Equilibrium Selection In Evolutionary Bargaining Models

The rapid growth of a global communication network together with the establishment of standard negotiation protocols currently leads to the development of multi-agent architectures in which artificial agents can negotiate on behalf of their users [1]. It is to be expected that the complexity of these kinds of systems will strongly increase if such bargaining agents become able to adapt their behavior. This raises two important and fundamental questions which we will address in this paper: (i) which complex dynamic behavior will emerge in systems with adaptive bargaining agents, and (ii) to which state will these systems converge over time.These issues are studied in a computational setting by using evolutionary algorithms (EAs). EAs are widely regarded to be an attractive tool to model collective learning in societies of boundedly rational agents [4, 2]. Negotiations between the agents are governed by a finite-horizon version of the "alternating-offers" protocol [5]. 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.Our simulations show that game theory can be used successfully to interpret the equilibrium-selecting behavior observed in computational experiments with bargaining agents. Deviations from classical game theory were, however, observed in several experiments. We encountered, for instance, strongly nonlinear oscillations in short bargaining games, a phenomenon not predicted by game theory. Also, in bargaining situations where players have identical, but weak, time preferences, or when a slight risk of premature breakdown exists, the finite horizon of the game is not fully exploited by the adaptive agents. Instead, the long-term bargaining outcome is very close to the prediction of Rubinstein's infinite-horizon model. Furthermore, in experiments with asymmetric time preferences we found that the agent in the strongest bargaining position does not always fully exploit his bargaining power (e.g., by proposing a take-it-or-leave-it deal in the last round), being under pressure by his opponent to reach an early agre ement.In a companion paper [3] this work is extended to negotiations over multiple issues, a particularly important aspect of electronic trading.References[1] K. Binmore and N. Vulkan. Applying game theory to automated negotiation. Netnomics, Vol. 1(1):1-9, 1999.[2] H. Dawid. Adaptive Learning by Genetic Algorithms: Analytical Results and Applications to Economic Models. Lecture Notes in Economics and Mathematical Systems, No. 441. Springer-Verlag, Berlin, 1996.[3] E.H. Gerding, D.D.B. van Bragt, and J.A. La Poutr'e. Multi-issue negotiation processes by evolutionary simulation (forthcoming).[4] T. Reichmann. Learning and behavioral stability: an economic interpretation of genetic algorithms. Journal of Evolutionary Economics, 9(2), 1999.[5] A. Rubinstein. Perfect equilibrium in a bargaining model. Econometrica, 50(1):155-162, 1982.