We consider the decentralized power allocation and spectrum sharing problem
in multi-user, multi-channel systems with strategic users. We present a
mechanism/game form that has the following desirable features. (1) It is
individually rational. (2) It is budget balanced at every Nash equilibrium of
the game induced by the game form as well as off equilibrium. (3) The
allocation corresponding to every Nash equilibrium (NE) of the game induced by
the mechanism is a Lindahl allocation, that is a weakly Pareto optimal
allocation.

Within the context of games on networks S. Goyal [1, pg. 39] posed the
following problem. Under any arbitrary but fixed topology, does there exist at
least one pure Nash equilibrium that exhibits a positive relation between the
cardinality of a player's set of neighbors and its utility payoff? In this
paper we present a class of topologies in which pure Nash equilibria with the
above property do not exist.

A sequential problem in decentralized detection is considered. Two observers
can make repeated noisy observations of a binary hypothesis on the state of the
environment. At any time, observer 1 can stop and send a final binary message
to observer 2 or it may continue to take more measurements. Every time observer
1 postpones its final message to observer 2, it incurs a penalty. Observer 2's
operation under two different scenarios is explored. In the first scenario,
observer 2 waits to receive the final message from observer 1 and then starts
taking measurements of its own.