22 research outputs found
Flows and Decompositions of Games: Harmonic and Potential Games
In this paper we introduce a novel flow representation for finite games in
strategic form. This representation allows us to develop a canonical direct sum
decomposition of an arbitrary game into three components, which we refer to as
the potential, harmonic and nonstrategic components. We analyze natural classes
of games that are induced by this decomposition, and in particular, focus on
games with no harmonic component and games with no potential component. We show
that the first class corresponds to the well-known potential games. We refer to
the second class of games as harmonic games, and study the structural and
equilibrium properties of this new class of games. Intuitively, the potential
component of a game captures interactions that can equivalently be represented
as a common interest game, while the harmonic part represents the conflicts
between the interests of the players. We make this intuition precise, by
studying the properties of these two classes, and show that indeed they have
quite distinct and remarkable characteristics. For instance, while finite
potential games always have pure Nash equilibria, harmonic games generically
never do. Moreover, we show that the nonstrategic component does not affect the
equilibria of a game, but plays a fundamental role in their efficiency
properties, thus decoupling the location of equilibria and their payoff-related
properties. Exploiting the properties of the decomposition framework, we obtain
explicit expressions for the projections of games onto the subspaces of
potential and harmonic games. This enables an extension of the properties of
potential and harmonic games to "nearby" games. We exemplify this point by
showing that the set of approximate equilibria of an arbitrary game can be
characterized through the equilibria of its projection onto the set of
potential games
Game Transformations that preserve Nash Equilibrium sets and/or Best Response sets
In the literature on simultaneous non-cooperative games, it is well-known
that a positive affine (linear) transformation (PAT) of the utility payoffs do
not change the best response sets and the Nash equilibrium set. PATs have been
successfully used to expand the classes of 2-player games for which we can
compute a Nash equilibrium in polynomial time.
We investigate which game transformations other than PATs also possess one of
the following properties: (i) The game transformation shall not change the Nash
equilibrium set when being applied on an arbitrary game. (ii) The game
transformation shall not change the best response sets when being applied on an
arbitrary game.
First, we prove that property (i) implies property (ii). Over a series of
further results, we derive that game transformations with property (ii) must be
positive affine. Therefore, we obtained two new and equivalent
characterisations with game theoretic meaning for what it means to be a
positive affine transformation.
All our results in particular hold for the 2-player case of bimatrix games.Comment: 18 pages, 0 figure
Bimátrix játékok Nash egyensúlypontjának meghatározásáról: könnyen kezelhető speciális esetek
A bimátrix játékok Nash egyensúlypontjának numerikus meghatározásával foglalkozunk. Ismerve a probléma nehézségét, néhány olyan speciális esetet tekintünk át, amikor a feladat polinomiális időben megoldható. Kijelölünk egy új osztályt, amely szintén polinomiális idejű algoritmushoz vezet. Az osztály definiálásában kulcsszerepe van a "majdnem negatív definit" mátrixoknak. Egy szükséges és egy elégséges feltételt adunk a majdnem negatív definit mátrixok jellemzésére
Solutions in multi-actor projects with collaboration and strategic incentives
This dissertation focuses on the mathematical analysis of projects involving decisions by multiple players. These players all have their own capabilities, requirements, and incentives, but their (monetary) outcome is dependent on the decisions of other players as well. Game theory is a mathematical tool to analyze the interactive decision-making process, generally paired with a method to ‘resolve’ the conflict situation. The way in which players interact in such a situation is commonly divided in two categories, distinguishing between cooperative and competitive (non-cooperative) behavior. This dissertation first studies two models within a cooperative framework, starting with the definition and analysis of a new influence measure for general, collaborative projects. The second model applies to situations where players cooperate on the construction of a new joint infrastructure, with a specific focus on cost allocation for CO2 transport infrastructure. Next, two-stage models are considered, in which a noncooperative first stage is followed by a cooperative second stage. Subsequently, social welfare loss in auctions with a corrupt auctioneer is studied. Finally, a new solution concept is presented that refines the notion of Nash equilibria for a general class of non-cooperative games
Essays on Economics and Computer Science
146 pagesThis dissertation considers a number of problems in pure and applied game theory. The first chapter considers the problem of how the introduction of fines and monitoring affects welfare in a routing game. I characterize equilibria of the game and discuss network topologies in which the introduction of fines can harm those agents which are not subject to them. The second, and primary, chapter considers the computational aspects of tenable strategy sets. I characterize these set-valued solution concepts using the more familiar framework of perturbed strategies, introduce strong alternatives to the problems of verifying whether a strategy block satisfies the conditions of tenability, and provide some hardness results regarding the verification of fine tenability. Additionally, I show an inclusion relation between the concept of coarse tenability and the notion of stability introduced by Kohlberg and Mertens (1986). Finally, I show how the methods developed for tenability provide an alternative characterization for proper equilibria in bimatrix games. This characterization gives a bound on the perturbations required in the definition of proper equilibria, though such bounds cannot be computed efficiently in general. The third, and final, chapter develops a model of contracting for content creation in an oligopolistic environment of attention intermediaries. I characterize symmetric equilibria in single-homing (exclusive) and multi-homing regimes. The focus is on the trade-off between reductions in incentives offered by intermediaries and the benefits of access to additional content for consumers. I show that when the extent of multi-homing is exogenous in the absence of exclusivity clauses, consumer surplus is always higher with multi-homing than under exclusivity, despite weaker incentives offered by platforms to content creators
Game theory approach to competitive economic dynamics
This thesis deals both with non-cooperative and cooperative games in order to apply the mathematical theory to competitive dynamics arising from economics, particularly quantity competition in oligopolies and pollution reduction models in IEA (International Environmental Agreements)
Game theory approach to competitive economic dynamics
This thesis deals both with non-cooperative and cooperative games in order to apply the mathematical theory to competitive dynamics arising from economics, particularly quantity competition in oligopolies and pollution reduction models in IEA (International Environmental Agreements)