Equilibria, stability and asymptotic dominance in a speculative market with heterogeneous traders

Abstract

We consider a simple pure exchange economy with two assets: one riskless, yielding a constant return on investment, and the other risky, paying a stochastic dividend. Trading takes place in discrete time and in each trading period the price of the risky asset is fixed by imposing a market clearing condition on the sum of individual demand functions. Individual demand for the risky asset is expressed as a fraction of wealth and depends on how traders forecast future price movement. Under these assumptions we derive the stochastic dynamical system describing the evolution of price and wealth.We study the set of equilibria of this system for the case when arbitrarily many heterogeneous agents operate in the market, and we provide an asymptotic characterization of their relative performance. Abstracting from precise specification of agents' investment decisions, we show that all possible equilibrium returns belong to a one-dimensional "Equilibrium Market Line". It turns out that the system possesses isolated equilibria where a single agent dominates the market and continuous manifolds of equilibria where many agents hold finite wealth shares. The mechanism via which the market endogenously selects the dominant traders displays an optimal character in the neighborhood of the equilibria, but, at the same time, leads to the impossibility of defining a global dominance order relation among strategies.JEL codes: G12, D83.

Complex Evolutionary Systems in Behavioral Finance

“…Figure 1.15 illustrates the individual degree of overreaction for the different groups. In the case of monotonic convergence (groups 2 and 5), there is no overreaction; in the case of permanent oscillations (groups 1,6,8,9) a majority of subjects shows some overreaction, but it is relatively small. In the case of dampened oscillations (groups 4, 7 and 10), with large temporary bubbles in the initial phases of the experiment, a majority of participants strongly overreacts.…”

“…As the intensity of choice increases, the fundamental steady state becomes unstable due to a pitchfork bifurcation in which two additional non-fundamental steady states −x * < 0 < x * are created. As the intensity of choice increases further, the two non-fundamental steady states also become unstable due to a Hopf-bifurcation, and limit cycles or even strange attractors can arise around each of the (unstable) non-fundamental steady states 9 . The evolutionary ABS may cycle around the positive non-fundamental steady state, cycle around the negative non-fundamental steady state or, driven by the noise, switch back and forth between cycles around the high and the low steady state, as illustrated in Figure 1.1.…”

Evolution and market behavior with endogenous investment rules

“…Both gaps have been partially filled by our previous works, see e.g. Anufriev and Bottazzi (2010), Anufriev et al (2006) or Anufriev and Dindo (2010), which study wealth-driven market selection on the general class of price dependent investment rules. Nevertheless, those works, being based on an essentially deterministic framework, do not tackle the information efficiency issue we are interested here.…”

“…No matter the shape of the investment rules, both single survivor and multiple survivors equilibria lie on the diagonal of the plot with coordinates α(p) and p. For analogies with previous works (Anufriev et al, 2006;Anufriev and Bottazzi, 2010;Anufriev and Dindo, 2010) we name it the "Equilibrium Market Curve" (EMC) to stress that it is the locus of all long-run market equilibria.…”

Wealth-driven competition in a speculative financial market: examples with maximizing agents

“…An important step in the direction of a general framework has been made in Anufriev, Bottazzi, and Pancotto (2006) and Anufriev and Bottazzi (2005), where some analytic results are obtained for a market populated by an arbitrarily large number of technical traders whose possible demand functions belong to a relatively large set. The only imposed restriction on the individual demand functions is that they have to be proportional to the current wealth.…”