We embed time inconsistent agents (players) in non-cooperative games. To solve such games, we introduce two solution concepts, which we refer to as equilibrium and naive backwards induction. When all players are sophisticated time inconsistent, these solution concepts are equivalent and coincide with the standard notions of SPNE and backwards induction (in finite games of perfect information). When some players are naive time inconsistent, however, these solution concepts (may, and most likely will) lead to different predictions. We apply these solution concepts on two well-known economic applications, the alternating-offers bargaining game and the durable good monopoly, and we explore their relative strengths and weaknesses.

The literature on time-inconsistent preferences introduced sophisticated, naive and partially naive types of agents that represent different levels of awareness of their time inconsistency. This paper incorporates time-inconsistent players in a sequential bargaining model. Under the complete information assumption, we first consider naive agents who never learn about their types and show that bargaining between such a player and a standard exponential agent ends in immediate agreement if the exponential agent offers first. A one period delay occurs if the naive player offers first. In addition, the more naive the player is, the higher share she gets. We then allow naive and partially naive agents to learn their types over time and show that there is a critical date before which there is no agreement. Hence, the existence of time-inconsistent players who can learn their types as they play the game can be a new explanation for delays in bargaining. The relationship among the degree of naivete, impatience level and bargaining delay is also characterized.

This paper studies an alternating-offers bargaining game between a time-consistent and a time-inconsistent player who processes information on own preference type imperfectly that flows during the course of the game. The time-inconsistency is modeled by quasi-hyperbolic discounting and the quot;naive backwards inductionquot; is used as the solution concept. By using cognitive and mood state approaches, we model learning of naive time-inconsistent player. The main result specifies a clear connection between the model parameters and the equilibrium in the most general sense. For special cases, critical delay times and probabilistic structure of the agreement and relations between them are characterized. Comparative statics imply that more naive players and players with milder self control problems are offered higher shares more frequently.

Dynamic games arise between players (individuals, firms, countries, animals, etc.) when the strategic interactions among them recur over time and decisions made during one period affect both current and future payoffs. Dynamic games provide conceptually rich paradigms and tools to deal with these situations.This volume provides a uniform approach to game theory and illustrates it with present-day applications to economics and management, including environmental, with the emphasis on dynamic games.At the end of each chapter a case study called game engineering (GE) is provided, to help readers understand how problems of high social priority, such as environmental negotiations, exploitation of common resources, can be modeled as games and how solutions can be engineered.

Game theory is a branch of modern applied mathematics that aims to analyze various problems of conflict between parties that have opposed, similar or simply different interests. Games are grouped into several classes according to some important features. In this volume zero-sum two-person games, strategic n-person games in normal form, cooperative games, games in extensive form with complete and incomplete information, differential pursuit games and differential cooperative n-person games are considered.

This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications. In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker’s preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent’s current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.

The aim of this volume is to consider intertemporal and strategic issues in the formulation of economic policy so that dynamic game methodology is appropriate. When changes in economic policy are evaluated the reactions and expectations of other economic agents cannot be ignored, and in a dynamic setting issues like time inconsistency, subgame perfectness, reputation and information become important.The papers contained in this volume are the revised versions of those presented at a conference held in 1988 at Tilburg University, The Netherlands. They include methodological contributions and strategic analyses of macroeconomic policy, resource economics, international policy coordination and the arms race.