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Dynamic Games

Any game can be represented in either normal form or extensive form, although for some games one of the two forms is more convenient to analyze. The extensive form representation of a game specifies: (1) the players in the game; (2a)when each player has the move; (2b)what each player can do at each of his or her opportunities to move (2c) what each player knows at each of his/her opportunities to move; and (3) the payoff received by each player for each combination of moves that could be chosen by the players. As an example of a Game in extensive form, consider the following member of the class of two-stage games of complete and perfect information.

1. Player 1 chooses an action a1 from the feasible set A1 = { L, R}
2. Player 2 observes a1 and then chooses an action a2 from the set A2L = { L' , R'} if a1=L or player 2 chooses an action a2 from the set A2R={L",R"} if a1 = R.
3. Payoffs are u1(a1,a2) and u2(a1,a2) as shown in the game tree below

The game theory begins with a decision node for player 1, where 1 chooses between L and R. If player 1 chooses L, then a decision node for player 2 is reached, where 2 chooses between L' and R'. Likewise, if player 1 chooses R then another decision node for player 2 is reached, where 2 chooses between L" and R". Following each of player 2's choices, a terminal node is reached (i.e., the game ends) and the indicated payoffs are received.

For instructions on designing games in extensive form using the EFG software of the ComLab Games click here. Or you can directly go to their web site which hosts the software.