Conflict modelling and resolution in a dynamic state

Abstract

A conflict is neither good (functional) nor bad (dysfunctional). The distinction depends on the type of conflict, 0 e's attitude and reaction to it thereby making it constructive or destructive. The absence a clear measuring strategy or framework, against which it can be evaluated, makes it even harder to differentiate between good and bad conflict. It is however accepted that if the result of a conflict is positive, then the conflict is considered "good" and if the result is negative, then the conflict is "bad". The formal models and quantitative analysis to explain how strategic actor's behaviour in a conflict setting are rare even-though model-based approaches are becoming more commonly used by statisticians and other scientists. These approaches to a great extent rely on fundamental or empirical models that are frequently described by systems of differential equations. The underlying objective of this research was to develop conflict modelling and resolution models applicable to a dynamic state using ordinary differential equations (ODE) with integrated logistic model. Solutions to the ODEs were obtained by the application of Laplace transformation. This research assumes that a conflict can be described by two main variables; control variables and state variables which reflect on the structural causes of a conflict. It is further assumed that a conflict can be described by a Bemoulli distribution with parameter Yi and that conflicts exist over a span of time with interplaying variables that can be dynamically modelled and the initial orboundary conditions can be estimated in a dynamic state. In developing the models, the Game theory and Bayesian theorem are used as the underlying theoretical concepts. The Game theory and Bayesian theorem are used with the assumption that conflicts can be described using statistical distributions. This research shows that modelling of a conflict requires accurate estimation of control variables (initial conditions) defined by a Bayesian probability distribution and the variables are independently and identically distributed (i.i.d). The developed model uses Baye's rule of probability distribution and the Game theory. In a dynamic state; the initial conditions are estimated as posteriori conditions by the model. Using the developed model for the estimation of initial conditions, a logistic conflict prediction model that gives the trend a conflict is likely to take at time tf has been developed. The model is derived from the solution of an exponential growth model and it integrates the initial conditions estimation model as one the parameters. A statistical model for conflict resolution using the concept of Bargaining Game Theory has also been developed. The model assumes that in a conflict there are two parties with opposing opinions where one makes an offer with a probability of acceptance or rejection. The Ultimatum Game Theory has been used to introduce constraints on the offers made by the parties, consequently increasing the minimum threshold on the demands associated with any offers. It provides an in-built mechanism through which a conflict resolution model guides anegotiation by ensunng that any offer made IS constrained with a higher likelihood of acceptance. The model compels the parties involved in a conflict to establish the demands from the other party and integrating them in any offer proposed hence boosting the chances of resolving a conflict. vii