Rational agent in the context of Expected utility theory

The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour.

The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e., the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is ${\displaystyle U(p)=\sum u(x_{k})p_{k}}$ where ${\displaystyle p_{k}}$ is the probability that outcome indexed by ${\displaystyle k}$ with payoff ${\displaystyle x_{k}}$ is realized, and function u expresses the utility of each respective payoff. Graphically the curvature of the u function captures the agent's risk attitude.

Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses expected utility and probability to model how individuals would behave rationally under uncertainty. It differs from the cognitive and behavioral sciences in that it is mainly prescriptive and concerned with identifying optimal decisions for a rational agent, rather than describing how people actually make decisions. Despite this, the field is important to the study of real human behavior by social scientists, as it lays the foundations to mathematically model and analyze individuals in fields such as sociology, economics, criminology, cognitive science, moral philosophy and political science.

Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social behavior. The theory tries to approximate, predict, or mathematically model human behavior by analyzing the behavior of a rational actor facing the same costs and benefits.

Rational choice models are most closely associated with economics, where mathematical analysis of behavior is standard. However, they are widely used throughout the social sciences, and are commonly applied to cognitive science, criminology, political science, and sociology.

In the philosophy of economics, economics is often divided into positive (or descriptive) and normative (or prescriptive) economics. Positive economics focuses on the description, quantification and explanation of economic phenomena, while normative economics discusses prescriptions for what actions individuals or societies should or should not take.

The positive-normative distinction is related to the subjective-objective and fact-value distinctions in philosophy. However, the two are not the same. Branches of normative economics such as social choice, game theory, and decision theory typically emphasize the study of prescriptive facts, such as mathematical prescriptions for what constitutes rational or irrational behavior (with irrationality identified by testing beliefs for self-contradiction). Economics also often involves the use of objective normative analyses (such as cost–benefit analyses) that try to identify the best decision to take, given a set of assumptions about value (which may be taken from policymakers or the public).

In economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that will lead to the highest possible total profit (or just profit in short). In neoclassical economics, which is currently the mainstream approach to microeconomics, the firm is assumed to be a "rational agent" (whether operating in a perfectly competitive market or otherwise) which wants to maximize its total profit, which is the difference between its total revenue and its total cost.

Measuring the total cost and total revenue is often impractical, as the firms do not have the necessary reliable information to determine costs at all levels of production. Instead, they take more practical approach by examining how small changes in production influence revenues and costs. When a firm produces an extra unit of product, the additional revenue gained from selling it is called the marginal revenue (${\displaystyle {\text{MR}}}$), and the additional cost to produce that unit is called the marginal cost (${\displaystyle {\text{MC}}}$). When the level of output is such that the marginal revenue is equal to the marginal cost (${\displaystyle {\text{MR}}={\text{MC}}}$), then the firm's total profit is said to be maximized. If the marginal revenue is greater than the marginal cost (${\displaystyle {\text{MR}}>{\text{MC}}}$), then its total profit is not maximized, because the firm can produce additional units to earn additional profit. In other words, in this case, it is in the "rational" interest of the firm to increase its output level until its total profit is maximized. On the other hand, if the marginal revenue is less than the marginal cost (${\displaystyle {\text{MR}}<{\text{MC}}}$), then too its total profit is not maximized, because producing one unit less will reduce total cost more than total revenue gained, thus giving the firm more total profit. In this case, a "rational" firm has an incentive to reduce its output level until its total profit is maximized.

The prisoner's dilemma is a game theory thought experiment involving two rational agents, each of whom can either cooperate for mutual benefit or betray their partner ("defect") for individual gain. The dilemma arises from the fact that while defecting is rational for each agent, cooperation yields a higher payoff for each. The puzzle was designed by Merrill Flood and Melvin Dresher in 1950 during their work at the RAND Corporation. They invited economist Armen Alchian and mathematician John Williams to play a hundred rounds of the game, observing that Alchian and Williams often chose to cooperate. When asked about the results, John Nash remarked that rational behavior in the iterated version of the game can differ from that in a single-round version. This insight anticipated a key result in game theory: cooperation can emerge in repeated interactions, even in situations where it is not rational in a one-off interaction.

Albert W. Tucker later named the game the "prisoner's dilemma" by framing the rewards in terms of prison sentences. The prisoner's dilemma models many real-world situations involving strategic behavior. In casual usage, the label "prisoner's dilemma" is applied to any situation in which two entities can gain important benefits by cooperating or suffer by failing to do so, but find it difficult or expensive to coordinate their choices.

In economics, dynamic inconsistency or time inconsistency is a situation in which a decision-maker's preferences change over time in such a way that a preference can become inconsistent at another point in time. This can be thought of as there being many different "selves" within decision makers, with each "self" representing the decision-maker at a different point in time; the inconsistency occurs when not all preferences are aligned.

The term "dynamic inconsistency" is more closely affiliated with game theory, whereas "time inconsistency" is more closely affiliated with behavioral economics.

Incentivisation or incentivization is the practice of building incentives into an arrangement or system in order to motivate the actors within it. It is based on the idea that individuals within such systems can perform better not only when they are coerced but also when they are given rewards.

Central to Kant's theory of the moral law is the categorical imperative. Kant formulated the categorical imperative in various ways. His principle of universalizability requires that, for an action to be permissible, it must be possible to apply it to all people without a contradiction occurring. Kant's formulation of humanity, the second formulation of the categorical imperative, states that as an end in itself, humans are required never to treat others merely as a means to an end, but always as ends in themselves. The formulation of autonomy concludes that rational agents are bound to the moral law by their own will, while Kant's concept of the Kingdom of Ends requires that people act as if the principles of their actions establish a law for a hypothetical kingdom.

Groundwork of the Metaphysics of Morals (1785; German: Grundlegung zur Metaphysik der Sitten; also known as the Foundations of the Metaphysics of Morals, Grounding of the Metaphysics of Morals, and the Grounding for the Metaphysics of Morals) is the first of Immanuel Kant's mature works on moral philosophy and the first of his trilogy of major works on ethics alongside the Critique of Practical Reason and The Metaphysics of Morals. It remains one of the most influential in the field. Kant conceives his investigation as a work of foundational ethics—one that clears the ground for future research by explaining the core concepts and principles of moral theory, and showing that they are normative for rational agents.

Kant proposes to lay bare the fundamental principle of morality and show that it applies to us. Central to the work is the role of what Kant refers to as the categorical imperative, which states that one must act only according to maxims which one could will to become a universal law. Kant argues that the rightness of an action is determined by the principle that a person chooses to act upon. This stands in stark contrast to the moral sense theories and teleological moral theories that dominated moral philosophy at the time of Kant's career.