08.DynamicCompleteInfo

08.DynamicCompleteInfo - DYNAMIC GAMES WITH COMPLETE...

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Unformatted text preview: DYNAMIC GAMES WITH COMPLETE INFORMATION: PLAYERS MAKE CHOICES IN A SEQUENTIAL ORDER, ONE AFTER THE OTHER (never at the same time); THERE IS NO UNCERTAINTY (except for the choices that players will makewhich is predictable if all players are rational) THE GAME IS REPRESENTED BY A TREECALLED THE EXTENSIVE FORM STRATEGY AND ACTION ARE DIFFERENT NOTIONS: A strategy is a complete contingent plan of action, an action is a choice made when a strategy is executed. EXAMPLE: DYNAMIC TRUST GAME AND ITS EXPERIMENT Consider two players: a Sender (alternatively, Proposer) and a Receiver (alternatively, Respondent). The Sender has $10 and moves first: She can keep the entire $10 or she can split it with the receiver. Any amount $ x that the Sender leaves to the Receiver is multiplied by three (becomes $ 3x ). The Receiver will then decide whether to keep the entire amount $3x or to send some $ y back to the Sender. This latter amount is not tripled. The game ends at that point. The extensive form is given below: 10 3x Sender x y => Payoffs: ( Sender: 10-x+y ; 0 Receiver: 3x y) 0 Receiver 1 Strategies : A complete contingent plan of action for each player : Senders strategy is to choose an x between 0 and 10 Receiver strategy is to determine the number y between 0 and 3x, for each x chosen by the Sender. Example of strategies : Sender : choose x = 2. Receiver : set y = x if x is between 0 and 5, set y = x + 1 if x is between 5 and 10. Another example of strategies : Sender: choose x = 4. Receiver: set y = x/2 for all x between 0 and 10. Notice: The receivers plan of action is a complete contingent plan of action: It tells us what the receiver will do for ALL possible evolution of the game (for all x that the sender could choose). IN DYNAMIC GAMES OF COMPLETE INFORMATION, WE REQUIRE THE STRATEGIES TO SURVIVE THE BACKWARD INDUCTION PROCEDURE . The solution to this game using backward induction goes like this: Consider the Receivers decision. Since the game ends after this point, the Receiver has no incentive to send any money back to the Sender. Knowing this the Sender should not send any money to the Receiver in the first place because she should not expect to get anything back. The principle of 2 backward induction dictates that the Sender should keep the entire $10. This way the Sender gets $10 and the Receiver gets $0! ( The PARETO EFFICIENT outcome is that the Sender send the entire $10 and the Receiver gives back some $y . If the Sender trusts the Receiver and sends her the entire $10, the Receiver receives $30. If the Receiver reciprocates the Senders trust, then there are numerous possible splits of $30 (say $15 each), which makes both the Sender and the Receiver better off than if the Sender sends nothing. However, if the Receiver does not reciprocate the Senders trust, then the Sender is worse off since she loses all or part of the $10 that she could have kept for herself.) The strategies that survive backward induction are: Sender offers x...
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08.DynamicCompleteInfo - DYNAMIC GAMES WITH COMPLETE...

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