Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

Cooperation and game theory, free software or the #15m movement: Two examples for universities

Closing talk of the Open Access Week 2011 at the UOC, by Josep Jover. Why do altruistic strategies beat selfish ones in the spheres of both free software and the #15m movement? The #15m movement, like software but unlike tangible goods, cannot be owned. It can be used (by joining it) by an indeterminate number of people without depriving anyone else of the chance to do the same. And that turns everything on its head: how universities manage information and what their mission is in this new society. In the immediate future, universities will be valued not for the information they harbour, which will always be richer and more extensive beyond their walls, but rather for their capacity to create critical masses, whether of knowledge research, skill-building, or networks of peers... universities must implement the new model or risk becoming obsolete.

Game Theory and Addiction

A brief one lecture introduction to Game Theory and Addiction techniques for building a games.

On social networks and game theory, some research problems

Seminar given as part of social networking course, to give a brief overview of some applied examples game theory used in social network simulation

Game Theory

The 2013 Version of the Game Theory Presentation, now with an extra game.

Using bargaining-game theory for negotiating concession period for BOT-type contract

This paper extends the build-operate-transfer (BOT) concession model (BOTCcM) to a new method for identifying a concession period by using bargaining-game theory. Concession period is one of the most important decision variables in arranging a BOT-type contract, and there are few methodologies available for helping to determine the value of this variable. The BOTCcM presents an alternative method by which a group of concession period solutions are produced. Nevertheless, a typical weakness in using BOTCcM is that the model cannot recommend a specific time span for concessionary. This paper introduces a new method called BOT bargaining concession model (BOTBaC) to enable the identification of a specific concession period, which takes into account the bargaining behavior of the two parties concerned in engaging a BOT contract, namely, the investor and the government concerned. The application of BOTBaC is demonstrated through using an example case.

Reactive Control for Transmission Overload Relief Based on Sensitivity Analysis and Cooperative Game Theory

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Game theory in sugarcane crop residue and available energy optimization

This work proposes a mathematical model to aid variety selection and planting quantity of sugarcane in order to reduce crop residues, maximize energy generated by this residue, and satisfy all the supply of the mill. We propose Linear Programming with two objective. The conflict between these objectives allows the use of the Nonzero-sum Game Theory. (C) 2003 Elsevier B.V. Ltd. All rights reserved.

A cooperative game theory analysis for transmission loss allocation

This paper presents an analysis and discussion, based on cooperative game theory, for the allocation of the cost of losses to generators and demands in transmission systems. We construct a cooperative game theory model in which the players are represented by equivalent bilateral exchanges and we search for a unique loss allocation solution, the Core. Other solution concepts, such as the Shapley Value, the Bilateral Shapley Value and the Kernel are also explored. Our main objective is to illustrate why is not possible to find an optimal solution for allocating the cost of losses to the users of a network. Results and relevant conclusions are presented for a 4-bus system and a 14-bus system. (c) 2007 Elsevier B.V. All rights reserved.

Hybrid heuristic-waterfilling game theory approach in MC-CDMA resource allocation

This paper discusses the power allocation with fixed rate constraint problem in multi-carrier code division multiple access (MC-CDMA) networks, that has been solved through game theoretic perspective by the use of an iterative water-filling algorithm (IWFA). The problem is analyzed under various interference density configurations, and its reliability is studied in terms of solution existence and uniqueness. Moreover, numerical results reveal the approach shortcoming, thus a new method combining swarm intelligence and IWFA is proposed to make practicable the use of game theoretic approaches in realistic MC-CDMA systems scenarios. The contribution of this paper is twofold: (i) provide a complete analysis for the existence and uniqueness of the game solution, from simple to more realist and complex interference scenarios; (ii) propose a hybrid power allocation optimization method combining swarm intelligence, game theory and IWFA. To corroborate the effectiveness of the proposed method, an outage probability analysis in realistic interference scenarios, and a complexity comparison with the classical IWFA are presented. (C) 2011 Elsevier B.V. All rights reserved.