Law of Large Numbers for Dynamic Bargaining Markets

Abstract

We describe the random meeting motion of a finite number of investors in markets with friction as a Markov pure-jump process with interactions. Using a sequence of these, we prove a functional law of large numbers relating the large motions with the finite market of the so-called continuum of agents.

Information Percolation in Segmented Markets

“…6 See also Ferland and Giroux (2008). Taking G to be the set of agents, we assume throughout the joint measurability of agents' type processes {θ it : i ∈ G} with respect to a σ-algebra B on Ω × G that allows the Fubini property that, for any measurable subset A of types,…”

Some New Results on Information Percolation

“…For simplicity, we now assume that (E, E) = (R d , B R d ). In such a setting, we can deduce, from this sequence of processes, an associated system of ODE's using the same techniques as in Ferland and Giroux [11] (see also Bezandry et al [1]). This implies that, for each time t, the laws of the sequence (X N 1 (t)) N ≥m converge to the probability law µ t where µ t is the solution of the Cauchy problem for the associated system of ODE's: We can think of µ •m t as the law at the root of the m-ary tree with only one interaction.…”

“…) n is the probability of having n branchings up to time t. The uniqueness of the solution follows from a standard application of Grönwall's lemma (see Ferland and Giroux [11]).…”

Some new results on information percolation

“…In such a setting, we can deduce, from this sequence of processes, an associated system of ODE's using the same techniques as in Ferland and Giroux [11] (see also Bezandry et al [1]). This implies that, for each time t, the laws of the sequence (X N 1 (t)) N ≥m converge to the probability law µ t where µ t is the solution of the Cauchy problem for the associated system of ODE's:…”

“…is the number of trees with n nodes, taking into account their branching orders; and p n (t) = #m(n) (m−1) n n! e −λt (1 − e −(m−1)λt ) n is the probability of having n branchings up to time t. The uniqueness of the solution follows from a standard application of Grönwall's lemma (see Ferland and Giroux [11]).…”