Microeconomics II-1: introduction to game theory

an elementary property of human beings: 

Man is capable of producing more complex behavior

than he is capable of understanding…”

– An agent’s well-being depends on the choices of other agents

– An agent’s best choice depends on what other agents do.

• You lose your friend at a Museum.
• You: “Where would I go if I were him?”
• Him: “Where would I go if I were her?”
• You need to think about what he thinks that you will do.
• And he needs to think about what you think that he 
thinks that…

break the infinite regress

and say something useful

in presence of Strategic interactions.

insight on situations in economics, business, politics, and international relations

when agents use a model of

other agents choices

to predict what they will do,

and then use that prediction

in deciding how to behave

a mathematical tool

for assessing the implications

of strategic reasoning

raise prices

In 1914, Henry Ford offered the unheard-of wage of $5 a day to workers in his automobile factories, more than double the going wage.
Þ His strategy may actually have increased the profits of the Ford Motor Company. How can higher labor costs increase profits ?

After the completion of a trial, the 12 jurors retire to the jury room. On the basis of their initial assessment, only 2 of them believe that the defendant is guilty. They start their deliberations by taking a vote.
Þ Each and every juror announces a vote of guilty. How can this happen?

Kim Jong-un has no desire to go to war against South Korea. President Trump does not know if Kim Jong-un wants to avoid war or not.
ÞCould it be best for Kim Jong-un to take actions which suggest that he is willing to use nuclear weapons on South Korea?
ÞShould president Trump take an aggressive stance and thereby call Kim Jong-un’s bluff, but at the risk of inducing Kim Jong-un to fire off nuclear weapons?

players – strategy - outcomes - strategic interaction

There are 2 or more players

where strategy matters 

The game has one or more outcomes,

e.g., someone wins, someone loses

 - The outcome depends on the strategies chosen by all players; there is strategic interaction.

Players, strategies, pay-offs

– how many players are there?
– does nature/chance play a role?

A complete description of the strategies of each player

A description of the consequences (payoffs)

for each player

for every possible profile

of strategy choices of all players

rationally.
– They try to obtain the highest possible payoff (select the best alternative for them => preferences).
– They are flawless in calculating which actions will attain this objective.

common knowledge:
– Each player knows the set of players, strategies and payoffs from all possible combinations of strategies: call this information “X.”
– Common knowledge means that each player knows that all players know X, that all players know that all players know X, that all players know that all players know that all players know X and so on,..., ad infinitum.

– 10 people in a group

– 100 CHF are available for the group. You will choose how to split this amount

– You will simply claim the amount you wish, individually.

– If the sum of your demands >100 CHF: you all have 0.

– If the sum of your demands <= 100 CHF you each obtain your claim.

Extensive and Strategic Forms