Theories of the Bargaining Process

[Front Matter and Publication Details]: Front matter for Alan Coddington's 'Theories of the Bargaining Process', including publication details, copyright information, and the title page featuring a foreword by Professor G. L. S. Shackle. [Foreword by Professor G. L. S. Shackle]: Professor G. L. S. Shackle provides a critique of mechanistic economic models that assume away ignorance and uncertainty. He introduces Coddington's work as a significant advancement that constructs specific models to study the nature of consistency in a bargainer’s system of expectations and intentions, highlighting the role of 'Stackelberg disequilibrium' and the correction of errors in the bargaining process. [Table of Contents]: The table of contents for the book, outlining chapters on the general framework, surveys of bargaining theory, closed loops, decision-making and expectations, and various approaches to bargaining theory. [Preface: Methodology and Empirical Content]: Coddington discusses the methodological foundations of bargaining theory, contrasting bilateral monopoly with perfect competition. He critiques the limitations of game theory in variable-sum situations and addresses the challenges of empirical content in economic models. He argues that economic 'facts' are created within conceptual frameworks and suggests that theories should initially be tested against 'stylised facts' or broad features of bargaining processes rather than rigorous, currently unavailable data. [Chapter I: The General Framework - Introduction and Economic Environment]: The chapter introduces the concept of social action and expectations as defined by Talcott Parsons and Kenneth Boulding. It explores the 'economic environment' as a theoretical construct for representing the behavior of other actors. Coddington argues for a shift from aggregate market behavior to individual decision-making in small group processes, specifically two-person bargaining, utilizing the sequential approach developed by J. G. Cross. [Chapter I: A Bargaining Situation and Formalisation]: This section formalizes the bargaining situation as a conflict involving both mutual and opposing interests. It defines the parameters of demands, utility functions, and the contract zone. Coddington distinguishes between 'Pareto optimality in the small' (at the moment of agreement) and 'Pareto optimality in the large' (viewed from the start), noting that time delays impact the perceived optimality of outcomes. [Chapter I: Indeterminacy and the Role of Expectations]: Coddington addresses the traditional view that bilateral monopoly is 'indeterminate,' arguing instead that it is the theory that is indeterminate. He suggests that introducing dynamic considerations and a theory of expectations can resolve this. The section emphasizes that the adjustment of expectations regarding an opponent's response is fundamental to the bargaining process, as actors lack complete knowledge and must revise their beliefs based on experience. [Chapter I: General Workings of the Model]: This section outlines the cyclical mechanism of the bargaining model. Each bargainer starts with initial expectations and a plan based on utility maximization (considering both the outcome and the time taken). As demands are exchanged, bargainers test their expectations against the actual responses of their opponent, leading to a cycle of expectation revision, plan adjustment, and new demands until agreement or breakdown occurs. [Chapter I: Mathematical Appendix - Notation and Utility Maximisation]: The appendix introduces a formal notation to distinguish between present time (T) and future time (t), and between actual demands and expected future demands. It establishes a utility-maximization model where bargainers choose demands to maximize utility based on expected outcomes and the expected time of agreement. Coddington notes that the dependence of utility on time is the primary driver of bargaining dynamics. [Chapter I: Mathematical Appendix - Dynamics of Expectation Adjustment]: Coddington formalizes the adjustment of expectations by introducing an adjustment variable (V) that responds to the discrepancy between expected and actual concession rates. The model assumes that expectations are revised at a rate proportional to the error in predicting the opponent's behavior. This completes the general theoretical framework, linking decision-making to the evolution of expectations over time. [Chapter II: A Brief Survey of Bargaining Theory - Introduction]: The chapter begins by defining the criteria for evaluating bargaining theories, focusing on five key questions: the likely agreement, determining factors, the course of development, conditions for agreement vs. breakdown, and the stability of equilibrium. Coddington notes that most existing theories focus on outcomes rather than the dynamic process, with J. G. Cross being a notable exception. [Existing Theories of the Bargaining Process: Edgeworth and von Neumann-Morgenstern]: Coddington begins a review of existing bargaining theories by establishing a framework using utility functions and a welfare frontier. He discusses Edgeworth's theory of indeterminacy in bilateral monopoly and the von Neumann-Morgenstern approach to non-zero-sum games, noting that both arrive at similar conclusions regarding the range of possible outcomes based on the disagreement point. [Zeuthen's Theory and Harsanyi's Reformulation]: This section examines Zeuthen's theory as reformulated by Harsanyi, which predicts an outcome that maximizes the product of the bargainers' utility gains. Coddington details the mathematical conditions for concessions and convergence, exploring how specific shapes of the welfare frontier (convexity vs. concavity) can lead to disagreement or multiple solutions. [Nash's Axiomatic Approach and Pen's General Theory]: Coddington compares Nash's axiomatic 'fixed threat' theory with Zeuthen's, noting they predict the same outcome but through different logic. He then critiques Pen's 'General Theory of Bargaining,' arguing that while it provides insight into risk and uncertainty, it ultimately fails to provide a determinate outcome because its equations are generally inconsistent. [Time Preference Theories: Foldes and Bishop]: This section reviews the theories of Foldes and Bishop, which incorporate future time and discounting into the bargaining process. Both authors argue that time preferences can lead to a determinate static equilibrium, with Bishop specifically developing a 'Zeuthen-Hicks' model where the bargainer with the smaller tolerable breakdown length concedes. [Cross's Dynamic Theory and Convergence Conditions]: Coddington introduces Cross's theory, which shifts the focus from static equilibrium to the dynamics of the process. He explains that in Cross's model, the outcome depends on initial conditions and learning parameters. The section provides a mathematical derivation of the convergence conditions required for bargainers to reach an agreement within the contract zone. [Chapter III: Closed Loops and Cross's Assumptions]: Coddington details the five core assumptions of Cross's bargaining model: independence, linearity, pure intransigence, exponential discounting, and costs of bargaining. He represents the model as a closed-loop system with feedback, drawing parallels to macroeconomic stabilization policy and the work of M.J. Bailey on expectation adjustment. [Chapter IV: Decision-Making and Expectations (The Cournot Problem)]: Coddington explores the 'Cournot problem' regarding the consistency between a bargainer's decisions and their expectations of the opponent's behavior. He introduces a critical distinction between 'self-generating' and 'self-replacing' decision rules, arguing that most existing bargaining theories rely on self-replacing rules where at least one party must be mistaken about the other's logic. [Higher Level Decision Rules and Game Theory Models]: The final section of the chunk analyzes the infinite regress of higher-level decision rules. Coddington discusses the mathematical complexity of sophisticated rules and the reality of limited intelligence (referencing Simon). He concludes with a 2x2 game theory model illustrating the conflict between intransigence and concession, highlighting the problems of equivalence and interchangeability in non-zero-sum games. [Limitations of the Environment Concept]: This section examines the limitations of treating a single bargaining opponent as an 'environment.' Coddington argues that while an aggregate of many decision-makers provides a stable environment, a single opponent introduces problems of consistency and infinite regress, as both parties may apply the same reasoning to each other simultaneously. [Chapter V: Different Approaches to a Theory of Bargaining - Game Theory]: Coddington introduces Chapter V by critiquing the game-theoretic approach to bargaining. He distinguishes between cooperative and non-cooperative models, arguing that for the study of negotiations, a non-cooperative model is more appropriate because it incorporates the negotiation process as part of the strategy rather than preplay communication. [Solution Concepts and Sequential Aspects in Game Theory]: The author discusses the profusion of solution concepts in non-zero-sum game theory and the limitations of the 'strategy' concept. He argues that collapsing the sequential interactions of bargaining into a single strategy removes the dynamics of the process. He invokes Herbert Simon's critique of global rationality, noting that the computational requirements for realistic bargaining strategies are astronomically high. [The Decision/Expectation/Adjustment Approach vs. Game Theory]: Coddington contrasts his decision/expectation/adjustment framework with game theory. He defines the 'Cross-type bargainer' who makes myopic, tactical choices based on imperfect knowledge rather than choosing a global strategy. He classifies this approach as a 'cataclysmic' model of conflict (following Rapoport), where the process is driven by built-in dynamics rather than total strategic control. [Chapter VI: Further Developments - Non-Linear Assumptions]: Chapter VI explores the theoretical consequences of relaxing the assumption of linear expectations. Coddington argues that linear expectations are unrealistic because they imply a bargainer could expect to reach agreements outside the contract zone. He proposes non-linear conditions for the expected time of agreement and analyzes how this affects the marginal time costs of demands. [Direct and Conjectural Interdependence in Adjustment]: Coddington distinguishes between 'direct' and 'conjectural' interdependence. Direct interdependence involves the immediate influence of one bargainer's demand on the other's, while conjectural interdependence operates through the revision of expectations. He analyzes the adjustment process as the motion of an equilibrium point in the demand plane as expectations shift. [Consistency of Decisions and the Intransigence Assumption]: The author examines the consistency of a bargainer's decisions over time. He postulates that a satisfactory model should not require a bargainer to revise a decision if their expectations are fulfilled. He concludes that within a framework of 'pure intransigence,' this consistency requires that the expected time function be separable, effectively eliminating direct interdependence in favor of conjectural adjustment. [An Illustrative Model and Numerical Solutions]: Coddington presents a specific non-linear model of bargaining and provides numerical solutions calculated via the Runge-Kutta-Merson method. The table illustrates how variations in discounting rates (a), learning rates (gamma), and initial demands (q0) affect the time to agreement and the final outcome for both symmetrical and asymmetrical cases. [Bibliography]: A comprehensive list of academic references cited in the work, covering game theory, economic behavior, bargaining processes, and mathematical economics. Key authors include Nash, Rapoport, Schelling, Simon, and Zeuthen. [Index]: Alphabetical index of terms, concepts, and authors mentioned throughout the book, providing page references for key topics such as bilateral monopoly, contract zone, and various bargaining theories.