Dynamic Unstructured Bargaining with Private Information: Theory, Experiment, and Outcome Prediction via Machine Learning

We study dynamic unstructured bargaining with deadlines and one-sided private information about the amount available to share (the “pie size”). Using mechanism design theory, we show that given the players’ incentives, the equilibrium incidence of bargaining failures (“strikes”) should increase with the pie size, and we derive a condition under which strikes are efficient. In our setting, no equilibrium satisfies both equality and efficiency in all pie sizes. We derive two equilibria that resolve the trade-off between equality and efficiency by favoring either equality or efficiency. Using a novel experimental paradigm, we confirm that strike incidence is decreasing in the pie size. Subjects reach equal splits in small pie games (in which strikes are efficient), while most payoffs are close to either the efficient or the equal equilibrium prediction, when the pie is large. We employ a machine learning approach to show that bargaining process features recorded early in the game improve out-of-sample prediction of disagreements at the deadline. The process feature predictions are as accurate as predictions from pie sizes only, and adding process and pie data together improves predictions even more

Evolutive equilibrium selection II: quantal response mechanisms

In this paper we develop a model of Evolutive Quantal Response (EQR) mechanisms, and contrast the outcomes with the Quantal Response Equilibria (QRE) as developed by McKelvey and Palfrey(1995). A clear distinction between the two approaches can be noted; EQR is based on a dynamic formulation of individual choice in the context of evolutionary game theory in which games are played repeatedly in populations, and the aim is to determine both the micro-configuration of strategy choices across the population, and the dynamics of the population frequencies of the strategies played. Quantal Response Equilibria focuses on the more traditional aspects of non-co-operative game theory, i.e. on equilibrium in beliefs regarding strategies.We focus attention on an analytical approach which enables closed form solutions to be constructed. We consider the case of all symmetric binary choice games, which will include analysis of all well known generic games in this context, such as Prisoner's dilemma, Stag-Hunt and Pure coordination games

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

Bargaining with Endogenous Deadlines

We develop a two-person negotiation model with complete information which makes endogenous both the deadline and the level of surplus destruction after the deadline. We show that the equilibrium outcome is always unique but might be inefficient. Moreover, as the bargaining period becomes short or as the players become very patient, the unique outcome is always inefficientbargaining;alternating-offers;deadlines;complete infomation

Bilateral negotiation of a meeting point in a maze: Demonstration

International audienceNegotiation between agents aims at reaching an agreement in which the conflicting interests of agents are accommodated. In this demonstration, we present a concrete negotiation scenario where two agents are situated in a maze and the negotiation outcome is a cell where they will meet. Their individual preferences match with a minimal distance computed from their partial knowledge of the environment. We illustrate a bargaining protocol which allows agents to submit several proposals at the same round and a negotiation strategy which consists in starting from the best deal for the agent and then concedes. The path between the agents emerges from the repeated negotiations

Limit Solutions for Finite Horizon Bargaining Problems

We investigate a random proposer bargaining game with a dead line. A bounded time interval is divided into bargaining periods of equal length and we study the limit of the subgame perfect equilibrium outcome as the number of bargaining periods goes to infinity while the dead line is kept fixed. This limit is close to the Raiffa solution when the time horizon is very short. If the dead line goes to infinity the limit outcome converges to the time preference Nash solution. The limit outcome is given an axiomatic characterization as well.Nash solution, Raiffa solution, bargaining

A non-cooperative foundation for the continuous Raiffa solution

This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl–Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player’s opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes

Optimal deadlines for agreements

Costly delay in negotiations can induce the negotiating parties to be more forthcoming with their information and improve the quality of the collective decision. Imposing a deadline may result in stalling, in which players at some point stop making concessions but switch back to conceding at the end, or a deadlock, in which concessions end permanently. Extending the deadline hurts the players in the first case but is beneficial in the second. When the initial conflict between the negotiating parties is intermediate, the optimal deadline is positive and finite, and is characterized by the shortest time that would allow efficient information aggregation in equilibrium.Repeated proposals, war of attrition, interdependent values

Bargaining with History Dependent Preferences

We study perfect information bilateral bargaining game with an infinite alternating-offers procedure, in which we add an assumption of history dependent preference. A player will devalue a share which gives her strictly lower discounted utility than what she was offered in earlier stages of the bargaining, namely, a ``worse off'' outcome. In a strong version of the assumption, each player prefers impasse to any ``worse off'' outcome. We characterize the essentially unique subgame perfect equilibrium path under the assumption. The equilibrium entails considerable delay and efficiency loss. As the players become infinitely patient, the efficiency loss goes to one half, and the equilibrium share goes to Nash solution. The assumption can also be weakened. We provide a sufficient condition on the extent of devaluation under which the feature of the equilibrium from strong assumption remainsBargaining, Delay, History Dependent Preference, Endogenous Commitment