Lottery (decision theory)

In decision theory , the lottery is a conceptual construct to be able to model the possibility of an uncertain future payout .

General assumptions

It is often assumed that a later payment to a decision maker depends on an environmental condition that is still unknown at the time of the decision and cannot be influenced by the decision maker. As a rule, however, one makes assumptions about the probability distribution of the amount of the payout.

The amount of the future payout can follow different distributions depending on the application. In the simplest case, a future payout that is low with a probability and high with a probability is sufficient to shed light on theoretical issues such as risk aversion . ${\displaystyle p}$ ${\displaystyle 1-p}$

Examples

A simple lottery is constructed by tossing a fair coin with a probability of 0.5 heads and a probability of 0.5 tails . For example, if a head is paid 100 €, if number 0 €.

Investing in stocks can also be seen as a lottery. If the payout is the value of the share at a certain future point in time, one usually assumes a log-normally distributed future payout.

notation

Formally, one describes a lottery with

${\displaystyle L=(x_{1},x_{2},...,x_{n};p_{1},p_{2},...,p_{n})}$,

where are the payouts and the probabilities. ${\displaystyle x_{1},x_{2},...}$ ${\displaystyle p_{1},p_{2},...}$

If the amount of payouts is not finite, a lottery can be defined using a distribution function.

literature

• Andreu Mas-Colell, Michael D. Whinston and Jerry R. Green: Microeconomic theory . Oxford University Press, New York c1995., ISBN 0195073401 , chap. 6th