What is the St Petersburg Paradox and why do people fail to play this game?
When arguing to people if they would play this game the first thing that comes to mind is the fact that
the expected utility of this game is positive. Even more than just positive, the expected value of this
game is infinity. So, when considering that people always should maximize expected value, they should
play the game for every amount lower than infinity. This is not true, so Bernoulli produced the concept
of “decreasing marginal utility.” People evaluate the utility they would derive from winning the game
with the utility they would receive when losing the game. So, for increasing amounts of money, the
fear of losing the game (utility of losing) would outweigh the utility of winning the game so they will
not play the game for endless amounts of money.
➔ Therefore, a gambler is rational if the utility of playing the game is higher than the utility of
losing the game.
What are the assumptions under the expected utility theory the behave rational? And explain them.
1. Comparability (completeness): you should always have a preference between one of the two
options or be indifferent to the two, when writing this in symbols the following statement can
be computed: X > Y or X < Y or X ~ Y. This can conclude that you must be able to compare the
two goods, and you should be able to make a choice.
2. Transitivity, following statement should hold: if X>Y and Y>Z then X>Z
3. Independence: your choice between X and Y should not depend on a third variable Z or a
context in which its perceived
4. Measurability: following statement must hold: if X > Y > Z than, Y= 𝛼X + (1-𝛼)Z
If all the following statements are satisfied, the person can make rational choices using the expected
utility function.
What can influence the expected utility function between different people?
When considering different choices in the world we see that people have different appetites for risk.
This will influence how people’s utility function is shaped and how the decision making is influenced.
We can consider three different profiles of risk:
1. Risk Averse: the utility function is shaped concave; this implies that the marginal utility they
derive from extra winning is lower than the one before. This would mean that they will prefer
40 euro for sure instead of the probability of 50% of receiving 100 euros.
2. Risk Neutral: the utility function is shaped linear; this implies that the taking the gamble would
be indifferent to the person than taking the sure amount of money.
3. Risk Prone/Loving: the utility function is shaped convex; this implies that the marginal utility
they derive for the extra winning is higher than the one before. When gambling the coin flip
for 100 Euro’s or nothing, they would need more than 50 euro’s certain to accept the offer for
certainty.
, What are the assumptions under the expected utility theory the behave rational? And explain them
and consider why people are not compiling with them?
1. Comparability (completeness): you should always have a preference between one of the two
options or be indifferent to the two, when writing this in symbols the following statement can
be computed: X > Y or X < Y or X ~ Y. This can conclude that you must be able to compare the
two goods, and you should be able to make a choice.
2. Transitivity, following statement should hold: if X>Y and Y>Z then X>Z
3. Independence: your choice between X and Y should not depend on a third variable Z or a
context in which its perceived
4. Measurability: following statement must hold: if X > Y > Z than, Y= 𝛼X + (1-𝛼)Z
If all the following statements are satisfied, the person can make rational choices using the expected
utility function.
But people deviate from these axioms because they use different biases when making decisions. People
think they act rational, but they can be considered quasi rational because of following biases:
1. Problem decomposition: people break down problems in separate parts when trying to solve
them, this leads to simplification of the problems and stops the interaction between the
different parts and can lead to suboptimal decision making.
2. Framing: people make decisions based upon how a problem is framed instead of looking at the
real values of the problem. This makes that people make choices based upon how the problem
is described and so make different decisions on the same outcome. This conflicts with the
independency axiom.
3. Mental accounting: People make decisions based upon things they mentally account for that
should not influence the decision-making process, a good example can be the sunken cost
fallacy where people consider cost made in the past when making new decisions. This is
irrational and conflicts with the independency axiom.
Other biases can be an influence as well like representativeness, availability heuristic, regret avoidance
(Allais paradox), …
➔ These problems can be incorporated when using Prospect theory.
Explain Prospect Theory and explain the difference with expected utility theory?
Prospect theory is an extended version of the utility theory function with some other assumptions that
reflect the different biases that make people quasi rational under utility theory like framing, problem
decomposition and mental accounting.
Prospect theory makes a difference between winning and losing and the apatite that people have for
these things. When making the graph people are more risk averse when it comes to winning, making
it a concave curve what reflect diminishing marginal utility. When looking at losing people are more
risk loving make the curve more convex. Another thing that Prospect theory so remarks is the concept
of loss aversion, because of the convexity of the curve in the losses, people outweigh the loss more
than that they way the winning of the same amount of money considering utility.
When talking about quasi rationality, framing is the most important concept in prospect theory. How a
problem is framed can make a distinction between if the problem is in the “gains” part or that the
When arguing to people if they would play this game the first thing that comes to mind is the fact that
the expected utility of this game is positive. Even more than just positive, the expected value of this
game is infinity. So, when considering that people always should maximize expected value, they should
play the game for every amount lower than infinity. This is not true, so Bernoulli produced the concept
of “decreasing marginal utility.” People evaluate the utility they would derive from winning the game
with the utility they would receive when losing the game. So, for increasing amounts of money, the
fear of losing the game (utility of losing) would outweigh the utility of winning the game so they will
not play the game for endless amounts of money.
➔ Therefore, a gambler is rational if the utility of playing the game is higher than the utility of
losing the game.
What are the assumptions under the expected utility theory the behave rational? And explain them.
1. Comparability (completeness): you should always have a preference between one of the two
options or be indifferent to the two, when writing this in symbols the following statement can
be computed: X > Y or X < Y or X ~ Y. This can conclude that you must be able to compare the
two goods, and you should be able to make a choice.
2. Transitivity, following statement should hold: if X>Y and Y>Z then X>Z
3. Independence: your choice between X and Y should not depend on a third variable Z or a
context in which its perceived
4. Measurability: following statement must hold: if X > Y > Z than, Y= 𝛼X + (1-𝛼)Z
If all the following statements are satisfied, the person can make rational choices using the expected
utility function.
What can influence the expected utility function between different people?
When considering different choices in the world we see that people have different appetites for risk.
This will influence how people’s utility function is shaped and how the decision making is influenced.
We can consider three different profiles of risk:
1. Risk Averse: the utility function is shaped concave; this implies that the marginal utility they
derive from extra winning is lower than the one before. This would mean that they will prefer
40 euro for sure instead of the probability of 50% of receiving 100 euros.
2. Risk Neutral: the utility function is shaped linear; this implies that the taking the gamble would
be indifferent to the person than taking the sure amount of money.
3. Risk Prone/Loving: the utility function is shaped convex; this implies that the marginal utility
they derive for the extra winning is higher than the one before. When gambling the coin flip
for 100 Euro’s or nothing, they would need more than 50 euro’s certain to accept the offer for
certainty.
, What are the assumptions under the expected utility theory the behave rational? And explain them
and consider why people are not compiling with them?
1. Comparability (completeness): you should always have a preference between one of the two
options or be indifferent to the two, when writing this in symbols the following statement can
be computed: X > Y or X < Y or X ~ Y. This can conclude that you must be able to compare the
two goods, and you should be able to make a choice.
2. Transitivity, following statement should hold: if X>Y and Y>Z then X>Z
3. Independence: your choice between X and Y should not depend on a third variable Z or a
context in which its perceived
4. Measurability: following statement must hold: if X > Y > Z than, Y= 𝛼X + (1-𝛼)Z
If all the following statements are satisfied, the person can make rational choices using the expected
utility function.
But people deviate from these axioms because they use different biases when making decisions. People
think they act rational, but they can be considered quasi rational because of following biases:
1. Problem decomposition: people break down problems in separate parts when trying to solve
them, this leads to simplification of the problems and stops the interaction between the
different parts and can lead to suboptimal decision making.
2. Framing: people make decisions based upon how a problem is framed instead of looking at the
real values of the problem. This makes that people make choices based upon how the problem
is described and so make different decisions on the same outcome. This conflicts with the
independency axiom.
3. Mental accounting: People make decisions based upon things they mentally account for that
should not influence the decision-making process, a good example can be the sunken cost
fallacy where people consider cost made in the past when making new decisions. This is
irrational and conflicts with the independency axiom.
Other biases can be an influence as well like representativeness, availability heuristic, regret avoidance
(Allais paradox), …
➔ These problems can be incorporated when using Prospect theory.
Explain Prospect Theory and explain the difference with expected utility theory?
Prospect theory is an extended version of the utility theory function with some other assumptions that
reflect the different biases that make people quasi rational under utility theory like framing, problem
decomposition and mental accounting.
Prospect theory makes a difference between winning and losing and the apatite that people have for
these things. When making the graph people are more risk averse when it comes to winning, making
it a concave curve what reflect diminishing marginal utility. When looking at losing people are more
risk loving make the curve more convex. Another thing that Prospect theory so remarks is the concept
of loss aversion, because of the convexity of the curve in the losses, people outweigh the loss more
than that they way the winning of the same amount of money considering utility.
When talking about quasi rationality, framing is the most important concept in prospect theory. How a
problem is framed can make a distinction between if the problem is in the “gains” part or that the
