Game Forms with Minimal Message Spaces

Power allocation and spectrum sharing in wireless networks: an implementation theory approach

“…Implicit in this interpretation of NE is the assumption that the game's environment e is stable, that is, it does not change before the agents reach their equilibrium strategies. Within the context of mechanism design, Nash's "mass-action" interpretation of NE has also been adopted by several economists including Reichelstein and Reiter (Reichelstein & Reiter 1988), and Groves and Ledyard (Groves & Ledyard 1987). The authors of (Reichelstein & Reiter 1988), (Groves & Ledyard 1987) consider resource allocation problems with strategic agents who have private information, adopt NE as the solution concept and state: "We interpret our analysis as applying to an unspecified (message exchange) process in which users grope to a stationary message and in which the Nash property is a necessary condition for stationarity" (Reichelstein and Reiter page 664 (Reichelstein & Reiter 1988)).…”

Decentralized Resource Allocation Mechanisms in Networks: Realization and Implementation

“…It is expected that, in general, an implementing mechanism with the Nash property in equilibrium messages will require a larger message space than the one that suffices for decentralized realization without regard to individual incentives. Reichelstein and Reiter [107] have shown that the statement above is true in the case of Nash implementation of Walrasian allocations in exchange environments. The following example from [107] illustrates the fact that Nash implementations require larger message spaces than the corresponding decentralized realizations.…”

“…Reichelstein and Reiter [107] have shown that the statement above is true in the case of Nash implementation of Walrasian allocations in exchange environments. The following example from [107] illustrates the fact that Nash implementations require larger message spaces than the corresponding decentralized realizations.…”

“…This penalty, along with the fact that he does not set his own price for good X, forces agent 2 to be truthful in his messages. In [107] the authors prove that this mechanism implements the social welfare maximizing rule in Nash equilibria.…”

“…In [107] the authors show that there is no mechanism of dimension 2 which implements in Nash equilibria the social welfare maximizing rule for this problem. In particular, they show that the pricing mechanism where agent 1 sets the price 12 Let X := {x1, x2, .…”