Dynamic Games, Extensive form, credibility and sub-game perfectness Flashcards
Define a dynamic (sequential move game).
Why it is useful to demonstrate it in extensive form?
Dynamic (sequential-move) games involve strategic situations in which there is a strict order of play.
Players need to consider how their current actions will influence the future actions of their rivals. Extensive form allows to show the decision nodes of each player, the terminal nodes and all the possible actions a player can take.
Define the 3 features of extensive form representation of sequential move games.
1) Decision nodes mark the specific points in the game where decisions are made, and are associated with the player who chooses an action at that node.
2) Terminal nodes mark the end of the game, they are labelled with the payoffs earned by the players if the game ends in the outcome represented by that terminal node.
3) The branches of the game tree represent the possible actions that can be taken by the players at any decision node.
Define backward induction
Players who get to move first can anticipate the response chosen by the second mover and thus the payoffs they will receive in all different actions. They can thus revert to their initial action choice to secure the most preferred outcome possible. this is called rollback or backward induction.
Explain at least one strand of the Airbus and Boeing game to show backward induction in practice.
the rational thing for Airbus to do is to ‘Enter’ the new market. Boeing will respond by playing ‘Stay out’. This is because if Boeing entered he would receive a payoff of -10 as if he stayed out he would receive a payoff of 0. Given 0 is better than -10 and Boeing is rational, the outcome of the game will be outcome [2], with Airbus earning profits of £50 million pounds (the highest profit for Airbus) and Boeing earning profits of zero.
What the Airbus and Boeing example show in terms of taking turns to make decision?
how can we demonstrate this
Airbus-Boeing game exhibits a first-mover advantage in the sense that moving first can help a player to secure a higher payoff than it would otherwise have achieved. it helps to draw the extensive form of the game when Boeing gets to pick first and show Airbus is now the onr in the worst position.
How does the ultimatum game, where there is a sum of money to be divided between the proposer and the accepter, show first mover advantage?
The initial decision node is where player 1 offers a division. The accepter can reject, the decision giving both a payoff of 0,0 or can accept the proposal. Knowing that a rational player will aim to maximise pay offs, 1>0, player 1 knows that player 2 should accept any division from 99,1. this uses roll back induction to figure out under what conditions will player 2 accept or rejects player 1’s division.
Is there always a first mover advantage?
I want to be like becks game shows that the first mover doesn’t always have the advantage. Wayne idolises Beckham and wants to dress like him every day.
Beckham wants to dress as differently as possible from Wayne.
when wayne can observe what Beckham is wearing (red or blue) before he chooses what to wear, Beckham gets a pay off of -1 and Wayne a pay off of 1,
However when Wayne moves first, Beckham can see what he decides to wear and gets a pay off of 2 whilst Wayne gets -1.
When does moving first give an advantage and when does moving second give an advantage?
First-mover advantage tends to arise when it is important for players to be able to commit themselves to a particular course of action in order to deter their rivals from behaving in a particular way.
Second-mover advantage is more important when there is a premium on being able to make flexible responses to the moves made by one’s opponent.
Examples, countries that industrialise later
What kinds of games can be shows in extensive form and what can be shown in normal form?
Both sequential move games and simultaneous games can be shows in extensive form and normal form.
Define a strategy
A player’s strategy is a complete plan of action that specifies how a player should act in response to all the various situations that might confront him/her in the course of playing a game.
How many strategies and how many contingencies do Airbus and Boeing have?
Airbus, when moving first, as only one contingency and thus two strategies. Boeing on the other hand has two contingencies, two situations, two decision nodes where he can be called into action. This leaves him with 4 strategies.
What are Boeing’s strategies.
S1= Enter no matter what S2= Do the opposite of Arbus S3= Do the same of Airbus S4= Stay out no mater what
What does it mean for a threat to be credible?
A promise/threat to do something is credible if and only if it is in the interests of the person who makes the promise/threat actually to carry it out when called upon to do so.
Define: Subgame perfect nash equilibrium
to count as a subgame perfect Nash equilibrium, a set of strategies must (i) be a Nash equilibrium and (ii) not involve non-credible promises or threats
is a set of strategies, one for each player, such that those strategies constitute a Nash equilibrium, both for the game as a whole, and also for every subgame of the game as a whole.
Define a subgame and state how many subgames are in the Airbus and Boeing model
A subgame is the part of an entire (extensive form) game that remains to be played beginning from any node at which the entire history of the game to that point is common knowledge (so that both players know that the subgame begins at that node). (B1 + B2)
