Dynamic games of complete information
Strategies in dynamic games
● When moving sequentially, the player has different choices - depending on
the other player’s actions
○ Optimal strategy depends on the other player
● Strategies in dynamic games are more complex
○ Players pick actions conditional on past observations
○ An action is specified for each possible decision made (decision nodes)
○ Decision nodes are where the players have to make a choice
● A player’s strategy is the list of actions they will take at each decision node
● Can draw a game tree (extensive form)
○ Shows the dynamic form of the game
○ Dots represent decision nodes
○ The terminal nodes are the last actions, leading to the final payoff
● The information set is what the player knows about the game / the stage they
are at
○ Knowledge is crucial - more important than time frames
● The equilibrium path shows what actually happens / the model’s predictions
○ Other branches are known as the off-equilibrium path - not optimal
● Can also be represented in normal form (a table)
Sequential rationality
● The NE does not seem plausible
● A strategy is sequentially rational for a player if it is the BR at every decision
node
○ Puts a limit on threats and promises
Bargaining problems
● Bargaining problems are situations where:
○ A mutually beneficial agreement could be made
○ Different parties have conflicting interests
○ Parties can leave at any time
● Can study bargaining problems through game theory or by the axiomatic
approach
○ Game theory - look at the strategies behind bargaining
○ Axiomatic approach - look at reasonable agreements
Alternating offers games
Strategies in dynamic games
● When moving sequentially, the player has different choices - depending on
the other player’s actions
○ Optimal strategy depends on the other player
● Strategies in dynamic games are more complex
○ Players pick actions conditional on past observations
○ An action is specified for each possible decision made (decision nodes)
○ Decision nodes are where the players have to make a choice
● A player’s strategy is the list of actions they will take at each decision node
● Can draw a game tree (extensive form)
○ Shows the dynamic form of the game
○ Dots represent decision nodes
○ The terminal nodes are the last actions, leading to the final payoff
● The information set is what the player knows about the game / the stage they
are at
○ Knowledge is crucial - more important than time frames
● The equilibrium path shows what actually happens / the model’s predictions
○ Other branches are known as the off-equilibrium path - not optimal
● Can also be represented in normal form (a table)
Sequential rationality
● The NE does not seem plausible
● A strategy is sequentially rational for a player if it is the BR at every decision
node
○ Puts a limit on threats and promises
Bargaining problems
● Bargaining problems are situations where:
○ A mutually beneficial agreement could be made
○ Different parties have conflicting interests
○ Parties can leave at any time
● Can study bargaining problems through game theory or by the axiomatic
approach
○ Game theory - look at the strategies behind bargaining
○ Axiomatic approach - look at reasonable agreements
Alternating offers games
