Distributed <inline-formula> <tex-math notation="TeX">$n$</tex-math></inline-formula>-Player Approachability and Consensus in Coalitional Games

Distributed n-player approachability via time and space average consensus

In this paper we consider repeated coalitional games with transferable utilities (TU) over networks. Namely, we consider a set of n players that have to distribute among themselves a vector of rewards (one for each player). In our network version there is no coordinator allocating the rewards, but the agents have to agree on a common time-averaged vector by updating the local estimates of the r...

Weighted Boolean Formula Games

We introduce a new class of succinct games, called weighted boolean formula games. Here,each player has a set of boolean formulas he wants to get satisfied. The boolean formulas ofall players involve a ground set of boolean variables, and every player controls some of thesevariables. The payoff of a player is the weighted sum of the values of his boolean formulas. For theseg...

Robust consensus in social networks and coalitional games ?

We study an n-player averaging process with dynamics subject to controls and adversarial disturbances. The model arises in two distinct application domains: i) coalitional games with transferable utilities (TU) and ii) opinion propagation. We study conditions under which the average allocations achieve robust consensus to some predefined target set.

A Closed-Form Formula for the Fair Allocation of Gains in Cooperative N-Person Games

Abstract   This paper provides a closed-form optimal solution to the multi-objective model of the fair allocation of gains obtained by cooperation among all players. The optimality of the proposed solution is first proved. Then, the properties of the proposed solution are investigated. At the end, a numerical example in inventory control environment is given to demonstrate the application and t...

Math 254a: the Analytic Class Number Formula, and Dirichlet Characters