This paper defines the extensive-form correlated equilibrium (EFCE) for extensive games with perfect recall. The EFCE concept extends Aumann's strategic-form correlated equilibrium (CE). Before the game starts, a correlation device generates a move for each information set. This move is recommended to the player only when the player reaches the information set. In two-player perfect-recall extensive games without chance moves, the set of EFCE can be described by a polynomial number of consistency and incentive constraints. Assuming P is not equal to NP, this is not possible for the set of CE, or if the game has chance moves.Key words: correlated equilibrium; extensive game; polynomial-time computable MSC2000 subject classification: Primary: 91A18; secondary: 91A05, 91A28, 68Q17 OR/MS subject classification: Primary: noncooperative games; secondary: computational complexity History: Received March 22, 2006; revised September 19, 2007, and March 20, 2008. 1. Introduction. Aumann [1] defined the concept of correlated equilibrium (abbreviated as CE, also for the plural equilibria) for games in strategic form. Before the game starts, a device selects private signals from a joint probability distribution and sends them to the players. In the canonical representation of a CE, these signals are strategies that players are recommended to play. This paper proposes a new concept of correlated equilibrium for extensive games, called extensive-form correlated equilibrium or EFCE. Like in a CE (which is defined in terms of the strategic form), the recommendations to the players are moves that are generated before the game starts. However, each recommended move is assumed to be in a "sealed envelope" and is only revealed to a player when he reaches the information set where he can make that move.As recommendations become local in this way, players know less. Consequently, the set of EFCE outcomes is larger than the set of CE outcomes. However, an EFCE is more restrictive than an agent-form correlated equilibrium (AFCE). In the agent form of the game, moves are chosen by a separate agent for each information set of the player. In an EFCE, players remain in control of their future actions, which is important when they consider deviating from their recommended moves.The EFCE is a natural definition of correlated equilibrium for extensive games with perfect recall as defined by Kuhn [25]. Earlier extensions of Aumann's concept applied only to multistage games, including Bayesian games and stochastic games, which have a special time and information structure. These earlier approaches are discussed in §2.4.The main motivation for the EFCE concept is computational. The algorithmic input is some description of the extensive game with its game tree, information sets, moves, chance probabilities and payoffs. Polynomial (or linear or exponential) size and time always refer to the size of this description. The strategic form of the extensive game has typically exponential size. Hence, there are also exponentially many linear constraint...

Many methods have been proposed to solve the image classification problem for a large number of categories. Among them, methods based on tree-based representations achieve good trade-off between accuracy and test time efficiency. While focusing on learning a tree-shaped hierarchy and the corresponding set of classifiers, most of them [11,2,14] use a greedy prediction algorithm for test time efficiency. We argue that the dramatic decrease in accuracy at high efficiency is caused by the specific design choice of the learning and greedy prediction algorithms. In this work, we propose a classifier which achieves a better trade-off between efficiency and accuracy with a given tree-shaped hierarchy. First, we convert the classification problem as finding the best path in the hierarchy, and a novel branchand-bound-like algorithm is introduced to efficiently search for the best path. Second, we jointly train the classifiers using a novel Structured SVM (SSVM) formulation with additional bound constraints. As a result, our method achieves a significant 4.65%, 5.43%, and 4.07% (relative 24.82%, 41.64%, and 109.79%) improvement in accuracy at high efficiency compared to state-of-the-art greedy "tree-based" methods [14] on , SUN [32] and ImageNet 1K [9] dataset, respectively. Finally, we show that our branch-and-bound-like algorithm naturally ranks the paths in the hierarchy (Fig. 8) so that users can further process them.

Dynamic Difficulty Adjustment (DDA) of Game AI aims at creating a satisfactory game experience by dynamically adjusting intelligence of game opponents. It can provide a level of challenge that is tailored to the player's personal ability. The Monte-Carlo Tree Search (MCTS) algorithm can be applied to generate intelligence of non-player characters (NPCs) in video games. And the performance of the NPCs controlled by MCTS can be adjusted by modulating the simulation time of MCTS.Hence the approach of DDA based on MCTS is proposed based on the application of MCTS. In this paper, the prey and predator game genre of Pac-Man is used as a test-bed, the process of creating DDA based on MCTS is demonstrated and the feasibility of this approach is validated. Furthermore, to increase the computational efficiency, an alternative approach of creating DDA based on knowledge from MCTS is also proposed and discussed.

No abstract

Perfluorooctanoic acid (PFOA) electrochemical elimination systems usually focus on anodic processes, while the cathodic reactions are generally neglected. In this study, an anodic oxidation system aided by cathodically produced bubbles was proposed for enhanced PFOA oxidation, by simply rotating the electrode orientation by 90°with the cathode at the bottom and the anode at the top (abbreviated as AO/ Rotation). In the AO/Rotation system, hydrogen bubbles that were inevitably generated at the cathode could concentrate PFOA and bring it to the anode for further oxidation; thus, PFOA removal increased by 50% at 4.5 V/standard hydrogen electrode. The first-order rate also increased from 2.7 × 10 −2 h −1 cm −2 for anode oxidation alone to 3.8 × 10 −2 h −1 cm −2 for AO/Rotation. N 2 sparging promoted the defluorination rate from 31% to 100% (100 mL/min) at 3 h, further proving the dominant contribution of bubble enrichment. The aerosol release is negligible in this system according to fluoride mass balance. Energy consumption of this new system was only 7 kWh•m −3 •log −1 , half of that in the direct AO process. These results demonstrate that cathodically produced bubbles for improved mass transfer should be well-utilized during the reactor design for energy-efficient PFOA removal.