Coalitional Bargaining Equilibria

This paper takes up the foundational issue of existence of stationary subgame perfect equi- libria in a general class of coalitional bargaining games that includes many known bargaining models and models of coalition formation. General sufficient conditions for existence of equilib- ria are currently lacking in many interesting environments: bargaining models with non-concave stage utility functions, models with a Pareto optimal status quo alternative and heterogeneous discount factors, and models of coalition formation in public good economies with consumption lower bounds. This paper establishes existence of stationary equilibrium under compactness and continuity conditions, without the structure of convexity or comprehensiveness used in the extant literature. The proof requires a precise selection of voting equilibria following different proposals. The result is applied to obtain equilibria in models of bargaining over taxes, coalition formation in NTU environments, and collective dynamic programming problems.

The Labor Market and Macro Volatility: A Nonstationary General-Equilibrium Analysis

The evolution of the aggregate labor market is far from smooth. I investigate the success of a macro model in replicating the observed levels of volatility of unemployment and other key variables. I take variations in productivity growth and in exogenous product demand (government purchases plus net exports) as the primary exogenous sources of fluctuations. The macro model embodies new ideas about the labor market, all based on equilibrium %u2013 the models I consider do not rest on inefficiency in the use of labor caused by an inappropriate wage. I find that non-standard features of the labor market are essential for understanding the volatility of unemployment. These models include simple equilibrium wage stickiness, where the sticky wage is an equilibrium selection rule. A second model based on modern bargaining theory delivers a different kind of stickiness and has a unique equilibrium. A third model posits fluctuations in matching efficiency that may arise from variations over time in the information about prospective jobs among job-seekers. Reasonable calibrations of each of the three models match the observed volatility of unemployment.

A note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"

In two recent contributions, Herbert Gintis introduces agent-based imitation models built upon evolutionary bargaining games where agents use private prices as strategies. He reports surprising convergence results for simulations performed in exchange economies where goods are strict complement. We investigate analyt- ically these results using the notion of stochastic stability.Exchange economies ; Bargaining Games ; Equilibrium Selection ; Stochastic Stability.

Equilibrium selection in alternating-offers bargaining models: the evolutionary computing approach

A systematic validation of evolutionary techniques in the field of bargaining is presented. For this purpose, the dynamic and equilibrium-selecting behavior of a multi-agent system consisting of adaptive bargaining agents is investigated. The agents' bargaining strategies are updated by an evolutionary algorithm (EA), an innovative computational method to simulate collective learnin g in societies of boundedly-rational agents. Negotiations between the agents are governed by the well-known``alternating-offers' protocol. Using this protocol, the influence of various important factors (like the finite length of the game, time preferences, exogenous breakdown, and risk aversiveness) is investigated. We show that game theory can be used successfully to interpret the equilibrium-selecting behavior observed in computational experiments with adaptive bargaining agents. Agreement between theory and experiment is especially good when the agents experience an intermediate time pressure. Deviations from classical game theory are, however, observed in several experiments. Violent nonlinear oscillations may for instance occur in the single-stage ultimatum game. We demonstrate that the specific evolutionary model governing agent selection is an important factor under these conditions. In multiple-stage games, the evolving agents do not always fully perceive and exploit the finite horizon of the game (even when time pressure is weak). This effect can be attributed to the boundedly-rational behavior of the adapting agents. Furthermore, when the agents discount their payoffs at a different rate, the agent with the largest discount factor is not able to exploit his bargaining power completely, being under pressure by his impatient opponent to reach an early agreement. Negotiations over multiple issues, a particularly important aspect of electronic trading, are studied in a companion paper cite{Gerding:00. We are currently investigating the behavior of more complex and powerful bargaining agents

Equilibrium selection in alternating-offers bargaining models : the evolutionary computing approach

This paper studies the dynamic and equilibrium-selecting behavior of a multi-agent system consisting of adaptive bargaining agents. We model an adaptive agent as a collection of strategies which is optimized by an evolutionary algorithm (EA). EAs are stochastic search methods based upon the principles of natural genetic systems. These algorithms have been used in the past, with considerable success, to solve difficult optimization problems. Examples include problems with huge search spaces, multiple local optima, discontinuities, and noise. Adaptive agents learn in three different ways in an evolutionary setting: (i) by selection and reproduction of successful strategies, (ii) by recombining or ``crossing over'' previously-tested strategies, and (iii) by random experimentation (by ``mutating'' existing strategies). Such agents are boundedly rational because they only experience the profit of their interactions with other agents and learn by trial-and-error instead of abstract reasoning. Their equilibrium-selecting behavior is interpreted in this paper by comparison with game-theoretic (subgame-perfect equilibrium) predictions for fully rational agents. This paper shows that game-theoretic approaches are very useful to interpret equilibrium-selecting behavior in evolutionary systems of adaptive bargaining agents. The adaptive agents are boundedly rational because they only experience the profit of their interactions with other agents. Nevertheless, they display behavior that is surprisingly "rational" and fully informed in many instances. Agreement between theory and experiment is especially good when the agents experience an intermediate time pressure. In extreme situations (i.e., when time pressure becomes either strong or weak) significant deviations from game-theoretic predictions can occur, however. A good example is the case of extreme time pressure. In this case, highly nonlinear transients can occur if the deal reached by the adaptive agents approaches the extreme outcome predicted by game theory. Two other experimental observations should also be mentioned here. First, the finite horizon of the negotiations is not always fully exploited by the last agent in turn (even if time pressure is rather weak). In fact, the boundedly-rational agents often act as if the length of the game is actually much longer. This lends more support to the "infinite-horizon" assumption frequently employed in game-theoretic work. This approximation may yield surprisingly accurate results when the agents do not perceive the deadline of the negotiations. Second, we observe (and explain) discrepancies between theory and experiment if the agents experience an unequal time pressure. More in general, this work presents a systematic validation of evolutionary and computational techniques in the field of bargaining. Our model has also served as a starting point for further explorations. Several important topics have been addressed in these works: complex multi-issue and multi-opponent bargaining problems, economic modelling issues, learning by co-evolution, the development of powerful bargaining strategies, etc. We hope that these different lines of research will be extended further in future works

An evolutionary intra-marriage bargaining model.

Chan, Kin Cheong.Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.Includes bibliographical references (leaves 42-44).Abstracts in English and Chinese.Abstracts --- p.iAcknowledgements --- p.iiiChapter 1 --- Introduction --- p.1Chapter 2 --- Literature Review --- p.4Chapter 2.1 --- lntra-Marriage Bargaining --- p.4Chapter 2.2 --- Evolutionary Analysis of Bargaining Models --- p.6Chapter 3 --- The Model --- p.8Chapter 3.1 --- Equilibrium --- p.9Chapter 4 --- Equlibrium Selection --- p.15Chapter 4.1 --- Convergence --- p.18Chapter 4.2 --- Mistake and Experimentation --- p.19Chapter 4.3 --- Nash Bargaining Solution --- p.26Chapter 5 --- Heterogeneous Popoluations --- p.30Chapter 6 --- Discussion --- p.33Appendix --- p.35Reference --- p.4

A bargaining model of legislative policy-making

We present a general model of legislative bargaining in which the status quo is an arbitrary point in a multidimensional policy space. In contrast to other bargaining models, the status quo is not assumed to be “bad,” and delay may be Pareto efficient. We prove existence of stationary equilibria. The possibility of equilibrium delay depends on four factors: risk aversion of the legislators, the dimensionality of the policy space, the voting rule, and the possibility of transfers across districts. If legislators are risk averse, if there is more than one policy dimension, and if voting is by majority rule, for example, then delay will almost never occur. In one dimension, delay is possible if and only if the status quo lies in the core of the voting rule, and then it is the only possible outcome. This "core selection" result yields a game-theoretic foundation for the well-known median voter theorem. Our comparative statics analysis yield two noteworthy insights: (i) if the status quo is close to the core, then equilibrium policy outcomes will also be close to the core (a moderate status quo produces moderate policy outcomes), and (ii) if legislators are patient, then equilibrium proposals will be close to the core (legislative patience leads to policy moderation)

A General Bargaining Model of Legislative Policy-making

We present a general model of legislative bargaining in which the status quo is an arbitrary point in a multidimensional policy space. In contrast to other bargaining models, the status quo is not assumed to be bad for all legislators, and delay may be Pareto efficient. We prove existence of stationary equilibria. We show that if all legislators are risk averse or if even limited transfers are possible, then delay is only possible if the status quo lies in the core. Thus, we expect immediate agreement in multidimensional models, where the core is typically empty. In one dimension, delay is possible if and only if the status quo lies in the core of the voting rule, and then it is the only possible outcome. Our comparative statics analysis yield two noteworthy insights: moderate status quos imply moderate policy outcomes, and legislative patience implies policy moderation

A comparative study of game theoretic and evolutionary models for software agents

Most of the existing work in the study of bargaining behaviour uses techniques from game theory. Game theoretic models for bargaining assume that players are perfectly rational and that this rationality in common knowledge. However, the perfect rationality assumption does not hold for real-life bargaining scenarios with humans as players, since results from experimental economics show that humans find their way to the best strategy through trial and error, and not typically by means of rational deliberation. Such players are said to be boundedly rational. In playing a game against an opponent with bounded rationality, the most effective strategy of a player is not the equilibrium strategy but the one that is the best reply to the opponent's strategy. The evolutionary model provides a means for studying the bargaining behaviour of boundedly rational players. This paper provides a comprehensive comparison of the game theoretic and evolutionary approaches to bargaining by examining their assumptions, goals, and limitations. We then study the implications of these differences from the perspective of the software agent developer