
on Computational Economics 
By:  Fontana Magda (University of Turin); Ferraris Gianluigi 
Abstract:  Agents capable of adaptive behavior can be obtained by means of AI tools. Thanks to these, they develop the ability to vary their Behavior in order to achieve satisfying results in the simulated environment. In the paper, artificially intelligent agents play an iterated prisoner' s dilemma against agents that reproduce (in a fix way) strategies that have emerged in Axelrod' s toumament. The objective of the adaptive agent is to earn a payoff higher than one of the Titfortat, the strategy which has shown the better performance in the Axelrod's experimental setup. In the work, Genetic Algorithms are employed to produce and modify rules that are apt to achieve the set task. The adaptive dynamics is analysed in depth in order to understand the issues related to the codification of knowledge and to the evaluation of diverse strategies. In order to highlight different nuances of these matters we have amended the method as to improve it and experimented different knowledge's codifications. 
Date:  2006–04 
URL:  http://d.repec.org/n?u=RePEc:uto:dipeco:200604&r=cmp 
By:  Fontana Magda (University of Turin) 
Abstract:  Economists lise different kinds of computer simulation. However, there is little attention on the theory of simulation, which is considered either a technology or an extension of mathematical theory or, else, a way of modelling that is alternative to verbal description and mathematical models. The paper suggests a systematisation of the relationship between simulations, mathematics and economics. In particular, it traces the evolution of simulation techniques, comments some of the contributions that deal with their nature, and, finally, illustrates with some examples their influence on economie theory. Keywords: Computer simulation, economie methodology, multiagent programming techniques. 
Date:  2005–05–12 
URL:  http://d.repec.org/n?u=RePEc:uto:cesmep:200506&r=cmp 
By:  Mishra, SK 
Abstract:  In this paper we compare the performance of the Barter method, a newly introduced populationbased (stochastic) heuristic to search the global optimum of a (continuous) multimodal function, with that of two other wellestablished and very powerful methods, namely, the Simulated Annealing (SA) and the Differential Evolution (DE) methods of global optimization. In all, 87 benchmark functions have been optimized 89 times. The DE succeeds in 82 cases, the Barter succeeds in 63 cases, while the Simulated Annealing method succeeds for a modest number of 51 cases. The DE as well as Barter methods are unstable for stochastic functions (YaoLiu#7 and FletcherPowell functions). In particular, Bukin6, Perm2 and Mishra2 functions have been hard for all the three methods. Seen as such, the barter method is much inferior to the DE, but it performs better than SA. A comparison of the Barter method with the Repulsive Particle Swarm method has indicated elsewhere that they are more or less comparable. The convergence rate of the Barter method is slower than the DE as well as the SA. This is because of the difficulty of ‘double coincidence’ in bartering. Barter activity takes place successfully in less than one percent trials. It may be noted that the DE and the SA have a longer history behind them and they have been improved many times. In the present exercise, the DE version used here employs the latest (available) schemes of crossover, mutation and recombination. In comparison to this, the Barter method is a nascent one. We need a thorough investigation into the nature and performance of the Barter method. We have found that when the DE optimizes, the terminal population is homogenous while in case of the Barter method it is not so. This property of the Barter method has several implications with respect to the AgentBased Computational Economics 
JEL:  C61 C63 
Date:  2006–11–01 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:639&r=cmp 
By:  Lamieri, Marco; Ietri, Daniele 
Abstract:  Market is not only the result of the behaviour of agents, as we can find other forms of contact and communication. Many of them are determined by proximity conditions in some kind of space: in this paper we pay a particular attention to relational space, that is the space determined by the relationships between individuals. The paper starts from a brief account on theoretical and empirical literature on social networks. Social networks represent people and their relationships as networks, in which individuals are nodes and the relationships between them are ties. In particular, graph theory is used in literature in order to demonstrate some properties of social networks summarised in the concept of Small Worlds. The concept may be used to explain how some phenomena involving relations among agents have effects on multiple different geographical scales, involving both the local and the global scale. The empirical section of the paper is introduced by a brief summary of simulation techniques in social science and economics as a way to investigate complexity. The model investigates the dynamics of a population of firms (potential innovators) and consumers interacting in a space defined as a social network. Consumers are represented in the model in order to create a competitive environment pushing enterprises into innovative process (we refer to Schumpeter’s definition): from interaction between consumers and firms innovation emerges as a relational good. 
Keywords:  Innovation; small world; computational economics; network; complexity 
JEL:  L20 L10 C63 O33 D24 
Date:  2004–04–27 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:445&r=cmp 
By:  Willenbockel, Dirk 
Abstract:  The misalignment of the Chinese currency exposed by the rapid buildup of China’s foreign exchange reserves over the past few years has been the subject of considerable recent debate. Recent econometric studies suggest a Renminbi undervaluation on the order of 10 to 30%. The modest revaluation of July 2005 is widely perceived as insufficient to correct China’s balanceofpayments disequilibrium and has not silenced charges that China is engaging in persistent onesided currency manipulation. Within China there are widespread concerns regarding the adverse employment effects of a major revaluation on labourintensive export sectors, yet the likely magnitude of these effects remains a controversial issue. The paper aims to shed light on this question by simulating the structural effects of a real exchange rate revaluation that lowers the current account surplusGDP by 4 percentagepoints using a 17sector computable general equilibrium model of the Chinese economy. 
Keywords:  Renminbi undervaluation; real exchange rate misalignment; applied general equilibrium analysis 
JEL:  F40 F17 C68 
Date:  2006–04 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:920&r=cmp 
By:  Mishra, SK 
Abstract:  In this paper we compare the performance of the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods of global optimization. To this end, seventy test functions have been chosen. Among these test functions, some are new while others are well known in the literature; some are unimodal, the others multimodal; some are small in dimension (no. of variables, x in f(x)), while the others are large in dimension; some are algebraic polynomial equations, while the other are transcendental, etc. FORTRAN programs of DE and RPS have been appended. Among 70 functions, a few have been run for small as well as large dimensions. In total, 73 optimization exercises have been done. DE has succeeded in 65 cases while RPS has succeeded in 55 cases. In almost all cases, DE has converged faster and given much more accurate results. The convergence of RPS is much slower even for lesser stringency on accuracy. Some test functions have been hard for both the methods. These are: ZeroSum (30D), Perm#1, Perm#2, Power and Bukin functions. From what we find, one cannot reach at the definite conclusion that the DE performs better or worse than the RPS. None could assure a supremacy over the other. Each one faltered in some cases; each one succeeded in some others. However, DE is unquestionably faster, more accurate and more frequently successful than the RPS. It may be argued, nevertheless, that alternative choice of adjustable parameters could have yielded better results in either method’s case. The protagonists of either method could suggest that. Our purpose is not to join with the one or the other. We simply want to highlight that in certain cases they both succeed, in certain other case they both fail and each one has some selective preference over some particular type of surfaces. What is needed is to identify such structures and surfaces that suit a particular method most. It is needed that we find out some criteria to classify the problems that suit (or does not suit) a particular method. This classification will highlight the comparative advantages of using a particular method for dealing with a particular class of problems. 
Keywords:  Global optimization; Stochastic search; Repulsive particle swarm; Differential Evolution; Clustering algorithm; Simulated annealing; Genetic algorithm; Tabu search; Ant Colony algorithm; Monte Carlo method; Box algorithm; NelderMead; Nonlinear programming; FORTRAN computer program; local optima; Benchmark; test functions 
JEL:  C63 C61 
Date:  2006–10–05 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:110&r=cmp 
By:  Mishra, SK 
Abstract:  The objective of this paper is to introduce a new populationbased (stochastic) heuristic to search the global optimum of a (continuous) multimodal function and to assess its performance (on a fairly large number of benchmark functions) visàvis that of two other wellestablished and very powerful methods, namely, the Particle Swarm (PS) and the Differential Evolution (DE) methods of global optimization. We will call this new method the Barter Method of global optimization. This method is based on the wellknown proposition in welfare economics that competitive equilibria, under fairly general conditions, tend to be Pareto optimal In its simplest version, implementation of this proposition may be outlined as follows: Let there be a fairly large number of individuals in a population and let each individual own (or draw from the environment) an melement real vector of resources, xi = (xi1, xi2, …, xim). For every xi there is a (singlevalued) function f(x) that may be used as a measure of the worth of xi that the individual would like to optimize. The optimand function f(.) is unique and common to all the individuals. Now, let the individuals in the (given) population enter into a barter of their resources with the condition that (i) a transaction is feasible across different persons and different resources only, and (ii) the resources will change hands (materialize) only if such a transaction is beneficial to (more desired by) both the parties (in the barter). The choice of the individuals, (i ,k) and the resources, (j, l) in every transaction and the quantum of transaction would be stochastic in nature. If such transactions are allowed for a large number of times, then at the end of the session: (a) every individual would be better off than what he was at the initial position, and (b) at least one individual would reach the global optimum. We have uses 75 test functions. The DE succeeds in 70 cases, the RPS succeeds in 60 cases, while the Barter method succeeds for a modest number of 51 cases. The DE as well as Barter methods are unstable for stochastic functions (YaoLiu#7 and FletcherPowell functions). In eight cases, the Barter method could not converge in 10000 iterations (due to slow convergence rate), while in 4 cases the MRPS could not converge. Seen as such, the barter method is inferior to the other two methods. Additionally, the convergence rate of the Barter method is slower than the DE as well as the MRPS. However, the DE and the RPS have a history of a full decade behind them and they have been improved many times. In the present exercise, the RPS is a modified version (MRPS) that has an extra ability for local search. The DE version used here uses the latest (available) schemes of crossover, mutation and recombination. In comparison to this, the Barter method is a nascent one. We need a thorough investigation into the nature and performance of the Barter method. 
Keywords:  Barter method; Differential Evolution; Repulsive Particle Swarm; Global optimization; nonconvex functions; local optima; Fortran; computer program; benchmark; test functions 
JEL:  C6 C63 C61 
Date:  2006–10–21 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:543&r=cmp 
By:  Mishra, SK 
Abstract:  This paper aims at comparing the performance of the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods of global optimization. To this end, some relatively difficult test functions have been chosen. Among these test functions, some are new while others are well known in the literature. We use DE method with the exponential crossover scheme as well as with no crossover (only probabilistic replacement). Our findings suggest that DE (with the exponential crossover scheme) mostly fails to find the optimum in case of the functions under study. Of course, it succeeds in case of some functions (perm#2, zerosum) for very small dimension, but begins to falter as soon as the dimension is increased. In case of DCS function, it works well up to dimension = 5. When we use no crossover (only probabilistic replacement) we obtain better results in case of several of the functions under study. In case of Perm#1, Perm#2, Zerosum, Kowalik, Hougen and Powersum functions, a remarkable advantage is there. Whether crossover or no crossover, DE falters when the optimand function has some element of randomness. This is indicated by the functions: YaoLiu#7, FletcherPowell, and “New function#2”. DE has no problems in optimizing the “New function #1”. But the “New function #2” proves to be a hard nut. However, RPS performs much better for such stochastic functions. When the FletcherPowell function is optimized with nonstochastic c vector, DE works fine. But as soon as c is stochastic, it becomes unstable. Thus, it may be observed that an introduction of stochasticity into the decision variables (or simply added to the function as in YaoLiu#7) interferes with the fundamentals of DE, which works through attainment of better and better (in the sense of Pareto improvement) population at each successive iteration. The paper concludes: (1) for different types of problems, different schemes of crossover (including none) may be suitable or unsuitable, (2) Stochasticity entering into the optimand function may make DE unstable, but RPS may function well. 
Keywords:  Differential Evolution; Repulsive Particle Swarm; Global optimization; nonconvex functions; Fortran; computer program; benchmark; test; Stochastic functions; FletcherPowell; Kowalik; Hougen; Powersum; Perm; Zerosum; New functions; Bukin function 
JEL:  C63 C61 
Date:  2006–10–13 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:449&r=cmp 