Module 7.2
Uncertainty and information (part 2)
Types of information
• Complete information: A game is one of complete information if all factors of the
game are common knowledge. Thus, each player is aware of all other players, the
timing of the game, and the sets of strategies and payoffs.
• Incomplete information: A game is said to have incomplete information when some
players do not know the payoffs of the others with certainty
• Perfect information: A game is one of perfect information if only one player moves
at a time and if each player knows every action of the other players who moved
before her at every point. Technically, every information set contains exactly one
node (is a singleton).
• Imperfect information: A game is one of imperfect information if a player does not
know exactly what actions the other players took up to that point. Technically, there
exists at least one information set that contains more than one node.
,PART 1:
Perfect information: The SPNE and non-credible threats
Games of perfect information
• We start with an example of a game of perfect information in extensive form and
how to represent it in strategic form.
• Consider the strategic interaction between Player 1 and Player 2 alongside.
• We want to represent this game in strategic or normal form.
Translating to strategic form
• Remember that in strategic form, every row or column represented a strategy for
that player.
• So, we need to know the players’ strategy sets in order to label the strategic form
table properly.
• S1={AGI, AGJ, AHI, AHJ, BGI, BGJ, BHI, BHJ}
• S2={CE, CF, DE, DF}
Remember, Player 1 moves at nodes 1, 4 and 5, with 2 actions at each.
,So, Player 1 will have 2x2x2 strategies.
Similarly, Player 2 will have 2x2 strategies from 2 moves at 2 nodes.
• S1={AGI, AGJ, AHI, AHJ, BGI, BGJ, BHI, BHJ}
• S2={CE, CF, DE, DF}
• We can now draw up our game table:
Filling the game table
• Filling the game table cell-by-cell in this case could be a nightmare because there are
so many cells.
• Instead, we could ask what strategy pairs certain payoffs correspond to and then fill
this in faster.
• What I mean by this is:
• Choose a set of payoffs to consider – e.g. (3,0).
• Now, what strategies for Player 1 and Player 2 will get us there?
, • To answer this, we must first recognise the general pattern of what a player’s
strategy looks like:
• Player 1: __ __ __
• Player 2: __ __
• Remember that each “space” represents a move at a specific node/information set …
• So now, we ask what moves are made at each node to get to (3, 0) and fill this into
our “strategy template”
• We know that Player 1 plays A at node 1, so we fill this in on our template.
• Then Player 2 plays C at node 2, so we fill this in on our template.
• This gets us to the terminal node with payoffs (3, 0).
Uncertainty and information (part 2)
Types of information
• Complete information: A game is one of complete information if all factors of the
game are common knowledge. Thus, each player is aware of all other players, the
timing of the game, and the sets of strategies and payoffs.
• Incomplete information: A game is said to have incomplete information when some
players do not know the payoffs of the others with certainty
• Perfect information: A game is one of perfect information if only one player moves
at a time and if each player knows every action of the other players who moved
before her at every point. Technically, every information set contains exactly one
node (is a singleton).
• Imperfect information: A game is one of imperfect information if a player does not
know exactly what actions the other players took up to that point. Technically, there
exists at least one information set that contains more than one node.
,PART 1:
Perfect information: The SPNE and non-credible threats
Games of perfect information
• We start with an example of a game of perfect information in extensive form and
how to represent it in strategic form.
• Consider the strategic interaction between Player 1 and Player 2 alongside.
• We want to represent this game in strategic or normal form.
Translating to strategic form
• Remember that in strategic form, every row or column represented a strategy for
that player.
• So, we need to know the players’ strategy sets in order to label the strategic form
table properly.
• S1={AGI, AGJ, AHI, AHJ, BGI, BGJ, BHI, BHJ}
• S2={CE, CF, DE, DF}
Remember, Player 1 moves at nodes 1, 4 and 5, with 2 actions at each.
,So, Player 1 will have 2x2x2 strategies.
Similarly, Player 2 will have 2x2 strategies from 2 moves at 2 nodes.
• S1={AGI, AGJ, AHI, AHJ, BGI, BGJ, BHI, BHJ}
• S2={CE, CF, DE, DF}
• We can now draw up our game table:
Filling the game table
• Filling the game table cell-by-cell in this case could be a nightmare because there are
so many cells.
• Instead, we could ask what strategy pairs certain payoffs correspond to and then fill
this in faster.
• What I mean by this is:
• Choose a set of payoffs to consider – e.g. (3,0).
• Now, what strategies for Player 1 and Player 2 will get us there?
, • To answer this, we must first recognise the general pattern of what a player’s
strategy looks like:
• Player 1: __ __ __
• Player 2: __ __
• Remember that each “space” represents a move at a specific node/information set …
• So now, we ask what moves are made at each node to get to (3, 0) and fill this into
our “strategy template”
• We know that Player 1 plays A at node 1, so we fill this in on our template.
• Then Player 2 plays C at node 2, so we fill this in on our template.
• This gets us to the terminal node with payoffs (3, 0).
