Decision Theory
Decision theory provides a general, mathematically rigorous account of decision making under uncertainty. The subject includes rational choice theory, which seeks to formulate and justify the normative principles that govern optimal decision making, and descriptive choice theory, which aims to explain how human beings actually make decisions. Within both these areas one may distinguish individual decision theory, which concerns the choices of a single agent with specific goals and knowledge, and game theory, which deals with interactions among individuals. This entry will focus on rational choice theory for the single agent, but some descriptive results will be mentioned in passing.
Decision Problems
It is standard to portray decision makers as facing choices among acts that cause desirable or undesirable consequences when performed in various states of the world. Acts characterize those aspects of the world that an agent can directly control. States specify contingencies beyond her control that might influence the consequences of acts. Each combination of an act A and state S fixes a unique consequence A(S) that describes the result of doing A in S. When there are only finitely many acts and states the decision situation can be represented as a matrix:
| S1 | S2… | Sn |
| A1 | A1(S1) | A1(S2)… | A1(Sn) |
| A2 | A2(S1) | A2(S2)… | A2(Sn) |
| A3 | A3(S1) | A3(S2)… | A3(Sn) |
| : | : | : | : |
| Am | Am(S1) | Am(S2)… | Am(Sn) |
The agent decides the row, the world decides the column, and these together determine the consequence.
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