An Approximate Subgame-Perfect Equilibrium Computation Technique for Repeated Games

This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in discounted repeated games. The process starts with a single hypercube approximation of the set of SPE. Then the initial hypercube is gradually partitioned on to a set of smaller adjacent hypercubes, while those hypercubes that cannot contain any point belonging to the set of SPE are simultaneously withdrawn. Whether a given hypercube can contain an equilibrium point is verified by an appropriate mathematical program. Three different formulations of the algorithm for both approximately computing the set of SPE payoffs and extracting players' strategies are then proposed: the first two that do not assume the presence of an external coordination between players, and the third one that assumes a certain level of coordination during game play for convexifying the set of continuation payoffs after any repeated game history. A special attention is paid to the question of extracting players' strategies and their representability in form of finite automata, an important feature for artificial agent systems.Comment: 26 pages, 13 figures, 1 tabl

Hypergame Analysis in E-Commerce: A Preliminary Report

In usual game theory, it is normally assumed that "all the players see the same game", i.e., they are aware of each other's strategies and preferences. This assumption is very strong for real life where differences in perception affecting the decision making process seem to be the rule rather the exception. Attempts have been made to incorporate misperceptions of various types, but most of these attempts are based on quantities (as probabilities, risk factors, etc.) which are too subjective in general. One approach that seems to be very attractive is to consider that the players are trying to play "different games" in a hypergame. In this paper, we present a hypergame approach as an analysis tool in the context of multiagent environments. Precisely, we first sketch a brief formal introduction to hypergames. Then we explain how agents can interact through communication or through a mediator when they have different views and particularly misperceptions on others' games. After that, we show how agents can take advantage of misperceptions. Finally, we conclude and present some future work. Dans les jeux classiques, il est supposé que "tous les joueurs voient le même jeu'', i.e., que les joueurs sont au courant des stratégies et des préférences des uns et des autres. Aux vu des applications réelles, cette supposition est très forte dans la mesure où les différences de perception affectant la prise de décision semblent plus relevées de la règle que de l'exception. Des tentatives ont été faites, par le passé, pour incorporer les distorsions aux niveaux des perceptions, mais la plupart de ces tentatives ont été essentiellement basées sur le "quantitatif" (comme les probabilités, les facteurs de risques, etc.) et par conséquent, trop subjectives en général. Une approche qui semble être attractive pour pallier à cela, consiste à voir les joueurs comme jouant "différents jeux'' dans une sorte d'hyper-jeu. Dans ce papier, nous présentons une approche "hyper-jeu'' comme outil d'analyse entre agents dans le cadre d'un environnement multi-agent. Nous donnons un aperçu (très succinct) de la formalisation d'un tel hyper-jeux et nous expliquerons ensuite, comment les agents pourraient intervenir via un agent-médiateur quand ils ont des perceptions différentes. Après cela, nous expliquerons comment les agents pourraient tirer avantage des perceptions différentes.Game Theory, Hypergame, Mediation, Théorie des jeux, hyper-jeux, médiation

Generative Adversarial Positive-Unlabelled Learning

In this work, we consider the task of classifying binary positive-unlabeled (PU) data. The existing discriminative learning based PU models attempt to seek an optimal reweighting strategy for U data, so that a decent decision boundary can be found. However, given limited P data, the conventional PU models tend to suffer from overfitting when adapted to very flexible deep neural networks. In contrast, we are the first to innovate a totally new paradigm to attack the binary PU task, from perspective of generative learning by leveraging the powerful generative adversarial networks (GAN). Our generative positive-unlabeled (GenPU) framework incorporates an array of discriminators and generators that are endowed with different roles in simultaneously producing positive and negative realistic samples. We provide theoretical analysis to justify that, at equilibrium, GenPU is capable of recovering both positive and negative data distributions. Moreover, we show GenPU is generalizable and closely related to the semi-supervised classification. Given rather limited P data, experiments on both synthetic and real-world dataset demonstrate the effectiveness of our proposed framework. With infinite realistic and diverse sample streams generated from GenPU, a very flexible classifier can then be trained using deep neural networks.Comment: 8 page

Multi-item Auctions for Automatic Negotiation

Available resources can often be limited with regard to the number of demands. In this paper we propose an approach for solving this problem which consists of using the mechanisms of multi-item auctions for allocating the resources to a set of software agents. We consider the resource problem as a market in which there are vendor agents and buyer agents trading on items representing the resources. These agents use multi-item auctions which are viewed here as a process of automatic negotiation, and implemented as a network of intelligent software agents. In this negotiation, agents exhibit different acquisition capabilities which let them act differently depending on the current context or situation of the market. For example, the "richer" an agent is, the more items it can buy, i.e. the more resources it can acquire. We present a model for this approach based on the English auction, then we discuss experimental evidence of such a model. Dans un environnement multiagent, les ressources peuvent toujours s'avérer insuffisantes relativement à un nombre élevé de demandes. Dans ce cahier, nous proposons une approche mixant les enchères et les agents logiciels en vue de contribuer à résoudre ce problème. Cette approche consiste en fait à utiliser le mécanisme d'enchères multi-articles en vue d'allouer les ressources à un ensemble d'agents. À cet effet, nous considérons le problème de ressources comme un marché dans lequel évoluent des agents acheteurs et des agents vendeurs négociant des articles représentant des ressources. Ces agents utilisent des enchères multi-articles et par conséquent ils constituent un processus de négociation automatisé et programmé comme un réseau d'agents logiciels. Dans ce type de négociation, chaque agent exhibe différentes capacités d'acquisition lui permettant ainsi d'agir différemment selon le contexte ou la situation de marché. Par exemple, plus on est riche, plus on peut acheter d'articles. Nous présentons pour ce modèle une enchère anglaise et nous discuterons ses résultats expérimentaux.Multi-agent systems, Negotiations, Multi-item auctions, Systèmes multiagents, négociations, enchères multi items

GIS analysis of the pre and post-diversion water balances in Owens Valley, California

Owens Valley, California is located at the western border of both the Basin and Range and Great Basin Provinces. The valley is hydrologically closed; the only outflow for ground and surface waters is evaporation to the atmosphere. Los Angeles Department of Water and Power (LADWP) began diverting water from Owens Valley in 1913 and has steadily increased the amount of water removed from the valley since then; LADWP has always assumed that the hydrologic system as it existed in 1913 was in equilibrium with modern climate. This study develops a geographical information systems (GIS) based model of Owens Valley to (1) estimate post-diversion mountain block recharge for southern Owens Valley to test the assumption of equilibrium between recharge and observed playa discharge, and (2) estimate equilibrium extent of pre-diversion Owens Lake based on modern climate. Results demonstrate that water managers may be overestimating mountain block recharge to the modern playa by 50% and that pre-diversion Owens Lake was not in hydrologic equilibrium with modern climate and was likely still shrinking due to late Holocene warming

Planning in Decentralized POMDPs with Predictive Policy Representations

We discuss the problem of policy representation in stochastic and partially observable systems, and address the case where the policy is a hidden parameter of the planning problem. We propose an adaptation of the Predictive State Representations (PSRs) to this problem by introducing tests (sequences of actions and observations) on policies. The new model, called the Predictive Policy Representations (PPRs), is potentially more compact than the other representations, such as decision trees or Finite-State Controllers (FSCs). In this paper, we show how PPRs can be used to improve the performances of a point-based algorithm for DEC-POMDP