Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/142597
Authors: 
Martins, Ana Paula
Year of Publication: 
2010
Series/Report no.: 
EERI Research Paper Series 36/2010
Abstract: 
This research states the stylised n (more than two) players’ splitting problem as a mathematical programme, relying on definitions of the values of the game and problem stationarity to generate tractable reduced forms, and derives the known solutions according to the properties of pertaining first-order conditions. On the one hand, boundary constraints are taken into consideration, required by the most general formulation possible with respect to the controls. On the other, distinction between FOC’s of optimizing behavior and equilibrium fitness is provided. Finally, the formal proof of the internal insufficiency of the usual approach to determine the equilibrium is advanced, and the imposing additional conditions – affecting cross multipliers - required for model solving forwarded and interpreted. Two different types of protocols (sets of rules of the game) were staged: alternate offers and synchronized ones. Perfect information (and foresight) of the players, infinite horizon, and offers exchange restricted to infinite-term settlements are always assumed. Each player makes a proposition of the division among the n participants. Periodic “outside” alternatives may differ according to whose offer is being analysed, and from those accruing to the players when none is forwarded. The alternate offers protocol is a generalization of the Rubinstein’s structure. At each round of negotiations, one and only one player, exogenously determined, can make an – the – offer. An agent must conciliate – and solve consistently – as many optimization problems as eventual proponents there are in the game.
Subjects: 
Non-Cooperative N-Person Games
Infinite Horizon
Mixed Strategy Games
Mixed Strategies under Perfect Information Games
Simultaneous Sequential Bargaining
Matching Equilibrium under Sequential Bargaining
Synchronous (Decisions) Equilibrium under Sequential Bargaining
Mechanism Design
Bargaining Protocols
Dynamic Programming
Stationary Problems (without State Variables)
JEL: 
C72
C78
C44
H56
D74
D31
C61
C62
Document Type: 
Working Paper

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