## Tesi etd-04262007-104745 |

Thesis type

Tesi di dottorato di ricerca

Author

Angelini, Natascia

URN

etd-04262007-104745

Title

COMPLEX DYNAMICS IN A CLASS OF DUOPOLY MODELS WITH HETEROGENEOUS FIRMS: PRODUCTION DECISIONS, COSTS AND MARKET SHARES

Settore scientifico disciplinare

SECS-S/06

Corso di studi

MATEMATICA PER LE DECISIONI ECONOMICHE

Supervisors

**Relatore**Prof. Nardini, Franco

Parole chiave

- Dynamic duopoly
- cumulated profits
- basins of attraction
- heterogeneous behavioral rules

Data inizio appello

15/12/2006;

Consultabilità

Parziale

Data di rilascio

15/12/2046

Riassunto analitico

In this thesis we consider a class of simple dynamic duopoly models in discrete-time, where the demand of the homogeneous good is assumed to be isoelastic. In each period both firms form naïve expectations about the opponent's next period output, whereas firms are assumed - in general - to be heterogeneous both with regard to their behavioral rules (production decisions) and in terms of their cost functions. As far as behavioral rules are concerned, we pay particular attention to the case where both firms adopt a best reply strategy and the case where one of the firms uses best reply while the other firm changes gradually its output towards increasing profit. The latter specifications deal with the case where at least one of the firms is unable to make large quantity and price changes during a single time period.

We perform bifurcations analysis with respect to the parameters which characterize the cost functions. We also analyze the impact of the speeds of adjustment in the case of gradual output changes. It turns out that the simple interactions designed in these models are able to produce complex asymptotic dynamics and coexisting attractors under very wide ranges of parameters.

While at the Cournot-Nash equilibrium the long-run market share is inversely related to the gap between the marginal costs of the two firms, when the Cournot-Nash equilibrium is unstable and other attracting sets exist in the phase-space, the effect of the cost structure is not that clear in general. In particular, when firms adopt heterogeneous behavioral rules, the adjustment parameters seem to play a major impact on the long run market power and the on the structure of the basins of attraction.

We perform bifurcations analysis with respect to the parameters which characterize the cost functions. We also analyze the impact of the speeds of adjustment in the case of gradual output changes. It turns out that the simple interactions designed in these models are able to produce complex asymptotic dynamics and coexisting attractors under very wide ranges of parameters.

While at the Cournot-Nash equilibrium the long-run market share is inversely related to the gap between the marginal costs of the two firms, when the Cournot-Nash equilibrium is unstable and other attracting sets exist in the phase-space, the effect of the cost structure is not that clear in general. In particular, when firms adopt heterogeneous behavioral rules, the adjustment parameters seem to play a major impact on the long run market power and the on the structure of the basins of attraction.

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