Evolutionary oligopoly games with cooperative and aggressive behaviors
- PDF / 883,779 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 94 Downloads / 188 Views
Evolutionary oligopoly games with cooperative and aggressive behaviors Gian Italo Bischi1 · Fabio Lamantia2,3 Received: 10 April 2020 / Accepted: 15 August 2020 © The Author(s) 2020
Abstract We propose an oligopoly model where players can choose between two kinds of behaviors, denoted as cooperative and aggressive, respectively. Each cooperative agent chooses the quantity to produce in order to maximize her own profit as well as the profits of other agents (at least partially), whereas an aggressive player decides the quantity to produce by maximizing his own profit while damaging (at least partially) competitors’ profits. At each discrete time, players face a binary choice to select the kind of behavior to adopt, according to a proportional imitation rule, expressed by a replicator equation based on a comparison between accumulated profits. This means that the behavioral decisions are driven by an evolutionary process where fitness is measured in terms of current profits as well as a weighted sum of past gains. The model proposed is expressed by a nonlinear two-dimensional iterated map, whose asymptotic behavior describes the long-run population distribution of cooperative and aggressive agents. We show under which conditions one of the following long-run behaviors prevails: (i) all players choose the same strategy; (ii) both behaviors coexist according to a mixed stationary equilibrium; and (iii) a self-sustained (i.e. endogenous) oscillatory (periodic or chaotic) time pattern occurs. The influence of memory and that of the levels of cooperative/aggressive attitudes on the dynamics are analyzed as well. Keywords Oligopoly games · Partial cooperation · Replicator dynamics · Discrete dynamical systems · Stability · Bifurcations
B
Fabio Lamantia [email protected] Gian Italo Bischi [email protected]
1
Department of Economics, Society, Politics (DESP), University of Urbino, Urbino, Italy
2
Department of Economics, Statistics and Finance (DESF), University of Calabria, Rende, Italy
3
Faculty of Economics, VŠB Technical University of Ostrava, Ostrava, Czech Republic
123
G. Bischi, F. Lamantia
1 Introduction In classical oligopoly models, the goal of each firm is to maximize (or at least to increase) its own profits. Typically in these models, strategic interaction only occurs indirectly because of the influence of competitors’ decisions on economic quantities regarding other competitors, such as the market price through the demand function or the production costs through cost externalities [for example, in the presence of spillover effects, see, e.g., D’Aspremont and Jacquemin (1988)]. However, even direct strategic interaction may be considered if some firms in the oligopoly market include (at least partially) competitors’ profits in their own objective function they wish to maximize (or increase). Following this idea, Cyert and DeGroot (1973) introduce partial cooperation by inserting a fraction of competitors’ profit (modulated by a coefficient of cooperation) in each objective function (see a
Data Loading...
