Decision Theory is a branch of mathematics which studies the effects of uncertainty on decision making. It involves the analysis of decision-making patterns in cases where outcomes are uncertain or uncertain in nature. It is used to determine the best decision in a given situation based on a possible range of outcomes.

Decision Theory is used in a wide range of fields, from financial management to software engineering, in order to determine the optimal decision in any given situation. The field also applies to human decision making in general, from personal finance and health decisions to business or military strategy decisions.

At its core, Decision Theory employs a set of principles and tools for analyzing and making decisions in the face of uncertain outcomes. For example, a Bayesian approach to decision making involves weighing possible outcomes against the probabilities of their occurrence, taking those probabilities into account when making a decision on a course of action.

A decision-theorist might also use analytical models such as game theory to understand how two or more players are likely to interact, given they have different motives or preferences. This can be used to develop better strategies and tactics.

Another decision-theoretic approach is to identify optimal strategies a priori, based on the expected payoff gained by selecting possible strategies in advance. This prior knowledge of strategies and goals can be used to structure decision-making processes in the face of uncertainty.

Decision Theory is also concerned with understanding the motivations that drive the decisions we make and the effects of our decisions on others in the world. It considers social norms, ethical considerations such as fairness and justice, and risk preferences when evaluating and comparing the potential outcomes of a decision.

Finally, Decision Theory often incorporates methods of decision analysis and risk management, such as sensitivity analysis and expected utility theory, for example. These techniques can be used to detect errors in reasoning and to develop more robust decision strategies.

In short, Decision Theory is a branch of mathematics which uses principles, tools, and analytical techniques to evaluate decision-making under uncertainty. It considers the effects of risk, uncertain outcomes, and motivations in order to understand how decisions are made, and to determine the best decision in a given situation. Decision Theory plays an increasingly important role in a range of fields, including finance, economics, software engineering, and military and scientific research.