Evolution, dynamics, and fixed points

Sign-compatible dynamics describe changes in the composition of a population driven by differences in fitness. A saturated equilibrium is a fixed point for sign-compatible dynamics where each subgroup with positive population share has highest fitness. An evolutionary stable equilibrium is a saturated equilibrium attracting all trajectories nearby, such that the Euclidean distance to it decreases monotonically. We address existence, multiplicity, and dynamical stability of fixed points of sign-compatible dynamics. A saturated equilibrium may be approximated by using a variable dimension restart algorithm for solving the nonlinear complementarity problem. Journal of Economic Literature Classification Numbers: C62, C68, C72, C73. Keywords: Sign-compatible population dynamics, saturated equilibrium, evolutionary stable equilibrium, dynamic stability, nonlinear complementarity problem.mathematical economics and econometrics

Consensus as a Nash Equilibrium of a Dynamic Game

Consensus formation in a social network is modeled by a dynamic game of a prescribed duration played by members of the network. Each member independently minimizes a cost function that represents his/her motive. An integral cost function penalizes a member's differences of opinion from the others as well as from his/her own initial opinion, weighted by influence and stubbornness parameters. Each member uses its rate of change of opinion as a control input. This defines a dynamic non-cooperative game that turns out to have a unique Nash equilibrium. Analytic explicit expressions are derived for the opinion trajectory of each member for two representative cases obtained by suitable assumptions on the graph topology of the network. These trajectories are then examined under different assumptions on the relative sizes of the influence and stubbornness parameters that appear in the cost functions.Comment: 7 pages, 9 figure, Pre-print from the Proceedings of the 12th International Conference on Signal Image Technology and Internet-based Systems (SITIS), 201

Learning-by-Doing, Organizational Forgetting, and Industry Dynamics

Learning-by-doing and organizational forgetting have been shown to be important in a variety of industrial settings. This paper provides a general model of dynamic competition that accounts for these economic fundamentals and shows how they shape industry structure and dynamics. Previously obtained results regarding the dominance properties of firms' pricing behavior no longer hold in this more general setting. We show that forgetting does not simply negate learning. Rather, learning and forgetting are distinct economic forces. In particular, a model with learning and forgetting can give rise to aggressive pricing behavior, market dominance, and multiple equilibria, whereas a model with learning alone cannot.

A simple framework for investigating the properties of policy games

The paper extensively studies the static model of non-cooperative linear quadratic games in which a set of agents chooses their instruments strategically to minimize their linear quadratic criterion. We first derive the necessary and sufficient conditions for the existence of a Nash equilibrium as well as for multiple equilibria to arise. Furthermore, we study the general condition for policy neutrality and Pareto efficiency of the equilibrium by introducing a new concept of decisiveness.Conflict of interest, Nash equilibrium existence, multiplicity, policy invariance, controllability, Pareto efficiency

Inflation versus taxation: Representative democracy and party nominations

Public Finance;Taxation;Inflation

Modelling Negotiated Decision Making: a Multilateral, Multiple Issues, Non-Cooperative Bargaining Model with Uncertainty

The relevance of bargaining to everyday life can easily be ascertained, yet the study of any bargaining process is extremely hard, involving a multiplicity of questions and complex issues. The objective of this paper is to provide new insights on some dimensions of the bargaining process – asymmetries and uncertainties in particular – by using a non-cooperative game theory approach. We develop a computational model which simulates the process of negotiation among more than two players, who bargain over the sharing of more than one pie. Through numerically simulating several multiple issues negotiation games among multiple players, we identify the main features of players’ optimal strategies and equilibrium agreements. As in most economic situations, uncertainty crucially affects also bargaining processes. Therefore, in our analysis, we introduce uncertainty over the size of the pies to be shared and assess the impacts on players’ strategic behaviour. Our results confirm that uncertainty crucially affects players’ behaviour and modifies the likelihood of a self-enforcing agreement to emerge. The model proposed here can have several applications, in particular in the field of natural resource management, where conflicts over how to share a resource of a finite size are increasing.Bargaining, Non-Cooperative Game Theory, Simulation Models, Uncertainty