Game theory in economics. Explains the background and how-to of every game. Examples and explanations included.
Bargaining and negotiation explored in detail. Extremely clear notes.
Games in games theory
o Games theory was devised to consider strategic situation
o A game has 3 elements: players, moves/strategies and the payoffs resulting from the
combination of moves.
o Payoffs: refer to the value to you of the outcome of the game
o Strategic interaction
o Likely that the outcomes, or equilibria, of the game can be computed assuming the
players act optimally, rationally and self-interestedly.
Sequential-move game:
o A type of game in the game theory where players take turns.
o Second payer can observe
- Each competitor is given the opportunity to evaluate their rival’s move before
deciding how to proceed
- To analyse sequential games, use the ‘extensive’ or ‘tree-form’ of a game. Here you can
look ahead and reason back (backward induction).
- E.G: having a dominant player and considering how to respond
o Equilibrium: when each player chooses a best available move, anticipating how the
other with react.
- A ‘Nash’ equilibrium: A situation where, if players play like this, no one has an
incentive to deviate from the situation.
o Entry game: suppose a potential entrant is deciding whether to enter an industry in
competition with an incumbent firm/monopoly.
- If the entrant decides to enter the industry, the incumbent has 2 paths of action:
accommodate the entry or fight the entry.
- Using game theory, it is possible to work out which option to take depending on the
payoffs.
- The second mover has the
advantage and anticipate the
decision. The monopoly goes
second in this case.
- If entrant decides not to enter,
they get a payoff of 0
- Blue figures are the
monopolist firm
, 11.11.19. Economics for management
o The equilibrium of this game is to figure out which of these possible alternatives will
create no incentive to deviate.
Deterring entry:
o Art of the game theory is to figure out how to change the game to your own advantage
o One way of deterring entry is to threaten to fight the entry and price low. The other
side have to believe you, however.
- To model this commitment, take away one of the incumbent’s options: the ability to
accommodate entry
o By committing to fight entry, the incumbent can benefit
o Must convince the firm that you are willing to price low because this is not as profitable.
Simultaneous move game
o They move at the same time. Cannot observe what the competitor is doing in this game
theory.
o All about strategic interaction
- Must analyse the game in order to figure out the other players next move
- Same 3 fundamental elements as sequential game. Also capable of reaching equilibrium
o The police suspect that accomplices Frank and Jesse robbed a bank, but they have no
direct evidence. They picked them up in their car, a parole violation, which carries a
sentence of two years. The US attorney offers both the same deal:
o If one implicates the other, the one who implicates goes free, while the other one receives
ten years in jail.
o If they both implicate, each receives five years in jail.
o If neither implicates the other, they both serve two years for violating parole.
- This is a ‘Nash equilibrium’.
Frank – Player 2. Column player
Implicate Say nothing
Implicate -5, -5 0, -10
Jesse – Player
1. Row player Say nothing -10, 0 -2, -2
o The only equilibrium is for both to implicate the other and serve five years
o But BOTH would be better off if both said nothing
o By following self-interest, the players thus make the group worse off
o The tension between conflict (self-interest) and cooperation (group interest) is inherent in
the prisoners’ dilemma game.
o If the players/prisoners could cooperate, they would make themselves better off.
o Nash equilibrium: if they both implicate each other
o Still follows the rational-actor paradigm.
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