This paper presents an exact penalization theory of the generalized Nash equilibrium problem (GNEP) that has its origin from renowned Arrow–Debreu general economic model. Whereas latter model is foundation much mathematical economics, GNEP provides a multiagent noncooperative competition found many contemporary applications in diverse engineering domains. The most salient feature distinguishes ...

Since it was shown that finding a Nash equilibrium is PPAD-complete [6], even for 2-player normal form games [2], a lot of attention has been given to -approximate Nash equilibria. Almost all results on -approximate Nash equilibria assume full knowledge of the game that is played. This thesis will focus on -approximate Nash equilibria in an uncoupled setup, players only have knowledge of their ...

We consider full-truthful Nash implementation, which requires truth telling by each agent to be a Nash equilibrium of a direct revelationmechanism, and every Nash equilibrium outcome of the mechanism to be f optimal. We show that restricted monotonicity plus an auxiliary condition is necessary and sufficient for full-truthful Nash implementation, and that full-truthful Nash implementation is eq...

Sequential game and Nash equilibrium are basic key concepts in game theory. In 1953, Kuhn showed that every sequential game has a Nash equilibrium. The two main steps of the proof are as follows: First, a procedure expecting a sequential game as an input is defined as “backward induction” in game theory. Second, it is proved that the procedure yields a Nash equilibrium. “Backward induction” act...

We develop a novel auction-based algorithm to allow users to fairly compete for a wireless fading channel. We use the second-price auction mechanism whereby user bids for the channel, during each time-slot, based on the fade state of the channel, and the user that makes the higher bid wins use of the channel by paying the second highest bid. Under the assumption that each user has a limited bud...

We study if (and when) the intersections and unions of social choice rules that are implementable with respect to a certain equilibrium concept are themselves implementable with respect to that equilibrium concept. While the results for dominant strategy equilibrium are mostly of negative nature, the situation is di¤erent in the case of Nash implementation. We …nd that the union of any set of N...