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Many situations, many types of games...
The interactions and their institutional and informational contexts may be very diverse necessitating, quite commonly, different types of games for analyzing them.
We distinguish different types of games following two important characteristics of these interactions:
Their temporality: Do the agents make their decisions in a sequential way, potentially observing decisions made before theirs, or are these decisions made simultaneously?
The nature of information available to the players during the game:
Do all agents completely know all characteristics of the game and of all players (complete vs incomplete information)?
If the game is sequential, can each agent perfectly observe the decisions made before her decisions (perfect vs imperfect information)?
When game is sequential, some players may not have perfect information: when it is their turn to play, they don’t know what some other players have chosen before them hence, they don’t know the exact situation (in the game) in which they are making their decision.
Decisions are more difficult to make in this type of games with imperfect information.
Nevertheless, simultaneous games where all agents have complete information are the simplest games to analyze are (even if the information cannot be perfect in such games)
On the other hand, In some games, some players may not completely know
some rules or characteristics of the game (what may happen to me when I choose action A vs action B?) or
some characteristics of some other players (who is exactly my competitor on the market, a dangerous low cost firm or an insignificant high cost firm?)
Hence, they don’t completely know which game they are playing, with whom exactly. In this case, it is much more difficult for them to anticipate the behavior of other players, and to determine the strategy that the player must adopt in these games with incomplete information.
We will come back to these important issues.
In simultaneous games, we need to determine
Who do play?
What actions may be chosen?
With which information about the game?
How much is the value of different outcomes for each player
The simplest way of representing this information is tabular
We call this representation the normal or strategic form of the game
A small contemporary example: The Lockout game
It is forbidden to go out of houses in my part of the city
I can stay home, or try to sneak out in the street as a distraction
A policeman checks the enforcement of the lockout but he cannot catch me if he stays in his corner
I cannot observe the policeman’s decision before taking mine, and vice versa
If I don’t go out, I get bored. If I go out, I am happier, but if the policeman catches me, I am in the worst situation for me
If the policeman stays in his corner, he cannot catch me, but he does not get tired
If he circulates in the streets, he becomes tired but he catches me, and gets a big bonus
If he does not circulate and I go out, someone else reports and he gets problems
Definition of the game:
Who are the players? The policeman and I: the set of players
What are the available strategies?
Me: To stay home (H) or to go out (G):
Policeman: To stay in his corner (S) or to circulate in the streets (C):
The sets of strategies of the players
Different potential outcomes of the game are
How much is the value of different outcomes for P and I? We know the order of preferences (given above)
Lets represent this situation in normal form
P
I
The outcomes in the game
P
I
Constructing the payoff matrix
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