Essays On The Existence Of Equilibria In Games

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Essays on the Existence of Equilibria in Games

Author : Idione Meneghel
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (923 download)

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Book Synopsis Essays on the Existence of Equilibria in Games by : Idione Meneghel

Download or read book Essays on the Existence of Equilibria in Games written by Idione Meneghel and published by . This book was released on 2013 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The question of existence of a Nash equilibrium is one of the most important questions in game theory. This thesis aims to advance our understanding of the question in two broad directions: 1) by providing weaker sets of sufficient conditions; and 2) by introducing novel techniques, which allow for straightforward proofs and results that give new economic insights. Discontinuous games: This project considers the existence problem in games in which strategy sets are compact and convex, but preferences of the players are represented by numerical functions that may not be continuous. One way to show existence of equilibrium in such games is to apply the 'better reply security' logic, introduced by Reny (1999), combined with some form of quasiconcavity of utility functions. As long as players have securing strategies that are robust to other players' small deviations, one can show that the game has an equilibrium. The novelty of the techniques used relies in combining three main ideas: 1) a local continuous selection of each player's strict upper contour set; 2) the idea of activating different players locally; and 3) a weak notion of convexity of preferences. Bayesian games: Games of incomplete information have been shown to apply to a huge variety of economic, political and other social interactions. Still, the question of existence of equilibria in such games has been largely dealt with on a case-by-case basis. That is, given a particular game with incomplete information, one has to find the equilibrium to prove that it exists. The reason is that the usual tools to prove existence (continuous and quasiconcave payoffs defined on convex and compact strategy sets) do not apply to the general framework of games with incomplete information. This project investigates sufficient conditions for the existence of pure-strategy Nash equilibrium in games of incomplete information. The assumption of nonatomicity of the distribution of types allows for an analysis that does not require convexity assumptions on action spaces and/or payoff functions"--Pages iv-v.

Essays in Dynamic Games

Author : Juan Escobar
Publisher :
ISBN 13 :
Total Pages : 130 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Essays in Dynamic Games by : Juan Escobar

Download or read book Essays in Dynamic Games written by Juan Escobar and published by . This book was released on 2009 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Essays on Evolutionary Game Theory and Its Applications

Author : Shota Fujishima
Publisher :
ISBN 13 :
Total Pages : 95 pages
Book Rating : 4.:/5 (856 download)

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Book Synopsis Essays on Evolutionary Game Theory and Its Applications by : Shota Fujishima

Download or read book Essays on Evolutionary Game Theory and Its Applications written by Shota Fujishima and published by . This book was released on 2013 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three essays on evolutionary game theory and its applications. The first essay considers mechanism design in the evolutionary game-theoretic framework. The second essay studies equilibrium selection of coordination games by using an evolutionary game-theoretic concept. The third essay formulates a multi-regional economic growth model as an evolutionary game and characterizes the stability of its equilibria under an evolutionary dynamic. The summaries of each essay are provided below. In the first essay, I consider an implementation problem in a class of congestion games with players that have heterogeneous costs of taking actions. One application is to traffic congestion with drivers having heterogeneous time costs. The planner would like to design a price scheme under which the economy converges to an epsilon-optimum from any initial state when he does not have full knowledge of the cost functions, and he can observe only the aggregate strategy distribution. Although the planner would like to internalize the externalities, the informational constraints compel him to estimate their values. Using the optimality and equilibrium conditions, I construct a practical estimation procedure that yields the true values of externalities in the long-run. Moreover, I show that our scheme makes the epsilon-optimum globally stable under the best response dynamic if the externalities among players taking the same action are sufficiently large relative to those among players taking different actions. In the second essay, I study the long-run outcomes of noisy asynchronous repeated games with players that are heterogeneous in in terms of their patience. The players repeatedly play a 2-by-2 coordination game with random pair-wise matching. The games are noisy because the players may make mistakes when choosing their actions and are asynchronous because only one player can move in each period. I characterize the long-run outcomes of Markov perfect equilibrium that are robust to the mistakes and show that if there is a sufficiently patient player, the efficient state can be the unique robust outcome even if it is risk-dominated. Because I need heterogeneity for the result, I argue that it enables the most patient player in effect to be the leader. In the third essay, I consider a microfounded urban growth model with two regions and a mass of mobile workers to study interactions among growth, agglomeration, and urban congestion. Unlike previous research in the urban growth literature, I formulate the model as a one-shot game and take an evolutionary game-theoretic approach for stability analysis. My approach enables us to analyze the stability of nonstationary equilibria in which populations of each region are not constant over time. I show that if both the expenditure share for housing and inter-regional transport cost are small, a stable stationary equilibrium does not exist. Moreover, in such a case, I show that there can exist a stable nonstationary equilibrium in which mobile workers agglomerate in one region at first but some of them migrate to the other region later. I argue that such a nonstationary location pattern is related to return migration.

Equilibrium Theory for Cournot Oligopolies and Related Games

Author : Pierre von Mouche
Publisher : Springer
ISBN 13 : 3319292544
Total Pages : 298 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Equilibrium Theory for Cournot Oligopolies and Related Games by : Pierre von Mouche

Download or read book Equilibrium Theory for Cournot Oligopolies and Related Games written by Pierre von Mouche and published by Springer. This book was released on 2016-04-22 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This state-of-the-art collection of papers on the theory of Cournotian competition focuses on two main subjects: oligopolistic Cournot competition and contests. The contributors present various applications of the Cournotian Equilibrium Theory, addressing topics such as equilibrium existence and uniqueness, equilibrium structure, dynamic processes, coalitional behavior and welfare. Special emphasis is placed on the aggregative nature of the games that are relevant to such theory. This contributed volume was written to celebrate the 80th birthday of Prof. Koji Okuguchi, a pioneer in oligopoly theory.

Three Essays on Dynamic Games

Author : Asaf Plan
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.:/5 (769 download)

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Book Synopsis Three Essays on Dynamic Games by : Asaf Plan

Download or read book Three Essays on Dynamic Games written by Asaf Plan and published by . This book was released on 2010 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1: This chapter considers a new class of dynamic, two-player games, where a stage game is continuously repeated but each player can only move at random times that she privately observes. A player's move is an adjustment of her action in the stage game, for example, a duopolist's change of price. Each move is perfectly observed by both players, but a foregone opportunity to move, like a choice to leave one's price unchanged, would not be directly observed by the other player. Some adjustments may be constrained in equilibrium by moral hazard, no matter how patient the players are. For example, a duopolist would not jump up to the monopoly price absent costly incentives. These incentives are provided by strategies that condition on the random waiting times between moves; punishing a player for moving slowly, lest she silently choose not to move. In contrast, if the players are patient enough to maintain the status quo, perhaps the monopoly price, then doing so does not require costly incentives. Deviation from the status quo would be perfectly observed, so punishment need not occur on the equilibrium path. Similarly, moves like jointly optimal price reductions do not require costly incentives. Again, the tempting deviation, to a larger price reduction, would be perfectly observed. This chapter provides a recursive framework for analyzing these games following Abreu, Pearce, and Stacchetti (1990) and the continuous time adaptation of Sannikov (2007). For a class of stage games with monotone public spillovers, like differentiated-product duopoly, I prove that optimal equilibria have three features corresponding to the discussion above: beginning at a "low" position, optimal, upward moves are impeded by moral hazard; beginning at a "high" position, optimal, downward moves are unimpeded by moral hazard; beginning at an intermediate position, optimally maintaining the status quo is similarly unimpeded. Corresponding cooperative dynamics are suggested in the older, non-game-theoretic literature on tacit collusion. Chapter 2: This chapter shows that in finite-horizon games of a certain class, small perturbations of the overall payoff function may yield large changes to unique equilibrium payoffs in periods far from the last. Such perturbations may tie together cooperation across periods in equilibrium, allowing substantial cooperation to accumulate in periods far from the last. Chapter 3: A dynamic choice problem faced by a time-inconsistent individual is typically modeled as a game played by a sequence of her temporal selves, solved by SPNE. It is recognized that this approach yields troublesomely many solutions for infinite-horizon problems, which is often attributed to the existence of implausible equilibria based on self-reward and punishment. This chapter presents a refinement applicable within the special class of strategically constant (SC) problems, which are those where all continuation problems are isomorphic. The refinement requires that each self's strategy be invariant, here that implies history-independence under the isomorphism. I argue that within the class of SC problems, this refinement does little more than rule out self-reward and punishment. The refinement substantially narrows down the set of equilibria in SC problems, but in some cases allows plausible equilibria that are excluded by other refinement approaches. The SC class is limited, but broader than it might seem at first.

Essays on Pure and Applied Game Theory

Author : Jen-Wen Chang
Publisher :
ISBN 13 :
Total Pages : 109 pages
Book Rating : 4.:/5 (17 download)

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Book Synopsis Essays on Pure and Applied Game Theory by : Jen-Wen Chang

Download or read book Essays on Pure and Applied Game Theory written by Jen-Wen Chang and published by . This book was released on 2016 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: In my dissertation, I provide two models of joint contribution games that are relevant to the phenomenon of crowdfunding. I also provide a characterization of Bayes Nash equilibrium. In the first chapter I build a model of crowdfunding. An entrepreneur finances her project with common value via crowdfunding. She chooses a funding mechanism (fixed or flexible), a price, and a funding goal. Under fixed funding money is refunded if the goal is not met; under flexible funding the entrepreneur keeps the money. Backers observe signals about the value and decide whether to contribute or postpone purchase to the retail stage. The optimal crowdfunding campaign is characterized. When the entrepreneur has commitment power, fixed funding generates more revenue than flexible funding. When the entrepreneur has no commitment power, fixed funding serves as a commitment device to eliminate moral hazard In the second chapter I consider a dynamic contribution game under two regimes. The first regime is that all but the last rounds are cheap talk, the other is that in all rounds contribution is sunk. With binary contribution levels and a continuum of types we show that one of the monotone equilibria in the first regime implements the ex-post efficient and ex-post individually rational allocation when the cheap talk period is long enough. In contrast, when commitment is required, no equilibria achieves the same allocation. However, with a continuum of contribution levels, all equilibria of the contribution game with cheap talk will be the same as a one-shot game with no cheap talk, due to severe free riding. In this case, dynamic contribution with commitment provides credibility and can significantly improve efficiency. In the third chapter, coauthored with Ichiro Obara, we prove the following characterization regarding types and Bayes equilibrium actions they play across games: Given any two types in any two countable type spaces, if for all finite games, the two types have the same pure Bayes Nash equilibrium action, then there exists a bijective belief morphism between them. As an application, our result implies that the universal space for Bayes Nash equilibrium that retains non-redundancy does not exist.

Optimal Control and Differential Games

Author : Georges Zaccour
Publisher : Springer Science & Business Media
ISBN 13 : 1461510473
Total Pages : 242 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Optimal Control and Differential Games by : Georges Zaccour

Download or read book Optimal Control and Differential Games written by Georges Zaccour and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control and differential games continue to attract strong interest from researchers interested in dynamical problems and models in management science. This volume explores the application of these methodologies to new as well as to classical decision problems in management sciences and economics. In Part I, optimal control and dynamical systems approaches are used to analyze problems in areas such as monetary policy, pollution control, relationship marketing, drug control, debt financing, and ethical behavior. In Part II differential games are applied to problems such as oligopolistic competition, common resource management, spillovers in foreign direct investments, marketing channels, incentive strategies, and the computation of Markov perfect Nash equilibria. Optimal Control and Differential Games is an excellent reference for researchers and graduate students covering a wide range of emerging and revisited problems in management science.

Essays in Game Theory

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
ISBN 13 : 1461226481
Total Pages : 209 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Essays in Game Theory by : Nimrod Megiddo

Download or read book Essays in Game Theory written by Nimrod Megiddo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of papers on game theory dedicated to Michael Maschler. Through his dedication and contributions to game theory, Maschler has become an important figure particularly in the area of cooperative games. Game theory has since become an important subject in operations research, economics and management science. As befits such a volume, the main themes covered are cooperative games, coalitions, repeated games, and a cost allocation games. All the contributions are authoritative surveys of a particular topic, so together they will present an invaluable overview of the field to all those working on game theory problems.

Essays in Evolutionary Game Theory

Author : Ratul Lahkar
Publisher :
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.:/5 (891 download)

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Book Synopsis Essays in Evolutionary Game Theory by : Ratul Lahkar

Download or read book Essays in Evolutionary Game Theory written by Ratul Lahkar and published by . This book was released on 2007 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Institutions, Equilibria and Efficiency

Author : Christian Schultz
Publisher : Springer Science & Business Media
ISBN 13 : 3540281614
Total Pages : 380 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Institutions, Equilibria and Efficiency by : Christian Schultz

Download or read book Institutions, Equilibria and Efficiency written by Christian Schultz and published by Springer Science & Business Media. This book was released on 2006-04-22 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways: Efficiency and price regulation are studied when markets are incomplete and existence of equilibria in such settings is proven under very general preference assumptions. The model is extended to include geographical location choice, a commodity space incorporating manufacturing imprecision and preferences for club-membership, schools and firms. Inefficiencies arising from household externalities or group membership are evaluated. Core equivalence is shown for bargaining economies. The theory of risk aversion is extended and the relation between risk taking and wealth is experimentally investigated. Other topics include determinacy in OLG with cash-in-advance constraints, income distribution and democracy in OLG, learning in OLG and in games, optimal pricing of derivative securities, the impact of heterogeneity at the individual level for aggregate consumption, and adaptive contracting in view of uncertainty.

Essays on Pareto Optimality in Cooperative Games

Author : Yaning Lin
Publisher : Springer Nature
ISBN 13 : 9811950490
Total Pages : 169 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Essays on Pareto Optimality in Cooperative Games by : Yaning Lin

Download or read book Essays on Pareto Optimality in Cooperative Games written by Yaning Lin and published by Springer Nature. This book was released on 2022-09-21 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on Pareto optimality in cooperative games. Most of the existing works focus on the Pareto optimality of deterministic continuous-time systems or for the regular convex LQ case. To expand on the available literature, we explore the existence conditions of Pareto solutions in stochastic differential game for more general cases. In addition, the LQ Pareto game for stochastic singular systems, Pareto-based guaranteed cost control for uncertain mean-field stochastic systems, and the existence conditions of Pareto solutions in cooperative difference game are also studied in detail. Addressing Pareto optimality for more general cases and wider systems is one of the major features of the book, making it particularly suitable for readers who are interested in multi-objective optimal control. Accordingly, it offers a valuable asset for researchers, engineers, and graduate students in the fields of control theory and control engineering, economics, management science, mathematics, etc.

Essays on Dynamic Games and Reputations

Author : Di Pei (Ph. D.)
Publisher :
ISBN 13 :
Total Pages : 189 pages
Book Rating : 4.:/5 (15 download)

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Book Synopsis Essays on Dynamic Games and Reputations by : Di Pei (Ph. D.)

Download or read book Essays on Dynamic Games and Reputations written by Di Pei (Ph. D.) and published by . This book was released on 2018 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis consists of three essays on dynamic games with incomplete information. In Chapter 1, I study reputation effects when individuals have persistent private information that matters for their opponents' payoffs. I examine a repeated game between a patient informed player and a sequence of myopic uninformed players. The informed player privately observes a persistent state, and is either a strategic type who can flexibly choose his actions or is one of the several commitment types that mechanically plays the same action in every period. Unlike the canonical models on reputation effects, the uninformed players' payoffs depend on the state. This interdependence of values introduces new challenges to reputation building, namely, the informed player could face a tradeo between establishing a reputation for commitment and signaling favorable information about the state. My results address the predictions on the informed player's payoff and behavior that apply across all Nash equilibria. When the stage game payoffs satisfy a monotone-supermodularity condition, I show that the informed long-run player can overcome the lack-of-commitment problem and secure a high payoff in every state and in every equilibrium. Under a condition on the distribution over states, he will play the same action in every period and maintain his reputation for commitment in every equilibrium. If the payoff structure is unrestricted and the probability of commitment types is small, then the informed player's return to reputation building can be low and can provide a strict incentive to abandon his reputation. In Chapter 2, I study the dynamics of an agent's reputation for competence when the labor market's information about his performance is disclosed by an intermediary who cannot commit. I show that this game admits a unique Markov Perfect Equilibrium (MPE). When the agent is patient, his effort is inverse U-shaped, while the rate of information disclosure is decreasing over time. I illustrate the inefficiencies of the unique MPE by comparing it with the equilibrium in the benchmark scenario where the market automatically observes all breakthroughs. I characterize a tractable subclass of non-Markov Equilibria and explain why allowing players to coordinate on payoff-irrelevant events can improve eciency on top of the unique MPE and the exogenous information benchmark. When the intermediary can commit, her optimal Markov disclosure policy has a deadline, after which no breakthrough will be disclosed. However, deadlines are not incentive compatible in the game without commitment, illustrating a time inconsistency problem faced by the intermediary. My model can be applied to professional service industries, such as law and consulting. My results provide an explanation to the observed wage and promotion patterns in Baker, Gibbs and Holmström (1994). In Chapter 3, I study repeated games in which a patient long-run player (e.g. a rm) wishes to win the trust of some myopic opponents (e.g. a sequence or a continuum of consumers) but has a strict incentive to betray them. Her benet from betrayal is persistent over time and is her private information. I examine the extent to which persistent private information can overcome this lack-of-commitment problem. My main result characterizes the set of payoffs a patient long-run player can attain in equilibrium. Interestingly, every type's highest equilibrium payoff only depends on her true benet from betrayal and the lowest possible benet in the support of her opponents' prior belief. When this lowest possible benet vanishes, every type can approximately attain her Stackelberg commitment payoff. My finding provides a strategic foundation for the (mixed) Stackelberg commitment types in the reputation models, both in terms of the highest attainable payoff and in terms of the commitment behaviors. Compared to the existing approaches that rely on the existence of crazy types that are either irrational or have drastically dierent preferences, there is common knowledge of rationality in my model, and moreover, players' ordinal preferences over stage game outcomes are common knowledge.

Game Theoretic Analysis

Author : Leon A Petrosyan
Publisher : World Scientific
ISBN 13 : 9811202028
Total Pages : 621 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Game Theoretic Analysis by : Leon A Petrosyan

Download or read book Game Theoretic Analysis written by Leon A Petrosyan and published by World Scientific. This book was released on 2019-10-14 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of recent novel contributions in game theory from a group of prominent authors in the field. It covers Non-cooperative Games, Equilibrium Analysis, Cooperative Games and Axiomatic Values in static and dynamic contexts.Part 1: Non-cooperative Games and Equilibrium AnalysisIn game theory, a non-cooperative game is a game with competition between individual players and in which only self-enforcing (e.g. through credible threats) alliances (or competition between groups of players, called 'coalitions') are possible due to the absence of external means to enforce cooperative behavior (e.g. contract law), as opposed to cooperative games. In fact, non-cooperative games are the foundation for the development of cooperative games by acting as the status quo. Non-cooperative games are generally analysed through the framework of equilibrium, which tries to predict players' individual strategies and payoffs. Indeed, equilibrium analysis is the centre of non-cooperative games. This volume on non-cooperative games and equilibrium analysis contains a variety of non-cooperative games and non-cooperative game equilibria from prominent authors in the field.Part 2: Cooperative Games and Axiomatic ValuesIt is well known that non-cooperative behaviours, in general, would not lead to a Pareto optimal outcome. Highly undesirable outcomes (like the prisoner's dilemma) and even devastating results (like the tragedy of the commons) could appear when the involved parties only care about their individual interests in a non-cooperative situation. Cooperative games offer the possibility of obtaining socially optimal and group efficient solutions to decision problems involving strategic actions. In addition, axiomatic values serve as guidance for establishing cooperative solutions. This volume on cooperative games and axiomatic values presents a collection of cooperative games and axiomatic values from prominent authors in the field.

Three Essays on Signaling Games

Author : Juhyun Park
Publisher :
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Three Essays on Signaling Games by : Juhyun Park

Download or read book Three Essays on Signaling Games written by Juhyun Park and published by . This book was released on 1988 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Essays in Dynamic Games

Author : Yuhta Ishii
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (882 download)

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Book Synopsis Essays in Dynamic Games by : Yuhta Ishii

Download or read book Essays in Dynamic Games written by Yuhta Ishii and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation presents three independent essays. Chapter 1, which is joint work with Mira Frick, studies a model of innovation adoption by a large population of long-lived consumers who face stochastic opportunities to adopt an innovation of uncertain quality. We study how the potential for social learning in an economy affects consumers' informational incentives and how these in turn shape the aggregate adoption dynamics of an innovation. For a class of Poisson learning processes, we establish the existence and uniqueness of equilibria. In line with empirical findings, equilibrium adoption patterns are either S-shaped or feature successions of concave bursts. In the former case, our analysis predicts a novel saturation effect: Due to informational free-riding, increased opportunities for social learning necessarily lead to temporary slow-downs in learning and do not produce welfare gains.

Essays on Two-player Games with Asymmetric Information

Author : Lan Sun
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (967 download)

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Book Synopsis Essays on Two-player Games with Asymmetric Information by : Lan Sun

Download or read book Essays on Two-player Games with Asymmetric Information written by Lan Sun and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Existence of Pure Strategy Nash Equilibria in Large Games

Author : Guilherme Carmona
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis On the Existence of Pure Strategy Nash Equilibria in Large Games by : Guilherme Carmona

Download or read book On the Existence of Pure Strategy Nash Equilibria in Large Games written by Guilherme Carmona and published by . This book was released on 2006 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an asymptotic version of Mas-Colell's theorem on the existence of pure strategy Nash equilibria in large games. Our result states that, if players' payoff functions are selected from an equicontinuous family, then all sufficiently large games have an pure, equilibrium for all gt; 0. We also show that our result is equivalent to Mas-Colell's existence theorem, implying that it can properly be considered as its asymptotic version.