{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Markov Perfect Equilibrium\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Markov Perfect Equilibrium](#Markov-Perfect-Equilibrium) \n", " - [Overview](#Overview) \n", " - [Background](#Background) \n", " - [Linear Markov perfect equilibria](#Linear-Markov-perfect-equilibria) \n", " - [Application](#Application) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "\n", "\n", "This lecture describes the concept of Markov perfect equilibrium.\n", "\n", "Markov perfect equilibrium is a key notion for analyzing economic problems involving dynamic strategic interaction, and a cornerstone of applied game theory.\n", "\n", "In this lecture we teach Markov perfect equilibrium by example.\n", "\n", "We will focus on settings with\n", "\n", "- two players \n", "- quadratic payoff functions \n", "- linear transition rules for the state \n", "\n", "\n", "Other references include chapter 7 of [[LS18]](../zreferences.html#ljungqvist2012)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using InstantiateFromURL\n", "# optionally add arguments to force installation: instantiate = true, precompile = true\n", "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using LinearAlgebra, Statistics, QuantEcon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Background\n", "\n", "\n", "\n", "Markov perfect equilibrium is a refinement of the concept of Nash equilibrium.\n", "\n", "It is used to study settings where multiple decision makers interact non-cooperatively over time, each seeking to pursue its own objective.\n", "\n", "The agents in the model face a common state vector, the time path of which is influenced by – and influences – their decisions.\n", "\n", "In particular, the transition law for the state that confronts each agent is affected by decision rules of other agents.\n", "\n", "Individual payoff maximization requires that each agent solve a dynamic programming problem that includes this transition law.\n", "\n", "Markov perfect equilibrium prevails when no agent wishes to revise its policy, taking as given the policies of all other agents.\n", "\n", "Well known examples include\n", "\n", "- Choice of price, output, location or capacity for firms in an industry (e.g., [[EP95]](../zreferences.html#ericson1995markov), [[Rya12]](../zreferences.html#ryan2012costs), [[DS10]](../zreferences.html#doraszelski2010computable)). \n", "- Rate of extraction from a shared natural resource, such as a fishery (e.g., [[LM80]](../zreferences.html#levhari1980great), [[VL11]](../zreferences.html#van2011dynamic)). \n", "\n", "\n", "Let’s examine a model of the first type." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: A duopoly model\n", "\n", "Two firms are the only producers of a good the demand for which is governed by a linear inverse demand function\n", "\n", "\n", "\n", "$$\n", "p = a_0 - a_1 (q_1 + q_2) \\tag{1}\n", "$$\n", "\n", "Here $ p = p_t $ is the price of the good, $ q_i = q_{it} $ is the output of firm $ i=1,2 $ at time $ t $ and $ a_0 > 0, a_1 >0 $.\n", "\n", "In [(1)](#equation-game2) and what follows,\n", "\n", "- the time subscript is suppressed when possible to simplify notation \n", "- $ \\hat x $ denotes a next period value of variable $ x $ \n", "\n", "\n", "Each firm recognizes that its output affects total output and therefore the market price.\n", "\n", "The one-period payoff function of firm $ i $ is price times quantity minus adjustment costs:\n", "\n", "\n", "\n", "$$\n", "\\pi_i = p q_i - \\gamma (\\hat q_i - q_i)^2, \\quad \\gamma > 0 , \\tag{2}\n", "$$\n", "\n", "Substituting the inverse demand curve [(1)](#equation-game2) into [(2)](#equation-game1) lets us express the one-period payoff as\n", "\n", "\n", "\n", "$$\n", "\\pi_i(q_i, q_{-i}, \\hat q_i) = a_0 q_i - a_1 q_i^2 - a_1 q_i q_{-i} - \\gamma (\\hat q_i - q_i)^2 , \\tag{3}\n", "$$\n", "\n", "where $ q_{-i} $ denotes the output of the firm other than $ i $.\n", "\n", "The objective of the firm is to maximize $ \\sum_{t=0}^\\infty \\beta^t \\pi_{it} $.\n", "\n", "Firm $ i $ chooses a decision rule that sets next period quantity $ \\hat q_i $ as a function $ f_i $ of the current state $ (q_i, q_{-i}) $.\n", "\n", "An essential aspect of a Markov perfect equilibrium is that each firm takes the decision rule of the other firm as known and given.\n", "\n", "Given $ f_{-i} $, the Bellman equation of firm $ i $ is\n", "\n", "\n", "\n", "$$\n", "v_i(q_i, q_{-i}) = \\max_{\\hat q_i}\n", " \\left\\{\\pi_i (q_i, q_{-i}, \\hat q_i) + \\beta v_i(\\hat q_i, f_{-i}(q_{-i}, q_i)) \\right\\} \\tag{4}\n", "$$\n", "\n", "**Definition** A *Markov perfect equilibrium* of the duopoly model is a pair of value functions $ (v_1, v_2) $ and a pair of policy functions $ (f_1, f_2) $ such that, for each $ i \\in \\{1, 2\\} $ and each possible state,\n", "\n", "- The value function $ v_i $ satisfies the Bellman equation [(4)](#equation-game4). \n", "- The maximizer on the right side of [(4)](#equation-game4) is equal to $ f_i(q_i, q_{-i}) $. \n", "\n", "\n", "The adjective “Markov” denotes that the equilibrium decision rules depend only on the current values of the state variables, not other parts of their histories.\n", "\n", "“Perfect” means complete, in the sense that the equilibrium is constructed by backward induction and hence builds in optimizing behavior for each firm at all possible future states.\n", "\n", "> - These include many states that will not be reached when we iterate forward on the pair of equilibrium strategies $ f_i $ starting from a given initial state. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computation\n", "\n", "One strategy for computing a Markov perfect equilibrium is iterating to convergence on pairs of Bellman equations and decision rules.\n", "\n", "In particular, let $ v_i^j,f_i^j $ be the value function and policy function for firm $ i $ at the $ j $-th iteration.\n", "\n", "Imagine constructing the iterates\n", "\n", "\n", "\n", "$$\n", "v_i^{j+1}(q_i, q_{-i}) = \\max_{\\hat q_i}\n", " \\left\\{\\pi_i (q_i, q_{-i}, \\hat q_i) + \\beta v^j_i(\\hat q_i, f_{-i}(q_{-i}, q_i)) \\right\\} \\tag{5}\n", "$$\n", "\n", "These iterations can be challenging to implement computationally.\n", "\n", "However, they simplify for the case in which the one-period payoff functions are quadratic and the transition laws are linear — which takes us to our next topic." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Markov perfect equilibria\n", "\n", "\n", "\n", "As we saw in the duopoly example, the study of Markov perfect equilibria in games with two players leads us to an interrelated pair of Bellman equations.\n", "\n", "In linear quadratic dynamic games, these “stacked Bellman equations” become “stacked Riccati equations” with a tractable mathematical structure.\n", "\n", "We’ll lay out that structure in a general setup and then apply it to some simple problems." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coupled linear regulator problems\n", "\n", "We consider a general linear quadratic regulator game with two players.\n", "\n", "For convenience, we’ll start with a finite horizon formulation, where $ t_0 $ is the initial date and $ t_1 $ is the common terminal date.\n", "\n", "Player $ i $ takes $ \\{u_{-it}\\} $ as given and minimizes\n", "\n", "\n", "\n", "$$\n", "\\sum_{t=t_0}^{t_1 - 1}\n", "\\beta^{t - t_0}\n", "\\left\\{\n", " x_t' R_i x_t +\n", " u_{it}' Q_i u_{it} +\n", " u_{-it}' S_i u_{-it} +\n", " 2 x_t' W_i u_{it} +\n", " 2 u_{-it}' M_i u_{it}\n", "\\right\\} \\tag{6}\n", "$$\n", "\n", "while the state evolves according to\n", "\n", "\n", "\n", "$$\n", "x_{t+1} = A x_t + B_1 u_{1t} + B_2 u_{2t} \\tag{7}\n", "$$\n", "\n", "Here\n", "\n", "- $ x_t $ is an $ n \\times 1 $ state vector and $ u_{it} $ is a $ k_i \\times 1 $ vector of controls for player $ i $ \n", "- $ R_i $ is $ n \\times n $ \n", "- $ S_i $ is $ k_{-i} \\times k_{-i} $ \n", "- $ Q_i $ is $ k_i \\times k_i $ \n", "- $ W_i $ is $ n \\times k_i $ \n", "- $ M_i $ is $ k_{-i} \\times k_i $ \n", "- $ A $ is $ n \\times n $ \n", "- $ B_i $ is $ n \\times k_i $ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing Equilibrium\n", "\n", "We formulate a linear Markov perfect equilibrium as follows.\n", "\n", "Player $ i $ employs linear decision rules $ u_{it} = - F_{it} x_t $, where $ F_{it} $ is a $ k_i \\times n $ matrix.\n", "\n", "A Markov perfect equilibrium is a pair of sequences $ \\{F_{1t}, F_{2t}\\} $ over $ t = t_0, \\ldots, t_1 - 1 $ such that\n", "\n", "- $ \\{F_{1t}\\} $ solves player 1’s problem, taking $ \\{F_{2t}\\} $ as given, and \n", "- $ \\{F_{2t}\\} $ solves player 2’s problem, taking $ \\{F_{1t}\\} $ as given \n", "\n", "\n", "If we take $ u_{2t} = - F_{2t} x_t $ and substitute it into [(6)](#equation-orig-1) and [(7)](#equation-orig-0), then player 1’s problem becomes minimization of\n", "\n", "\n", "\n", "$$\n", "\\sum_{t=t_0}^{t_1 - 1}\n", "\\beta^{t - t_0}\n", " \\left\\{\n", " x_t' \\Pi_{1t} x_t +\n", " u_{1t}' Q_1 u_{1t} +\n", " 2 u_{1t}' \\Gamma_{1t} x_t\n", " \\right\\} \\tag{8}\n", "$$\n", "\n", "subject to\n", "\n", "\n", "\n", "$$\n", "x_{t+1} = \\Lambda_{1t} x_t + B_1 u_{1t}, \\tag{9}\n", "$$\n", "\n", "where\n", "\n", "- $ \\Lambda_{it} := A - B_{-i} F_{-it} $ \n", "- $ \\Pi_{it} := R_i + F_{-it}' S_i F_{-it} $ \n", "- $ \\Gamma_{it} := W_i' - M_i' F_{-it} $ \n", "\n", "\n", "This is an LQ dynamic programming problem that can be solved by working backwards.\n", "\n", "The policy rule that solves this problem is\n", "\n", "\n", "\n", "$$\n", "F_{1t}\n", "= (Q_1 + \\beta B_1' P_{1t+1} B_1)^{-1}\n", "(\\beta B_1' P_{1t+1} \\Lambda_{1t} + \\Gamma_{1t}) \\tag{10}\n", "$$\n", "\n", "where $ P_{1t} $ solves the matrix Riccati difference equation\n", "\n", "\n", "\n", "$$\n", "P_{1t} =\n", "\\Pi_{1t} -\n", "(\\beta B_1' P_{1t+1} \\Lambda_{1t} + \\Gamma_{1t})' (Q_1 + \\beta B_1' P_{1t+1} B_1)^{-1}\n", "(\\beta B_1' P_{1t+1} \\Lambda_{1t} + \\Gamma_{1t}) +\n", "\\beta \\Lambda_{1t}' P_{1t+1} \\Lambda_{1t} \\tag{11}\n", "$$\n", "\n", "Similarly, the policy that solves player 2’s problem is\n", "\n", "\n", "\n", "$$\n", "F_{2t} =\n", "(Q_2 + \\beta B_2' P_{2t+1} B_2)^{-1}\n", "(\\beta B_2' P_{2t+1} \\Lambda_{2t} + \\Gamma_{2t}) \\tag{12}\n", "$$\n", "\n", "where $ P_{2t} $ solves\n", "\n", "\n", "\n", "$$\n", "P_{2t} =\n", "\\Pi_{2t} - (\\beta B_2' P_{2t+1} \\Lambda_{2t} + \\Gamma_{2t})' (Q_2 + \\beta B_2' P_{2t+1} B_2)^{-1}\n", "(\\beta B_2' P_{2t+1} \\Lambda_{2t} + \\Gamma_{2t}) +\n", "\\beta \\Lambda_{2t}' P_{2t+1} \\Lambda_{2t} \\tag{13}\n", "$$\n", "\n", "Here in all cases $ t = t_0, \\ldots, t_1 - 1 $ and the terminal conditions are $ P_{it_1} = 0 $.\n", "\n", "The solution procedure is to use equations [(10)](#equation-orig-3), [(11)](#equation-orig-4), [(12)](#equation-orig-5), and [(13)](#equation-orig-6), and “work backwards” from time $ t_1 - 1 $.\n", "\n", "Since we’re working backwards, $ P_{1t+1} $ and $ P_{2t+1} $ are taken as given at each stage.\n", "\n", "Moreover, since\n", "\n", "- some terms on the right hand side of [(10)](#equation-orig-3) contain $ F_{2t} $ \n", "- some terms on the right hand side of [(12)](#equation-orig-5) contain $ F_{1t} $ \n", "\n", "\n", "we need to solve these $ k_1 + k_2 $ equations simultaneously." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Key insight\n", "\n", "A key insight is that equations [(10)](#equation-orig-3) and [(12)](#equation-orig-5) are linear in $ F_{1t} $ and $ F_{2t} $.\n", "\n", "After these equations have been solved, we can take $ F_{it} $ and solve for $ P_{it} $ in [(11)](#equation-orig-4) and [(13)](#equation-orig-6)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Infinite horizon\n", "\n", "We often want to compute the solutions of such games for infinite horizons, in the hope that the decision rules $ F_{it} $ settle down to be time invariant as $ t_1 \\rightarrow +\\infty $.\n", "\n", "In practice, we usually fix $ t_1 $ and compute the equilibrium of an infinite horizon game by driving $ t_0 \\rightarrow - \\infty $.\n", "\n", "This is the approach we adopt in the next section." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation\n", "\n", "We use the function [nnash](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/lqnash.jl) from [QuantEcon.jl](http://quantecon.org/quantecon-jl) that computes a Markov perfect equilibrium of the infinite horizon linear quadratic dynamic game in the manner described above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Application\n", "\n", "\n", "\n", "Let’s use these procedures to treat some applications, starting with the duopoly model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A duopoly model\n", "\n", "To map the duopoly model into coupled linear-quadratic dynamic programming problems, define the state\n", "and controls as\n", "\n", "$$\n", "x_t :=\n", "\\begin{bmatrix}\n", " 1 \\\\\n", " q_{1t} \\\\\n", " q_{2t}\n", "\\end{bmatrix}\n", "\\quad \\text{and} \\quad\n", "u_{it} :=\n", "q_{i,t+1} - q_{it}, \\quad i=1,2\n", "$$\n", "\n", "If we write\n", "\n", "$$\n", "x_t' R_i x_t + u_{it}' Q_i u_{it}\n", "$$\n", "\n", "where $ Q_1 = Q_2 = \\gamma $,\n", "\n", "$$\n", "R_1 :=\n", "\\begin{bmatrix}\n", " 0 & -\\frac{a_0}{2} & 0 \\\\\n", " -\\frac{a_0}{2} & a_1 & \\frac{a_1}{2} \\\\\n", " 0 & \\frac{a_1}{2} & 0\n", "\\end{bmatrix}\n", "\\quad \\text{and} \\quad\n", "R_2 :=\n", "\\begin{bmatrix}\n", " 0 & 0 & -\\frac{a_0}{2} \\\\\n", " 0 & 0 & \\frac{a_1}{2} \\\\\n", " -\\frac{a_0}{2} & \\frac{a_1}{2} & a_1\n", "\\end{bmatrix}\n", "$$\n", "\n", "then we recover the one-period payoffs in expression [(3)](#equation-game3).\n", "\n", "The law of motion for the state $ x_t $ is $ x_{t+1} = A x_t + B_1 u_{1t} + B_2 u_{2t} $ where\n", "\n", "$$\n", "A :=\n", "\\begin{bmatrix}\n", " 1 & 0 & 0 \\\\\n", " 0 & 1 & 0 \\\\\n", " 0 & 0 & 1\n", "\\end{bmatrix},\n", "\\quad\n", "B_1 :=\n", "\\begin{bmatrix}\n", " 0 \\\\\n", " 1 \\\\\n", " 0\n", "\\end{bmatrix},\n", "\\quad\n", "B_2 :=\n", "\\begin{bmatrix}\n", " 0 \\\\\n", " 0 \\\\\n", " 1\n", "\\end{bmatrix}\n", "$$\n", "\n", "The optimal decision rule of firm $ i $ will take the form $ u_{it} = - F_i x_t $, inducing the following closed loop system for the evolution of $ x $ in the Markov perfect equilibrium:\n", "\n", "\n", "\n", "$$\n", "x_{t+1} = (A - B_1 F_1 -B_1 F_2 ) x_t \\tag{14}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameters and Solution\n", "\n", "Consider the previously presented duopoly model with parameter values of:\n", "\n", "- $ a_0 = 10 $ \n", "- $ a_1 = 2 $ \n", "- $ \\beta = 0.96 $ \n", "- $ \\gamma = 12 $ \n", "\n", "\n", "From these we compute the infinite horizon MPE using the following code" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computed policies for firm 1 and firm 2:\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "F1 = [-0.6684661455442794 0.295124817744414 0.07584666305807419]\n", "F2 = [-0.6684661455442794 0.07584666305807419 0.295124817744414]\n" ] } ], "source": [ "using QuantEcon, LinearAlgebra\n", "\n", "# parameters\n", "a0 = 10.0\n", "a1 = 2.0\n", "β = 0.96\n", "γ = 12.0\n", "\n", "# in LQ form\n", "A = I + zeros(3, 3)\n", "B1 = [0.0, 1.0, 0.0]\n", "B2 = [0.0, 0.0, 1.0]\n", "\n", "R1 = [ 0.0 -a0 / 2.0 0.0;\n", " -a0 / 2.0 a1 a1 / 2.0;\n", " 0.0 a1 / 2.0 0.0]\n", "\n", "R2 = [ 0.0 0.0 -a0 / 2.0;\n", " 0.0 0.0 a1 / 2.0;\n", " -a0 / 2.0 a1 / 2.0 a1]\n", "\n", "Q1 = Q2 = γ\n", "S1 = S2 = W1 = W2 = M1 = M2 = 0.0\n", "\n", "# solve using QE's nnash function\n", "F1, F2, P1, P2 = nnash(A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2,\n", " beta=β)\n", "\n", "# display policies\n", "println(\"Computed policies for firm 1 and firm 2:\")\n", "println(\"F1 = $F1\")\n", "println(\"F2 = $F2\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Running the code produces the following output.\n", "\n", "One way to see that $ F_i $ is indeed optimal for firm $ i $ taking $ F_2 $ as given is to use [QuantEcon.jl](http://quantecon.org/quantecon-jl)’s LQ type.\n", "\n", "In particular, let’s take F2 as computed above, plug it into [(8)](#equation-eq-mpe-p1p) and [(9)](#equation-eq-mpe-p1d) to get firm 1’s problem and solve it using LQ.\n", "\n", "We hope that the resulting policy will agree with F1 as computed above" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "1×3 Array{Float64,2}:\n", " -0.668466 0.295125 0.0758467" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Λ1 = A - (B2 * F2)\n", "lq1 = QuantEcon.LQ(Q1, R1, Λ1, B1, bet=β)\n", "P1_ih, F1_ih, d = stationary_values(lq1)\n", "F1_ih" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is close enough for rock and roll, as they say in the trade.\n", "\n", "Indeed, isapprox agrees with our assessment" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isapprox(F1, F1_ih, atol=1e-7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dynamics\n", "\n", "Let’s now investigate the dynamics of price and output in this simple duopoly model under the MPE policies.\n", "\n", "Given our optimal policies $ F1 $ and $ F2 $, the state evolves according to [(14)](#equation-eq-mpe-cle).\n", "\n", "The following program\n", "\n", "- imports $ F1 $ and $ F2 $ from the previous program along with all parameters \n", "- computes the evolution of $ x_t $ using [(14)](#equation-eq-mpe-cle) \n", "- extracts and plots industry output $ q_t = q_{1t} + q_{2t} $ and price $ p_t = a_0 - a_1 q_t $ " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots\n", "gr(fmt=:png);\n", "\n", "AF = A - B1 * F1 - B2 * F2\n", "n = 20\n", "x = zeros(3, n)\n", "x[:, 1] = [1 1 1]\n", "for t in 1:n-1\n", " x[:, t+1] = AF * x[:, t]\n", "end\n", "q1 = x[2, :]\n", "q2 = x[3, :]\n", "q = q1 + q2 # total output, MPE\n", "p = a0 .- a1 * q # price, MPE\n", "\n", "plt = plot(q, color=:blue, lw=2, alpha=0.75, label=\"total output\")\n", "plot!(plt, p, color=:green, lw=2, alpha=0.75, label=\"price\")\n", "plot!(plt, title=\"Output and prices, duopoly MPE\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the initial condition has been set to $ q_{10} = q_{20} = 1.0 $.\n", "\n", "To gain some perspective we can compare this to what happens in the monopoly case.\n", "\n", "The first panel in the next figure compares output of the monopolist and industry output under the MPE, as a function of time.\n", "\n", "The second panel shows analogous curves for price\n", "\n", "\n", "\n", "\n", "\n", " \n", "Here parameters are the same as above for both the MPE and monopoly solutions.\n", "\n", "The monopolist initial condition is $ q_0 = 2.0 $ to mimic the industry initial condition $ q_{10} = q_{20} = 1.0 $ in the MPE case.\n", "\n", "As expected, output is higher and prices are lower under duopoly than monopoly." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Replicate the [pair of figures](#mpe-vs-monopolist) showing the comparison of output and prices for the monopolist and duopoly under MPE.\n", "\n", "Parameters are as in duopoly_mpe.jl and you can use that code to compute MPE policies under duopoly.\n", "\n", "The optimal policy in the monopolist case can be computed using [QuantEcon.jl](http://quantecon.org/quantecon-jl)’s LQ type." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "In this exercise we consider a slightly more sophisticated duopoly problem.\n", "\n", "It takes the form of infinite horizon linear quadratic game proposed by Judd [[Jud90]](../zreferences.html#judd1990).\n", "\n", "Two firms set prices and quantities of two goods interrelated through their demand curves.\n", "\n", "Relevant variables are defined as follows:\n", "\n", "- $ I_{it} $ = inventories of firm $ i $ at beginning of $ t $ \n", "- $ q_{it} $ = production of firm $ i $ during period $ t $ \n", "- $ p_{it} $ = price charged by firm $ i $ during period $ t $ \n", "- $ S_{it} $ = sales made by firm $ i $ during period $ t $ \n", "- $ E_{it} $ = costs of production of firm $ i $ during period $ t $ \n", "- $ C_{it} $ = costs of carrying inventories for firm $ i $ during $ t $ \n", "\n", "\n", "The firms’ cost functions are\n", "\n", "- $ C_{it} = c_{i1} + c_{i2} I_{it} + 0.5 c_{i3} I_{it}^2 $ \n", "- $ E_{it} = e_{i1} + e_{i2}q_{it} + 0.5 e_{i3} q_{it}^2 $ where $ e_{ij}, c_{ij} $ are positive scalars \n", "\n", "\n", "Inventories obey the laws of motion\n", "\n", "$$\n", "I_{i,t+1} = (1 - \\delta) I_{it} + q_{it} - S_{it}\n", "$$\n", "\n", "Demand is governed by the linear schedule\n", "\n", "$$\n", "S_t = D p_{it} + b\n", "$$\n", "\n", "where\n", "\n", "- $ S_t = \\begin{bmatrix} S_{1t} & S_{2t} \\end{bmatrix}' $ \n", "- $ D $ is a $ 2\\times 2 $ negative definite matrix and \n", "- $ b $ is a vector of constants \n", "\n", "\n", "Firm $ i $ maximizes the undiscounted sum\n", "\n", "$$\n", "\\lim_{T \\to \\infty}\\ {1 \\over T}\\ \\sum^T_{t=0}\\ \\left( p_{it} S_{it} - E_{it} - C_{it} \\right)\n", "$$\n", "\n", "We can convert this to a linear quadratic problem by taking\n", "\n", "$$\n", "u_{it} =\n", "\\begin{bmatrix}\n", " p_{it} \\\\\n", " q_{it}\n", "\\end{bmatrix}\n", "\\quad \\text{and} \\quad\n", "x_t =\n", "\\begin{bmatrix}\n", " I_{1t} \\\\\n", " I_{2t} \\\\\n", " 1\n", "\\end{bmatrix}\n", "$$\n", "\n", "Decision rules for price and quantity take the form $ u_{it} = -F_i x_t $.\n", "\n", "The Markov perfect equilibrium of Judd’s model can be computed by filling in the matrices appropriately.\n", "\n", "The exercise is to calculate these matrices and compute the following figures.\n", "\n", "The first figure shows the dynamics of inventories for each firm when the parameters are" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "3-element Array{Int64,1}:\n", " 10\n", " 10\n", " 3" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "δ = 0.02\n", "D = [ -1 0.5;\n", " 0.5 -1]\n", "b = [25, 25]\n", "c1 = c2 = [1, -2, 1]\n", "e1 = e2 = [10, 10, 3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", " \n", "Inventories trend to a common steady state.\n", "\n", "If we increase the depreciation rate to $ \\delta = 0.05 $, then we expect steady state inventories to fall.\n", "\n", "This is indeed the case, as the next figure shows\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "First let’s compute the duopoly MPE under the stated parameters" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "([-0.6684661455442794 0.295124817744414 0.07584666305807419], [-0.6684661455442794 0.07584666305807419 0.295124817744414], [-100.74013291681779 -13.28370101134053 2.435873888234418; -13.283701011340526 5.441368457863284 1.9305445296892967; 2.4358738882344166 1.9305445296892967 -0.18944247543524873], [-100.74013291681771 2.435873888234418 -13.283701011340526; 2.435873888234417 -0.18944247543524873 1.9305445296892967; -13.283701011340526 1.9305445296892967 5.441368457863284])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# parameters\n", "a0 = 10.0\n", "a1 = 2.0\n", "β = 0.96\n", "γ = 12.0\n", "\n", "# in LQ form\n", "A = I + zeros(3, 3)\n", "B1 = [0.0, 1.0, 0.0]\n", "B2 = [0.0, 0.0, 1.0]\n", "\n", "R1 = [ 0.0 -a0 / 2.0 0.0;\n", " -a0 / 2.0 a1 a1 / 2.0;\n", " 0.0 a1 / 2.0 0.0]\n", "\n", "R2 = [ 0.0 0.0 -a0 / 2.0;\n", " 0.0 0.0 a1 / 2.0;\n", " -a0 / 2.0 a1 / 2.0 a1]\n", "\n", "Q1 = Q2 = γ\n", "S1 = S2 = W1 = W2 = M1 = M2 = 0.0\n", "\n", "# solve using QE's nnash function\n", "F1, F2, P1, P2 = nnash(A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2,\n", " beta=β)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we evaluate the time path of industry output and prices given\n", "initial condition $ q_{10} = q_{20} = 1 $" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": true }, "outputs": [], "source": [ "AF = A - B1 * F1 - B2 * F2\n", "n = 20\n", "x = zeros(3, n)\n", "x[:, 1] = [1 1 1]\n", "for t in 1:(n-1)\n", " x[:, t+1] = AF * x[:, t]\n", "end\n", "q1 = x[2, :]\n", "q2 = x[3, :]\n", "q = q1 + q2 # Total output, MPE\n", "p = a0 .- a1 * q # Price, MPE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next let’s have a look at the monopoly solution.\n", "\n", "For the state and control we take\n", "\n", "$$\n", "x_t = q_t - \\bar q\n", "\\quad \\text{and} \\quad\n", "u_t = q_{t+1} - q_t\n", "$$\n", "\n", "To convert to an LQ problem we set\n", "\n", "$$\n", "R = a_1\n", "\\quad \\text{and} \\quad\n", "Q = \\gamma\n", "$$\n", "\n", "in the payoff function $ x_t' R x_t + u_t' Q u_t $ and\n", "\n", "$$\n", "A = B = 1\n", "$$\n", "\n", "in the law of motion $ x_{t+1} = A x_t + B u_t $.\n", "\n", "We solve for the optimal policy $ u_t = - Fx_t $ and track the\n", "resulting dynamics of $ \\{q_t\\} $, starting at $ q_0 = 2.0 $." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": true }, "outputs": [], "source": [ "R = a1\n", "Q = γ\n", "A = B = 1\n", "lq_alt = QuantEcon.LQ(Q, R, A, B, bet=β)\n", "P, F, d = stationary_values(lq_alt)\n", "q̄ = a0 / (2.0 * a1)\n", "qm = zeros(n)\n", "qm[1] = 2\n", "x0 = qm[1]-q̄\n", "x = x0\n", "for i in 2:n\n", " x = A * x - B * F[1] * x\n", " qm[i] = float(x) + q̄\n", "end\n", "pm = a0 .- a1 * qm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let’s have a look at the different time paths" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plt_q = plot(qm, color=:blue, lw=2, alpha=0.75, label=\"monopolist output\")\n", "plot!(plt_q, q, color=:green, lw=2, alpha=0.75, label=\"MPE total output\")\n", "plot!(plt_q, xlabel=\"time\", ylabel=\"output\", ylim=(2,4),legend=:topright)\n", "\n", "plt_p = plot(pm, color=:blue, lw=2, alpha=0.75, label=\"monopolist price\")\n", "plot!(plt_p, p, color=:green, lw=2, alpha=0.75, label=\"MPE price\")\n", "plot!(plt_p, xlabel=\"time\", ylabel=\"price\",legend=:topright)\n", "\n", "plot(plt_q, plt_p, layout=(2,1), size=(700,600))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "We treat the case $ \\delta = 0.02 $" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "0.98" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "δ = 0.02\n", "D = [-1 0.5;\n", " 0.5 -1]\n", "b = [25, 25]\n", "c1 = c2 = [1, -2, 1]\n", "e1 = e2 = [10, 10, 3]\n", "δ_1 = 1-δ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recalling that the control and state are\n", "\n", "$$\n", "u_{it} =\n", "\\begin{bmatrix}\n", " p_{it} \\\\\n", " q_{it}\n", "\\end{bmatrix}\n", "\\quad \\text{and} \\quad\n", "x_t =\n", "\\begin{bmatrix}\n", " I_{1t} \\\\\n", " I_{2t} \\\\\n", " 1\n", "\\end{bmatrix}\n", "$$\n", "\n", "we set up the matrices as follows:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "2×2 Array{Float64,2}:\n", " 0.0 0.0\n", " 0.0 0.25" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# create matrices needed to compute the Nash feedback equilibrium\n", "A = [δ_1 0 -δ_1 * b[1];\n", " 0 δ_1 -δ_1 * b[2];\n", " 0 0 1]\n", "\n", "B1 = δ_1 * [1 -D[1, 1];\n", " 0 -D[2, 1];\n", " 0 0]\n", "B2 = δ_1 * [0 -D[1, 2];\n", " 1 -D[2, 2];\n", " 0 0]\n", "\n", "R1 = -[0.5 * c1[3] 0 0.5 * c1[2];\n", " 0 0 0;\n", " 0.5 * c1[2] 0 c1[1]]\n", "\n", "R2 = -[0 0 0;\n", " 0 0.5 * c2[3] 0.5*c2[2];\n", " 0 0.5 * c2[2] c2[1]]\n", "\n", "Q1 = [-0.5*e1[3] 0;\n", " 0 D[1, 1]]\n", "Q2 = [-0.5*e2[3] 0;\n", " 0 D[2, 2]]\n", "\n", "S1 = zeros(2, 2)\n", "S2 = copy(S1)\n", "\n", "W1 = [ 0.0 0.0;\n", " 0.0 0.0;\n", " -0.5 * e1[2] b[1] / 2.0]\n", "W2 = [ 0.0 0.0;\n", " 0.0 0.0;\n", " -0.5 * e2[2] b[2] / 2.0]\n", "\n", "M1 = [0.0 0.0;\n", " 0.0 D[1, 2] / 2.0]\n", "M2 = copy(M1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now compute the equilibrium using `qe.nnash`" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Firm 1's feedback rule:\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[0.24366658220856505 0.02723606266195122 -6.827882926030329; 0.3923707338756386 0.13969645088599783 -37.734107288592014]\n", "\n", "Firm 2's feedback rule:\n", "\n", "[0.027236062661951208 0.243666582208565 -6.827882926030323; 0.1396964508859978 0.39237073387563864 -37.73410728859201]\n" ] } ], "source": [ "F1, F2, P1, P2 = nnash(A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2)\n", "\n", "println(\"\\nFirm 1's feedback rule:\\n\")\n", "println(F1)\n", "\n", "println(\"\\nFirm 2's feedback rule:\\n\")\n", "println(F2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let’s look at the dynamics of inventories, and reproduce the graph\n", "corresponding to $ \\delta = 0.02 $" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "AF = A - B1 * F1 - B2 * F2\n", "n = 25\n", "x = zeros(3, n)\n", "x[:, 1] = [2 0 1]\n", "for t in 1:(n-1)\n", " x[:, t+1] = AF * x[:, t]\n", "end\n", "I1 = x[1, :]\n", "I2 = x[2, :]\n", "\n", "plot(I1, color=:blue, lw=2, alpha=0.75, label=\"inventories, firm 1\")\n", "plot!(I2, color=:green, lw=2, alpha=0.75, label=\"inventories, firm 2\")\n", "plot!(title=\"delta = 0.02\")" ] } ], "metadata": { "date": 1591310625.7392113, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "markov_perf.rst", "filename_with_path": "multi_agent_models/markov_perf", "kernelspec": { "display_name": "Julia 1.4.2", "language": "julia", "name": "julia-1.4" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.4.2" }, "title": "Markov Perfect Equilibrium" }, "nbformat": 4, "nbformat_minor": 2 }