Splitting Games: Nash Equilibrium and the Optimisation Problem

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: EERI Research Paper Series ; No. 36/2010

Classification and Topics

• Classification: Wirtschaft ; Noncooperative Games ; Bargaining Theory; Matching Theory ; Operations Research; Statistical Decision Theory ; National Security and War ; Conflict; Conflict Resolution; Alliances; Revolutions ; Personal Income, Wealth, and Their Distributions ; Optimization Techniques; Programming Models; Dynamic Analysis ; Existence and Stability Conditions of Equilibrium
• Subject: 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)

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Martins, Ana Paula
• Event: Veröffentlichung
• (who): Economics and Econometrics Research Institute (EERI)
• (where): Brussels
• (when): 2010

Further information

• Handle: http://hdl.handle.net/10419/142597
• Last update: 10.03.2025, 11:44 AM CET