H1: Game theory: fundamentals
Game theory in managerial economics
Game = mathematical representation of agents, goals, information and capabilities
- Predict the likely outcomes when multiple players have conflicting goals
- Understand what factors can give an edge to different players or affect
outcomes
- Identify pitfalls that undermine desirable, and how to mitigate them
In real life: decision-makers have goals/preferences about the outcome of their
interactions
In a game:
- Represent preferences by assigning a numerical value = payoff
- Players may disagree on what outcome is most desirable
- Strategies are actions or sequence of actions that agents can choose to
achieve their goals
- The outcome of a game is the result of all player’s strategies, and chance if
the game involves stochastic/random elements
2 assumptions:
- They have rational preferences: each player can rank outcomes from their ost
favourite to least
=> necessary in order to have a payoff representation
- They are playoff maximizing: Players choose their strategies in order to
achieve the highest payoff themselves
=> This does not mean agents are selfish, preference can be very equitable
outcome (e.g. person may assign high payoff to more fair outcome)
=> The first one is more restrictive (?)
Strategic games
- Static: one shot game (players interact only once), simultaneous choice (no
knowledge about choice of other players)
=> Multiple choices might occur, outcome is only observed at the end
- Complete information: All players know the capabilities of all other players
and consequences of all strategies
=> Does not mean certainty, you have knowledge about the risks and the
probabilities
=> Asymmetric information: one party has more than another, which means
the outcomes and their probabilities are unknown
1
, Rock-paper-scissor: Static and complete information (dynamic if repeated)
Chess: Complete information but dynamic => Move at different times, move
more than once
Sealed bid auction: Static and asymmetric: One move, you don’t know what
others know
Poker: Dynamic and asymmetric: multiple moves, you don’t know what others
know
Strategic games: abstract form described by (sl28)
- Set of players: P = (player1, player2)
- Set of actions
- Payoff function
Payoff-matrix sl29 ev
Elimination of dominant strategies sl36
- Would player 1 ever use strategy H? => No, there is always a strategy that is
strictly better (strat. D)
=> H is a Dominated strategy, should never be played
- Player 2 is rational so he knows that 1 is as well and that H will never be
played
=> X is very appealing then, it always gives the highest pay-off
=> Dominant strategy
- Player 1 knows that 2 will always play 1 because they are rational
=> Chooses their best possible outcome if 2 plays X
=> Equilibrium at (XD)
2
Game theory in managerial economics
Game = mathematical representation of agents, goals, information and capabilities
- Predict the likely outcomes when multiple players have conflicting goals
- Understand what factors can give an edge to different players or affect
outcomes
- Identify pitfalls that undermine desirable, and how to mitigate them
In real life: decision-makers have goals/preferences about the outcome of their
interactions
In a game:
- Represent preferences by assigning a numerical value = payoff
- Players may disagree on what outcome is most desirable
- Strategies are actions or sequence of actions that agents can choose to
achieve their goals
- The outcome of a game is the result of all player’s strategies, and chance if
the game involves stochastic/random elements
2 assumptions:
- They have rational preferences: each player can rank outcomes from their ost
favourite to least
=> necessary in order to have a payoff representation
- They are playoff maximizing: Players choose their strategies in order to
achieve the highest payoff themselves
=> This does not mean agents are selfish, preference can be very equitable
outcome (e.g. person may assign high payoff to more fair outcome)
=> The first one is more restrictive (?)
Strategic games
- Static: one shot game (players interact only once), simultaneous choice (no
knowledge about choice of other players)
=> Multiple choices might occur, outcome is only observed at the end
- Complete information: All players know the capabilities of all other players
and consequences of all strategies
=> Does not mean certainty, you have knowledge about the risks and the
probabilities
=> Asymmetric information: one party has more than another, which means
the outcomes and their probabilities are unknown
1
, Rock-paper-scissor: Static and complete information (dynamic if repeated)
Chess: Complete information but dynamic => Move at different times, move
more than once
Sealed bid auction: Static and asymmetric: One move, you don’t know what
others know
Poker: Dynamic and asymmetric: multiple moves, you don’t know what others
know
Strategic games: abstract form described by (sl28)
- Set of players: P = (player1, player2)
- Set of actions
- Payoff function
Payoff-matrix sl29 ev
Elimination of dominant strategies sl36
- Would player 1 ever use strategy H? => No, there is always a strategy that is
strictly better (strat. D)
=> H is a Dominated strategy, should never be played
- Player 2 is rational so he knows that 1 is as well and that H will never be
played
=> X is very appealing then, it always gives the highest pay-off
=> Dominant strategy
- Player 1 knows that 2 will always play 1 because they are rational
=> Chooses their best possible outcome if 2 plays X
=> Equilibrium at (XD)
2
