International Trade and Strategy: Game Theory Flashcards
What is a problem?
- difference between current and preferred situation
What are the components of a problem statement?
- the nature of the current situation
- the nature of the preferred situation
- a central objective that distinguishes the two
What are the elements of decision problems?
- decisions: choice between two or more alternatives, rectangle
- uncertain events: situation outside the control of the decision maker, could result in either of two or more possible outcomes, oval
- objectives: criterion for evluating the deriablitiy of a situation, rectable with rounded corners
What is an Influence Diagram?
- visual representation o the relationship between decision elements
What is a Decision Tree?
- detailed visual representation of all the paths that may prevail within a decision problem’s planning horizon
- according to alternatives associated with each decision
- possible outcomes associated with each uncertain event
What are the steps to structuring a decision problem?
- Create three lists: decisions, uncertain events, objectives
- Sort lists in decreasing order of importance
- Create initial influence diagram: decision –> objective
- Add elements one at a time until initial lists are exhausted
- Evaluate the overall strucutre and revise if necessary
- Ask others to evaluate the overall structure and revise if necessary
What is the basic risky decision?
specifications:
- basik risky decision with multiple objectives
- basic risky policy with multiple objectives
What is the difference between a basic risky decision and a basic risky policy?
- in a basic risky decision, the decision does not influence the uncertain event
- in a basic risky policy, the decision does influence the uncertain event
What kind of decisions are there?
- basic risky decision
- basic risky policy
- basic risky decision with multiple objectives
- basic risky policy with multiple objectives
- multiple objective, no-risk deicison
- multiple objective, multiple-apprach, no-risk decision
What kind of decisions are there?
- basic risky decision
- basic risky policy
- basic risky decision with multiple objectives
- basic risky policy with multiple objectives
- multiple objective, no-risk deicison
- multiple objective, multiple-apprach, no-risk decision
- multiple-period sequential decision
- prototype decision
What is the environment for Game Theory?
- we’re not alone on the market
- our competitors might choose the same strategy
Which solution is the best solution?
- not easy to identify
- if money is the only objective –> the alternative that results in the greatest income or the smallest cost
- maximizing monetary value
Which solution is the best solution in no-risk decisions?
- not easy to identify
- if money is the only objective and there is no risk (no-risk decision problem) –> the alternative that results in the greatest income or the smallest cost
- maximizing monetary value
What is the formula for the Expected Monetary Value?
EMV = (p * outcome) + (p * outcome)
EMV = (p1 *x1) + (p2 * x2) + … + (pk * xk)
where,
pk = the probability of outome k
xk = the monetary payoff associated with the outcome k
k = the number of outcomes associated with an uncertain event x
What is the Net present value (NPV) and how to calculate it?
- useful for comparison
How do you solve complicated decision problems?
- reduce them to no-risk problems
- one node at a time, from right to left
- decisions: chose best solution
- uncertainties: average the outcomes
- continue until only the primary decision remains
- -> no-risk, single-criterion decision, chose the largest EMV
Which are the steps for solving a decision tree?
- identify rightmost node
- determine the EMV associated with the node –> decision: chose alternative with highest EMV, uncertainty: average payoff
- replace node with EMV
- return to step 1 until diagram is completely analyzed –> best alternative for primary decision
What kind of models do exist?
- deterministic models
- pribability models
- simulation models
- discipline specific models
What are the three uses of probabilities?
- express long-term frequency of a recurring chance event
- quantify a lack of knowledge about a past event
- express likelihood that unique future event will occur
What is the certainty equivalent approach?
Certainty equivalent (CE) for risk lottery: - maximum amount a decision maker is willing to pay in order not to face a risk
What is the risk premium?
- the difference between a decision maker’s certainty equivalent and the expected monetary value
- Risk Premium = EMV - CE
What are the three basic attitudes that can be identified by the sign of the risk premium?
positive:
- risk aversion
- decision maker is willing to pay extra in order to avoid risk
zero:
- risk neutral
- deicison maker is only interested in expected payoff
negative:
- risk seeking/ risk taker
What is the risk premium?
- the difference between a decision maker’s certainty equivalent and the expected monetary value
- Risk Premium = EMV - CE
What are the diminishing marginal returns of utility? (absteigender Grenznutzen)
- additional satisfaction obtained from successive million dollars does not increase one’s happiness as much as the first million
What is a utility scale?
- satisfaction associated with an outcome = utility
- not always proportional
- if not proportional –> maximize expected utility (EU)
1. convert values into associated utilities
2. maximize like EMVs
What is a score card?
- table that reports each alternative’s desirability (utility) according to each objective
- rows: objectives
- columns: alternatives
What is a utility scale?
- satisfaction associated with an outcome = utility
- not always proportional
- if not proportional –> maximize expected utility (EU)
1. convert values into associated utilities
2. maximize like EMVs
How to use the scorecard
- create a summary scorecard with all the combinations
- prepare utility scales for the non-monetary objectives
2a. rank the alternatives for each objective
2b. best alternative = 100, worst = 0
2c. use direct approach or certainty equivalent approach to give a value to the other alternatives
How to use the scorecard
- create a summary scorecard with all the combinations
- prepare utility scales for the non-monetary objectives
2a. rank the alternatives for each objective
2b. best alternative = 100, worst = 0
2c. use direct approach or certainty equivalent approach to give a value to the other alternatives - put values into scorecard
- apply multi-attribute utility theory
What are tradeoff weights?
- proportion of a decision maker’s total concern placed on each alternative
What is total satisfaction?
- weighted average of each outcome’s desirability accross all objectives, where the weights represent each objective’s relative importance
- formula:
Total satisfaction = Ewi*Ui
–> additive utility function
Summary: how to solve a scorecard?
- identify different objectives
- list the different alternatives –> compute utilities
- for each objective, rank the different alternatives
- -> build utility scale for ranking alternatives - for each objective compute weights –> sum of weights = 100
- fill in the score card
- compute the total utility of each alternative according to the objective and its weight
- choose the alternative with the highest multiple-attribute utility
What are cooperative and non-cooperative games?
x
How is the payoff designed?
g
What is a symmetric 2x2 game?
g
