coordinate their strategies ex ante---makes the use of behavioral strategies unsatisfactory. We introduce Soft Team Actor-Critic (STAC) as a solution to the teams coordination problem that does not require any prior domain knowledge. STAC allows team members to effectively exploit ex ante communication via exogenous signals that are shared among the team. STAC reaches near-optimal coordinated strategies both in perfectly observable and partially observable games, where previous deep RL algorithms fail to reach optimal coordinated behaviors.
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