Ebook Game Theory in Jurisprudence mobi,epub

prudence; Part III is devoted to the applications of game theory to more specific legal-philosophical issues that emerge in the context of concrete branches of the legal system. The Epilogue is a reflection on the relations between economic approach to law, the so called Law and Economics (postulating the analysis of law in terms of economic rationality and economic efficiency), whose game-theoretic approach to law is a special variety, and the projects of the naturalization of law. The book ends with Appendix in which the problem (only mentioned in Chapter 1) of the relationships between instrumental rationality and emotions is analyzed in detail. PART ONE INTRODUCTION TO GAME THEORY Chapter 1 The basics of game theory 1. Twelve questions about game theory In this chapter we shall present the basics of game theory to which we appeal in the following chapters devoted to the applications of game theory in jurisprudence. Our method of presentation will consist in asking twelve essential questions about game theory and in attempting to answer them in a concise manner. 2. What is game theory? Game theory is a branch of rational choice theory, the other two branches being decision theory and social choice theory. What distinguishes game theory from the other branches of rational choice theory is that it deals with strategic situations, , in situations in which there is more than one agent and each agents decision depends on what she expects the other agents to do because the outcomes of each agents decision depend on the decisions of those other agents. The twofold task of game theory is to provide theoretical models of these situations and to provide criteria of rational choice in them. In subsequent sections we shall present at length the manner in which game theory realizes this task. In this section we would like to devote some attention to the other branch of rational choice theory, viz., decision theory, because we shall appeal to its solution concepts in several parts of this book. Decision theory studies decisions in parametric situations, which can be divided into two types: (1) (most frequent): situations in which there is only one person who "interacts" with the world (, an agents decision whether to take an umbrella or not when going outside will depend on her subjective probability distribution on variously defined states of the world, say, "it will rain", "it will not rain", or "it will rain lightly", "it will rain heavily", "it will not rain"); (2) (less frequent): situations in which there is a large number of persons, the outcomes of each persons decision depend on the decisions of other persons, but various possible decisions of the others persons have to be viewed by each person as the states of the world, because for computational reasons it is impossible to form separate expectations regarding each other persons decision (, the states of the world on which a persons decision depends as to whether to buy or sell stocks are in fact determined by the decisions of others but each person makes the decision, for computational reasons, in a parametric rather than a strategic way). Thus, one can say that in situations (1) the states of the world are determined by the states of nature, whereas in situations (2) they are determined by a large number of human decisions. Now, the twofold task of decision theory (analogous to that of game theory) is to provide theoretical models of parametric situations and to provide criteria of rational choice in them. As for the former: depending on the relation between actions and outcomes, four kinds of a decision problem were distinguished, viz.: decision problem under certainty, if the relation is deterministic; decision problem under risk, if at least one action is correlated with a lottery, , a set of possible outcomes, each of these outcomes being assigned objective probability; decision problem under uncertainty, if at least one action is correlated with a lottery whose outcomes cannot be assigned any probabilities (or at best can be assigned subjective probabilities); decision problem under ignorance, if, for at least one action, it is not known what outcomes it leads to. As for the latter: decision theory teaches us that an agent making a decision under certainty or under risk decides rationally iff she selects the action which maximizes her utility function. More accurately, under the conditions of certainty, a rational agent will choose the action determining the outcome that maximizes the value of her utility function. Under the conditions of risk, in which an agents actions are connected probabilistically with the outcomes, a rational agent will choose the action that maximizes the expected value of her utility function.[2] The expected value of a utility function for a given action is called the expected utility of this action. Thus, one can say that a rational agent making a decision under risk chooses the action with maximum expected utility.