1. The document is a lecture on probability and game theory given by Dr. Stephen Kinsella.
2. It covers four ideas related to probability including expected value and fair games. It also discusses risk aversion and how it relates to diminishing marginal utility.
3. The lecture introduces game theory and defines the three components of any game as players, payoffs, and strategies. It defines a Nash equilibrium as a set of strategies that are optimal responses to each other.
16. Utility
U
0 20 30 33 35 40 50 Income
(thousands
of euros)
17. Utility
U
0 20 30 33 35 40 50 Income
(thousands
of euros)
Here’s a person a person with three options.
Contender may:
1. retain current income level (€35,000) without taking any risk;
2. take a fair bet with a 50-50 chance of winning or losing €5,000;
3. take a fair bet with a a 50-50 chance of winning or losing
€15,000.
19. Utility
U
U1
Income
0 20 25 35 (thousands
of euros)
20. Utility
U
U1
Income
0 20 25 35 (thousands
of euros)
Assume that during next year a person with €10,000 current
income faces a 50 percent chance of incurring €4,000 in
unexpected medical bills.
Without insurance, the person’s utility would be U1, - i.e. the
utility of the average of €6000 and €10,000.
29. A Nash equilibrium is a set of
strategies, one for each player,
that are each best responses
against one another.
30.
31. In a two-player games, a Nash
equilibrium is a pair of
strategies (a*,b*) such that a* is
an optimal strategy for A
against b* and b* is an optimal
strategy for B against A*.