5.2 Rational Processes 5 Equilibrium Selection 5.1 the Tracing Procedure

15 prior distribution, that is we have p ij = 1=8. In the other cases p ij are taken as normalized random numbers in the interval 0; 100]. When the prior distribution is uniform, 40% of the processes converge to a solution of the CSP, and the others come up with precisely one constraint not satissed. In the second set of examples the percentage of processes ending with a solution increases a bit and we have 55% of the processes ending with a solution. Some observations are in order. First of all we note that all of the processes converge, which is not a fact we have been able to prove in general. Second, it seems that a random initial distribution has a better median behaviour than uniform prior distribution. And this could be interpreted saying that an initial noise may be of some help in nding a solution. Finally we observe that the choice of 0;?1 (a = 0, b = ?1) is motivated by a partial evaluation of diierent choices of the parameters a and b. We think that a more extensive study could reveal interesting diierentiations in the behaviour of processes which adopt diierent utility functions. 6 Conclusions In this paper we have shown how to translate a CSP into a non-cooperative game. We have studied the relationships between the equilibrium theory in games and the solution concept in CSP. Evolutionary processes, rst introduced in application of game theory to economics Brown, 1951] and biology Smith, 1982], can be usefully adopted to model the development of a mutual agreement on a particular instantiation of the search variables. Each variable is to be considered an elementary processing unit, that can increase or decrease the probability to assume a certain value, according to the computation of the expected utility of every possible choice. An evolutionary process simulates a step by step interaction and updating cycle. If the P HS (G; p;) process converges then for each variable there exists a value that has probability 1 to be chosen. The set of those values represents the outcome of the CSP. The computation can be done in parallel by the variables and only bayesian reasoning is needed. The limit point of such a process can be viewed as the outcome of a course of mutual interaction between bayesian reasoners. Even if this limit point is not a solution of the CSP …