Chapter 2 Flashcards
Lotteries, expected utility
How does game theory introduce randomness into decision-making?
Randomness is introduced through lotteries, which are probability distributions over outcomes.
What is the role of “Nature” in game theory?
In game theory, Nature acts as another “player” that chooses outcomes based on a lottery.
What is expected utility, and how is it calculated?
Expected utility is the weighted average of utilities over all possible outcomes of a lottery, calculated as E[u(x) ∣ p] = ∑ p(xk)u(xk)
What is the von Neumann-Morgenstern utility theorem?
The theorem states that if a preference satisfies rationality, continuity, and independence axioms, it can be represented by a utility function where preferences correspond to expected utilities.
What does the continuity axiom imply in decision-making?
Small changes in probabilities should not abruptly change the preference between lotteries.
What distinguishes risk-neutral, risk-averse, and risk-loving players?
Risk-neutral players are indifferent to risk, risk-averse players prefer certainty over equivalent risky outcomes, and risk-loving players prefer risk over certainty.
What is backward induction in decision-making?
Backward induction is solving a decision tree by starting at the final nodes and working backwards to determine the optimal strategy.
How does a discount factor affect decisions in sequential games?
A discount factor 𝛿 reduces the value of future payoffs, making earlier rewards more attractive.
What is the value of information in game theory?
The value of information is the increase in expected utility when a player knows Nature’s choice beforehand.
How can the value of information be quantified?
By comparing the expected utility with knowledge of Nature’s choice to the expected utility without it.
