Mathematical Analysis In Game Theory On The Economic Analysis Of Law

This research uses mathematical insight through game theory to understand the legal process,litigation and some aspects of torts.There are eight chapters in this thesis where the first chapter provides the background rationale about law and economics,game theory and the recent developments in the field.Chapter two dives into the recent trends in economic analysis law while chapter three expounds the game theoretic reasoning in law.Chapter four then uses a contract scenario in e-commerce to explain expectation damages and demonstrates how risk-benefit can be analyzed in case of non-performance in contract law through an economic approach.In chapter five a game theoretic mechanism per stochastic options pricing methodology is applied in the games played by the litigants.A 'fair' bargain formularization is designed to optimize the outcomes of a legal negotiation.The above mentioned mechanism provides a wider insight into the nature of the legal process both axiologically and instrumentally.Chapter six argues that an optimal transaction cost in a legal dispute or negotiation is more efficient than low or high.We also devised an optimal transaction cost algorithm which could help litigants,legal experts and practitioners in reaching socially optimal outcomes in the justice system.Chapter seven demonstrates how the probability of winning in a legal dispute is correlated with attorney fees and its influence on the adjudication based on the Gabuthy-Morand's model.Then we finally discuss our conclusions in chapter eight.Uncertainty in the judgment,transaction costs,relative optimism,reasonable bargain affect private agreements and trials.When information is asymmetric,the relative optimisms of litigants cause a disruption in negotiations,the probability of reaching settlements is reduced,thence voluntary exchange of information not only induces private agreements but also increases efficiency in the legal process just as the undertaking of trading stocks based on non-insider information increases market efficiency.Symmetric information on the other hand increases transparency thereby increasing the probability of settlement.The axiological methodology discussed in this thesis will provide a clearer logical estimation of the legal bargain.It will serve as a stepping stone for further research into the generalization of how legal bargain positions can be deduced in order to induce cooperation and reduce trials within the walls of optimal transaction costs.Most existing methods for legal negotiations are based on pure intuition and qualitative reasoning1,hence a more straight-forward approach based on mathematical induction provides a much clearer way of legal reasoning in this respect.Additionally,most existing literature focuses on minimum transaction cost as a way to induce efficiency2,this thesis however will propose on how to estimate an optimal transaction cost in a legal process could be deduced.via backwards induction analysis this thesis will demonstrate the decision-making process and probabilistic outcomes of the legal process in game theory and will devise a method for estimating the reasonable bargain to induce the WTA(willingness to accept)of the plaintiff and WTP(willingness to pay)of the defendant in a negotiation.Arnold likened the operation of the judicial system to a theatrical performance where the judges are actors from whose play lines moral lessons could be learned,the litigants who have sponsored the show are not welcome to the show because the principles of substantive law is constantly aimed at preventing or reducing the rate of litigation by referring the litigants to re-negotiations,arbitration or telling them to resort to the action of a commission3.The question Arnold was putting across was that if the play is not sponsored by the litigants then the audience will loose the opportunity to learn the moral lessons of the play.Meaning,the occurrence of trials produce precedent for resolving future cases,so if the law is structured so as to reduce the number of trials by inducing private agreements then less precedent might be created.Less precedent also means more uncertainty in the future judgments which will further induce more private cooperation especially with risk averse litigants.Nevertheless,when precedent is lacking,courts find it difficult to pass judgments that reflect with the social norms so injurers exercise less precaution thereby resulting in more trials.The focus of this research is devising a quantitative method of analyzing the legal process through game theory and mathematical analysis to reduce the impediments of cooperation in a legal dispute in order to reach socially optimal outcomes.